%[text] # 454MI: Introduction to MATLAB - Part 6L-1 - The Laplace Transform %[text] %[text:tableOfContents]{"heading":"Table of Contents"} %[text] %[text] %[text:anchor:H_0F439577] ## Introduction %[text] In this live script, we illustrate how to use the **Matlab Symbolic Toolbox** to determine the Laplace transform of a causal function of time $f(t)$ and the inverse Laplace transform corresponding to a given rational, strictly proper or simply proper function $F(s)$ of the complex variable $s$. %[text] What you will learn: %[text] - How to compute the Laplace transform and the inverse transform using the Symbolic Math Toolbox. %[text] - What are the Laplace transform main properties and theorems. \ %% %[text] %[text:anchor:H_48f6] ## The Laplace Transform %[text] %[text:anchor:H_3183] ### %[text] %[text:anchor:H_9c13] ### Introduction and Motivations %[text] %[text] %[text:anchor:H_5955] What is a **transform**? %[text] %[text:anchor:H_4bbb] - A **mapping** of a mathematical **function** from one domain to another. %[text] - A change in perspective, not a change of the function. \ %[text] Why use transforms? %[text] - Some mathematical **problems** are **difficult to solve in their natural domain**. %[text] - Transform to and solve in a **new domain**, where **the problem is simplified**. %[text] - Solved the problem in the new domain, **transform the solution back** into the original domain. %[text] - Trade off the extra effort of transforming/inverse-transforming for simplification of the solution procedure. %[text] - An example: the phasor method. \ %[text] So, what is the **Laplace transform**? %[text] - An **integral transform** mapping functions from the time domain to the Laplace domain or s-domain. \ %[text]{"align":"center"} $f(t) \\quad \\overset{\\mathcal{L}}\\longleftrightarrow \\quad F(s)$ %[text] - Time-domain functions are functions of time $t$. %[text] - Laplace-domain functions are functions of the complex frequency $s$ \ %[text]{"align":"center"} $s \\in \\mathbb{C}\\,,\\;s = \\sigma+j\\,\\omega \\quad \\Longrightarrow \\quad \\begin{array}{rcl} \\sigma &=& \\text{Re}(s) \\\\\n\\omega &=& \\text{Im}(s)\n\\end{array}$ %[text]{"align":"center"} %[text] %[text:anchor:H_25da] #### Motivations %[text] We’ll use Laplace transforms to solve **differential equations** and **integro-differential equations**. %[text] Examples: %[text] ![rlc-circuit.png](text:image:171f)$\\;\\Longleftrightarrow \\;\n\\left\\{ \\begin{array}{rcl} \nL\\,\\displaystyle \\frac{d\\;}{d\\,t}\\,I(t) +R\\,I(t) + \\frac{1}{C}\\,\\int\_0^{t} I(\\tau)\\,d \\tau &=& V\_S(t) \\\\ \\\\\nI(0) &=& I\_0\n\\end{array} \\right. \\quad I(t) = ?\\,,\\; t \\ge 0$ %[text] %[text] $\\left\\{\\begin{array}{l}\n\\dot{x}(t) = A\\,x(t) + B\\,u(t) \\\\\nx(0) = x\_0 \\\\\nu(t)\\,,\\; t \\ge 0\n\\end{array} \\right. \\quad x(t) = ?\\,,\\; t \\ge 0$ %[text] %[text] - Differential and integro-differential equations in the time domain: they can be **difficult** **to** **solve**. %[text] - Apply the Laplace transform: transform to the s-domain. %[text] - Differential and integro-differential equations become **algebraic equations**: **easy to solve**! %[text] - Transform the s-domain solution back to the time domain. \ %[text] %% %[text] %[text:anchor:H_2f0e] ### Causal Functions %[text] - We are interested in functions in the time domain $f(t)$ defined for t ≥ 0, assuming they are null for all negative times, i.e $f(t) \\equiv 0 \\; \\forall t\<0$ %[text] - Time domain functions that have this property are called **causal** **functions**. \ %[text] %[text:anchor:H_2d43] #### Example: The Heaviside Function %[text] This is the first example of a causal function: %[text]{"align":"center"} $\\mathbf{1}(t):= \\left\\{ \\begin{array}{rcl} 0, &\\;& \\forall t \<0 \\\\ 1, &\\;& \\forall t \\ge 0 \\end{array} \\right. \\qquad (\\triangle)$ %[text]{"align":"center"} ![heaviside_function.png](text:image:6cb5) %[text] %[text] The Heaviside function is defined in the Symbolic Math Toolbox and it corresponds to the MATLAB function **`heaviside`**. %[text] **Pay** **attention**: by default, the definition of this function in the Symbolic Math Toolbox is different: clear sympref('default'); disp(heaviside(sym([-10, -1/10000, 0, +1/10000, 10]))) %[output:39427d4a] tVALs = (-2:1e-2:2); % refer to Part 3 of "Introduction to MATLAB" plot(tVALs, heaviside(sym(tVALs)), 'LineStyle', 'none', 'Marker','o', 'MarkerSize', 6, ... %[output:4a709224] 'MarkerEdgeColor','r', 'MarkerFaceColor','r') %[output:4a709224] grid on; xlabel('time t [s]'); ylabel('f(t)'); %[output:4a709224] title('Heaviside Function') %[output:4a709224] ylim([-0.25, 1.25]) %[output:4a709224] %[text] Note the function value at $t=0$ (recall the default configuration of the Symbolic Math Toolbox, analysed at the beginning of the live script [*Introduction to MATLAB Part 6 - Symbolic Math Computations*](file:./Intro_MATLAB4DDDS_p6.m) ). %[text] To adapt the Heaviside function, we have to modify the toolbox configuration preferences, as follows: sympref('HeavisideAtOrigin', 1); % forcing the setting for the Heaviside function disp(heaviside(sym([-10, -1/10000, 0, +1/10000, 10]))) %[output:592d93e9] %[text] Now the behaviour of the Heaviside function is in accordance with the definition $(\\triangle)$. % tVALs = (-2:1e-2:2); plot(tVALs, heaviside(sym(tVALs)), 'LineStyle', 'none', 'Marker','o', 'MarkerSize', 4, ... %[output:494a5d6a] 'MarkerEdgeColor','b', 'MarkerFaceColor','b') %[output:494a5d6a] grid on; xlabel('time t [s]'); ylabel('f(t)'); %[output:494a5d6a] title('Heaviside Function') %[output:494a5d6a] ylim([-0.25, 1.25]); %[output:494a5d6a] %% %[text] %[text:anchor:H_71d3] #### Another Example %[text] Usually we will use the Heaviside function $1(t)$ to emphasize that we are considering a causal function: %[text]{"align":"center"} $f(t) = \\left\[3\\,\\sin\\left(4\\,t+\\frac{\\pi}{3} \\right) \\right\]\\cdot 1(t) \\quad \\Longleftrightarrow \\quad \nf(t) = \\left\\{ \\begin{array}{lcl}\n0\\,, &\\;& \\forall t\<0 \\\\\n3\\,\\sin\\left(4\\,t+\\frac{\\pi}{3} \\right) \\,,&\\;& \\forall t \\ge 0\n\\end{array} \\right..$ %[text]{"align":"center"} ![causalfunExample.png](text:image:097e) %[text] How do you do this in MATLAB? syms t f_causal(t) = 3*sin(4*t+pi/3)*heaviside(t) %[output:4ae48099] tVALs = (-2:1e-3:2); plot(tVALs, f_causal(sym(tVALs)), 'LineStyle', 'none', 'Marker','o', 'MarkerSize', 4, ... %[output:28e3767d] 'MarkerEdgeColor','g', 'MarkerFaceColor','g') %[output:28e3767d] grid on; xlabel('time t [s]'); ylabel('f(t)'); %[output:28e3767d] title('A Causal Function') %[output:28e3767d] ylim([-3.25, 3.25]); %[output:28e3767d] %% %[text] %[text:anchor:H_5b9c] ### The Unilateral or One-Sided Laplace Transform %[text] %[text] %[text:anchor:H_24b0] #### Definition %[text] Given a causal function $f(t)$, the Laplace transform of $f(t)$ is the function $F(s) := \\mathcal{L}\\left(f\\right)$ defined by %[text]{"align":"center"} $F(s) := \\int\_0^{+\\infty} f(t)\\,e^{-s\\,t}\\,d\\,t$ %[text] for those $s \\in \\mathbb{C}$ for which the integral makes sense. %[text] - $F$ is a complex-valued function of complex numbers; %[text] - $s$ is called the (*complex*) *frequency* variable, with units $\\text{s}^{-1}$; $t$ is called the time variable (meas. units $\\text{s}$); %[text] - the lower limit of integration is $t=0$: the transform is called the **unilateral** or **one-sided Laplace transform**. %[text] - **Common notation convention**: lower case letter denotes the time-domain function $f(t)$; capital letter denotes its Laplace transform $F(s) = \\mathcal{L}\\left(f(t) \\right)$ \ %[text] %[text:anchor:H_9c83] #### Existence %[text] Which class or classes of functions possess a Laplace transform? %[text] - **Fact 1**: $f(t)$ is continuous for $t=0$; if not, $f(t)$ must contain **no impulses at** $t=0$. %[text] - **Fact 2**: any continuous, bounded, causal function $f(t)$ admits Laplace transform. %[text] - **Fact 3**: any piecewise continuous, causal function $f(t)$ admits Laplace transform. \ %[text] Piecewise continuous function $\\Longleftrightarrow$ jump discontinuities and no vertical asymptotes. %% %[text] **Examples:** %[text] The function defined by %[text]{"align":"center"} $f(t) = \\left\\{ \\begin{array}{rcl}\nt^2\\,, & \\;& 0 \\le t \\le 1 \\\\\n3-t\\,, & \\;& 1 \< t \\le 2 \\\\\nt+1 \\,, &\\;& 2 \< t \n\\end{array}\\right.$ %[text] is piecewise continuous on $\[0, +\\infty )$. clear t tVALs syms t assume(t>0) f_pc(t) = symfun(piecewise( (0<=t & t<=1), t^2, ... (1avoid inserting the Heaviside function explicitly to mark a function as causal **unless** you are dealing with [delayed causal functions](internal:H_2417). \ clear variables syms t s ft1(t) = exp(t)*heaviside(t) %[output:5c05afee] ft2(t) = exp(t) %[output:3a94a861] Fs1 = laplace(ft1, t, s) %[output:8dd3f121] Fs2 = laplace(ft2, t, s) %[output:2bb7fbf7] %% %[text] %[text:anchor:H_1978] ### Laplace Transforms Properties %[text] %[text] %[text:anchor:H_580b] #### Linearity %[text] - The Laplace transform is linear. %[text] - If $f(t)$ and $g(t)$ are any causal functions, for which the Laplace transform exists, and $a$ is any scalar, we have \ clear variables syms t s syms f(t) g(t) syms F(s) G(s) syms a omogeneityL = laplace(a*f(t)) %[output:8bdef976] omogeneityL = subs(omogeneityL, laplace(f(t)), F(s)) %[output:097dda95] superpositionl = laplace(f(t)+g(t), t, s); superpositionl = subs(superpositionl, [laplace(f(t)), laplace(g(t))], [F(s), G(s)]) %[output:4b6fb331] %% %[text] An example: clear variables syms t s f(t) = 1*heaviside(t); g(t) = exp(t); F(s) = laplace(f(t), t, s); G(s) = laplace(g(t), t, s); disp([F, G]) %[output:5a5d3b42] L(s) = laplace(3*f(t)+2*g(t), t, s) %[output:53511389] L(s) = collect(L, s) %[output:86b60f23] L(s) = simplify(L) %[output:015c3e2b] %[text] For details about the commands **`subs`**, **`collect`**, and **`simplify`**: help sym/subs %[output:6d4d8700] help sym/collect %[output:42dbd8e4] help sym/simplify %[output:547714bd] %% %[text] %[text:anchor:H_79b0] #### Transform of a Derivative %[text] If the causal function $f(t)$ is continuous at $t=0$, then %[text]{"align":"center"} $\\mathcal{L} \\left( \\dot{f}(t) \\right) = s\\,F(s)-f(0)$ clear variables syms t s syms f(t) dot_f(t) syms F(s) dot_f(t) = diff(f(t), 1); % the 1st derivative Dot_F(s) = laplace(dot_f, t, s) %[output:032b39ac] Dot_F(s) = subs(Dot_F(s), laplace(f(t), t, s), F(s)) %[output:5769dbf1] %[text] %[text] An example: %[text]{"align":"center"} $f(t) = 2\\,\\left(e^{t}-1) \\cdot 1(t) \\; \\Longrightarrow \\; \\dot{f}(t) = 2e^{t} \\,,\\quad t \\ge 0$ clear variables syms t s syms f(t) dot_f(t) syms F(s) DotF(s) f(t) = 2*(exp(t)-1); % causal symbolic function of time t %[text] Let's verify the continuity of $f(t)$ at $t=0$: f0left = limit(f, t, 0, 'left') %[output:1b5ce807] f0right = limit(f, t, 0, 'right') %[output:7e6c361e] f(0) % the value of f(t) when t=0 %[output:86567dd4] %[text] F(s) = laplace(f, t, s) % Laplace transform of f(t) %[output:19f6fc47] dot_f(t) = diff(f,t,1) % the 1st derivative of f(t) %[output:74e21690] DotF(s) = laplace(dot_f(t), t, s) % the Laplace transform of dot_f %[output:5e165995] % the Laplace transform of the derivative of f(t) DotF_ALT(s) = laplace(diff(f, t, 1), t, s) %[output:5e8549f0] % the Laplace transform, applying the derivative property "by hand" DotF_ALT2(s) = collect( (s*F(s)-f(0)), s) %[output:6eec2fe6] %[text] %[text] For details about the command diff: help diff %[output:5bd0d790] %% %[text] %[text:anchor:H_8b13] #### Higher-Order Derivatives %[text] - Applying derivative formula twice yields \ %[text]{"align":"center"} $\\begin{array}{rcl}\n\\mathcal{L} \\left(\\ddot{f} \\right) &=& s\\,\\mathcal{L} \\left(\\dot{f} \\right) - \\dot{f}(0) \\\\\n&=& s\\,\\big( s\\,F(s) - f(0) \\big) - \\dot{f}(0) \\\\\n&= &s^2 \\,F(s) -s\\, f(0) - \\dot{f}(0)\n\\end{array}$ %[text] %[text] - A similar formula holds for the $k$-th order derivative \ %[text]{"align":"center"} $\\mathcal{L} \\left(f^{(k)} \\right) = s^{k} \\,F(s) -\\sum\_{n=0}^{k-1} \\, s^{k-n-1}\\,f^{(n)}(0)$ %[text] %[text] %[text:anchor:H_3d56] **Examples:** clear variables syms t s syms f(t) dot_f(t) ddot_f(t) dot_f(t) = diff(f, 1); % the 1st derivative ddot_f(t) = diff(f, 2); % the 2nd derivative Dot_F(s) = laplace(dot_f, t, s) %[output:0e91bc61] DDot_F(s) = laplace(ddot_f, t, s) %[output:601da2c6] %% %[text] Given the causal function %[text]{"align":"center"} $f(t) = 2\\,\\left(e^{3\\,t}-1) \\cdot 1(t) \\; \\Longrightarrow \\; \\dot{f}(t) = 6e^{3\\,t} \\,,\\; t \\ge 0 \\; \\Longrightarrow \\; \\ddot{f}(t) = 18e^{3\\,t} \\,,\\; t \\ge 0 $ clear variables syms t s syms f(t) dot_f(t) ddot_f(t) f(t) = 2*(exp(3*t)-1) %[output:611c63af] dot_f(t) = diff(f, 1) % the 1st derivative %[output:0974595f] ddot_f(t) = diff(f, 2) % the 2nd derivative %[output:7acee9c9] DDot_F(s) = laplace(ddot_f, t, s) %[output:873134f4] DDotF_ALT(s) = s^2*laplace(f, t, s)-s*f(0)-dot_f(0) %[output:9f5645bb] collect(DDot_F, s) %[output:97b112d3] %% %[text] %[text:anchor:H_7787] #### Transform of an Integral %[text] Let $g(t)$ be the running integral of a causal function $f(t)$: %[text]{"align":"center"} $\\quad g(t) = \\displaystyle \\int\_0^{t} f(\\tau)\\,d \\tau \\;\\Longleftrightarrow \\; G(s) = \\mathcal{L}\\left(g(t) \\right) = \\frac{1}{s}\\,F(s)$ %[text] where $F(s) = \\mathcal{L}\\left(f(t) \\right)$. %[text] An example: clear variables syms t s tau assume(tau >=0) assumptions %[output:857d5f8f] syms f(t) g(t) f(t) = heaviside(t); F(s) = laplace(f, t, s) %[output:7f3f529a] assumeAlso(t>0) g(t) = int(f(tau), tau, 0, t) %[output:2b876c5c] G(s) = simplify(laplace(g(t), t, s)) %[output:78acb64b] %% %[text] %[text:anchor:H_9c2e] #### Multiplication by t %[text] Let $f(t)$ be a causal function and define $g(t) = t \\cdot f(t)$. Then $G(s) = \\mathcal{L}\\left(g(t) \\right) = - \\frac{d}{d\\,s} F(s)$, where $F(s) = \\mathcal{L}\\left(f(t) \\right)$ %[text] Examples: %[text]{"align":"center"} $f(t) = e^{t}\\cdot 1(t)\\,,\\; g(t) = t\\,e^{t}\\cdot 1(t) \\quad \\Longleftrightarrow \\quad\n\\mathcal{L}\\left(g(t)\\right) = -\\frac{d}{d\\,s} \\left(\\frac{1}{s-1}\\right) = \\frac{1}{(s-1)^2}$ clear variables syms t s f(t) = exp(t); g(t) = t*exp(t); F(s) = laplace(f, t, s); G(s) = laplace(g, t, s) %[output:3a726a45] G_ALT = -diff(F, s, 1) %[output:32c9fdc7] %% %[text]{"align":"center"} $f(t) = t\\,e^{t}\\cdot 1(t)\\,,\\; g(t) = t^2\\,e^{t}\\cdot 1(t) \\quad \\Longleftrightarrow \\quad\n\\mathcal{L}\\left(g(t)\\right) = -\\frac{d}{d\\,s}\\left(\\frac{1}{(s-1)^2}\\right) = \\frac{2}{(s-1)^3}$ clear variables syms t s f(t) = exp(t); F(s) = laplace(f, t, s); f1(t) = t*exp(t); g1(t) = t^2*exp(t); F1(s) = laplace(f1, t, s); G1(s) = laplace(g1, t, s) %[output:868fcd89] G1_ALT = -diff(F1, s, 1) %[output:0d62e1ee] G1_ALT_ALT = -diff(-diff(F, s, 1), s, 1) %[output:63a03cdc] %% %[text] %[text:anchor:H_2fa8] #### Exponential Scaling (Frequency Shifting) %[text] Let $f(t)$ be a causal function, with Laplace transform $F(s)$, and let g(t) be defined as ( $a$ is a scalar value) %[text]{"align":"center"} $g(t) = e^{a\\,t} \\cdot f(t) \\quad \\Longleftrightarrow \\quad \\mathcal{L}\\left(g(t)\\right) = G(s) = F(s-a)$ %[text] An example: %[text] - given $\\mathcal{L}\\left\[ \\left(\\cos(\\omega t)\\right)\\cdot 1(t) \\right\] = \\frac{s}{s^2+\\omega^2}$ then \ %[text]{"align":"center"} $\n\\mathcal{L}\\left\[ \\left( e^{-t}\\cos( t)\\right)\\cdot 1(t) \\right\] = \\frac{(s+1)}{(s+1)^2+1} \n= \\frac{s+1}{s^2+2s+2}\n$ clear variables syms t s omega f(t) = cos(omega*t) %[output:136a23d2] g(t) = exp(-t)*f(t) %[output:4eea0856] F(s) = laplace(f, t, s) %[output:0eec2c77] G(s) = laplace(g, t, s) %[output:63568579] subs(F(s), omega, 1) %[output:43a15e3a] collect(subs(G(s), omega, 1)) %[output:1d9ef650] %% %[text] %[text:anchor:H_2417] #### Time Shifting (Time Delay) %[text] - Let $f(t)$ be a causal function, with Laplace transform $F(s)$. %[text] - Define the causal function $g(t)$ as \ %[text]{"align":"center"} $g(t) = f\\left(t-T \\right) \\cdot 1\\left(t-T\\right)\\;, \\qquad T\>0$ %[text] - Then: \ %[text]{"align":"center"} $\\mathcal{L} \\left(g(t) \\right) = G(s) = e^{-s\\,T}\\,F(s)$ %[text] An example: %[text]{"align":"center"} $f(t) = 1(t-a) -1(t-b) \\quad \\Longleftrightarrow \\quad F(s) = \\mathcal{L}\\left(1(t-a)\\right) - \\mathcal{L}\\left(1(t-b)\\right) = \\frac{e^{-a\\,s}-e^{-b\\,s}}{s}\n$ clear variables syms t s a = sym(2); % the first delay term b = sym(5); % the second delay term f(t) = heaviside(t-a)-heaviside(t-b) %[output:76b427b7] % let's plot the pulse tVALs = (-2:1e-3:10); plot(tVALs, f(sym(tVALs)), 'LineStyle', 'none', 'Marker', 'square',... %[output:7a9a7687] 'MarkerSize', 4, 'MarkerFaceColor', '#0072BD', 'MarkerEdgeColor', '#0072BD'); %[output:7a9a7687] % fplot(f, [-2, 10], 'LineWidth', 3); grid on %[output:7a9a7687] title('a rectangular pulse from t=2 to t=5') %[output:7a9a7687] xlabel('time t [s]'); %[output:7a9a7687] ylabel('pulse f(t)'); %[output:7a9a7687] ylim([-0.2, 1.2]); %[output:7a9a7687] % the corresponding Laplace transform F(s) = collect(laplace(f, t, s), s) %[output:108100a7] %% %[text] Another example: %[text]{"align":"center"} $f(t) = \\left\[ 3 e^{-0.75 t} \\sin \\left(16 t +\\frac{\\pi}{3}\\right) \\right\] \\cdot 1(t) \\;, \\quad g(t) = f\\left(t- 1.5 \\right) \\cdot 1(t-1.5) \\;\\Longrightarrow \\; \ng(t) = \\left\[ 3\\, e^{-0.75 (t-1.5)} \\sin \\left(16 (t-1.5) +\\frac{\\pi}{3}\\right) \\right\] \\cdot 1(t-1.5)$ clear variables syms t s f(t) = ( 3 * exp(-0.75*t) * sin(16*t+pi/3) )*heaviside(t) %[output:5ac46136] T = sym(1.5); % the delay % the delayed function g(t) = f(t-T) % <<<<<<<-- Pay attention to the notation! <<<<<<<-- %[output:187df4ac] g_ALT(t) = ( 3*exp(-0.75*(t-T)) * sin(16*(t-T)+pi/3) )* heaviside(t-T) %[output:59e4a83f] % let's draw both the functions f and g tVALs = (-1:1e-3:5); plot(tVALs, f(sym(tVALs)), 'LineStyle', 'none', 'Marker', 'square',... %[output:68d0a11e] 'MarkerSize', 4, 'MarkerFaceColor', '#0072BD', 'MarkerEdgeColor', '#0072BD'); %[output:68d0a11e] hold on; grid on; %[output:68d0a11e] plot(tVALs, g(sym(tVALs)), 'LineStyle', 'none', 'Marker', 'square',... %[output:68d0a11e] 'MarkerSize', 2, 'MarkerFaceColor', '#D95319', 'MarkerEdgeColor', '#D95319'); %[output:68d0a11e] hold off %[output:68d0a11e] xlabel('time t [s]'); %[output:68d0a11e] ylabel('f(t) and g(t)'); %[output:68d0a11e] legend('f(t)', 'g(t)','Location', 'best', 'FontSize', 14) %[output:68d0a11e] title('A causal function vs. a delayed causal function') %[output:68d0a11e] ylim([-2.75, 3.25]) %[output:68d0a11e] %% %[text] %[text:anchor:H_8a13] #### Convolution %[text] %[text:anchor:H_238e] The convolution of causal functions $f(t)$ and $g(t)$ is the causal function $h(t)$, defined as follows: %[text]{"align":"center"} $h := f\*g \\; \\longleftrightarrow \\; h(t) = \\int\_{0}^{t} f(\\tau) g(t-\\tau)\\, d\\tau$ %[text] - **Note**: same as $h(t) = \\displaystyle \\int\_{0}^{t} f(t-\\tau) g(\\tau)\\, d\\tau$, i.e $f \* g = g \* f$ \ %[text]{"align":"center"} $H(s) = \\mathcal{L} \\left(f \* g \\right) = F(s) \\, G(s)$ %[text] %[text] - The (very great) importance of this property will soon become clear (refer to **Part** **2, pp. 27-32** of the course material). %[text] - Laplace transform turns convolution in time domain into multiplication in the frequency domain! \ %% %[text] %[text:anchor:H_2ae7] ## The Inverse Laplace Transform %[text] %[text] Given a Laplace transform $F(s)$, the **unique** corresponding **causal** **function** $f(t)$ can be recovered via: %[text]{"align":"center"} $f(t) = \\frac{1}{2 \\pi j} \\int\_{\\sigma-j \\infty}^{\\sigma+j \\infty}\\, F(s)\\, e^{st}\\, ds$ %[text] where $\\sigma$ is large enough that $F(s)$ is defined for $\\text{Re}\\left(s\\right) \\ge \\sigma$. %[text] **Luckily, we do not use that formula! Instead, we will use the Symbolic Math Toolbox command ilaplace!** help ilaplace %[output:3fa42227] %[text] %[text:anchor:H_7651] #### %[text] %[text:anchor:H_594b] ### Important Remark %[text] The **functions** in the time domain $f(t)$, with which we will deal, will always be %[text] - **causal** functions, %[text] - **piecewise** **continuous** functions, %[text] - they contain **no** **impulses** **at the time** $t=0$ \ %[text] Thus, the corresponding **Laplace** **transforms** $F(s)$ will always be **rational** **polynomial** **functions** %[text]{"align":"center"} $F(s) = \\frac{b\_m s^m +b\_{m-1} s^{m-1}+ \\cdots +b\_1 s + b\_0}{a\_n s^n +a\_{n-1} s^{n-1} + \\cdots +a\_1 s + a\_0} = \\frac{N(s)}{D(s)} \\qquad \\forall i \\, a\_i \\in \\mathbb{R},\\; \\forall j\\, b\_j \\in \\mathbb{R}$ %[text] Furthermore, the degree of the numerator polynomial will be less than that of the denominator polynomial: $m \< n$. %[text] %[text:anchor:H_7aaa] ### %[text] %[text:anchor:H_304d] ### Computation of the Inverse Laplace Transform: Sum of Partial Fractions %[text] %[text] For the sake of completeness, we present the classical approach for determining the inverse Laplace transform. %[text] Starting from a Laplace transform $F(s)$ that is a strictly proper rational function, it is **always** possible to express the function as a sum of partial fractions: %[text]{"align":"center"} $\\begin{array}{rcl}\nF(s) &=& \\displaystyle \\frac{C\_{1,1}}{(s-p\_1)} + \\cdots +\\frac{C\_{1,n\_{1}}}{(s-p\_1)^{n\_1}} + \n \\displaystyle \\frac{C\_{2,1}}{(s-p\_2)} + \\cdots +\\frac{C\_{2,n\_{2}}}{(s-p\_2)^{n\_2}} + \\cdots +\\displaystyle \\frac{C\_{q,1}}{(s-p\_q)} + \\cdots +\\frac{C\_{q,n\_{q}}}{(s-p\_q)^{n\_q}}\n\\end{array} $ %[text] where $C\_{i,\\,j} \\in \\mathbb{C}\\,,\\quad i=1,\\,2,\\,\\ldots,\\,q \\;,\\quad j=1,\\,2,\\,\\ldots,\\, n\_i $ and $\\sum\_{i=1}^{q} n\_i = n$. %[text] Owing to the linearity of the inverse Laplace transform, the time domain function we are looking for will be the linear combination of elementary exponential functions: %[text]{"align":"center"} $\\mathcal{L}^{-1}\\left(F(s) \\right) = \\displaystyle \\sum\_{i=1}^{q} \\sum\_{j=1}^{n\_i} \\mathcal{L}^{-1} \\left\[\\displaystyle \\frac{C\_{i,j}}{(s-p\_i)^{j}} \\right\] \\; \\Longrightarrow \\;\n\\mathcal{L}^{-1}\\left(F(s) \\right) = \\displaystyle \\sum\_{i=1}^{q} \\sum\_{j=1}^{n\_i} \\displaystyle \\frac{C\_{i,j}}{(j-1)!}\\,t^{j-1}\\,e^{p\_i\\,t} \\cdot 1(t)$ %[text] How to calculate the $C\_{i,j}$ coefficients? %[text]{"align":"center"} $C\_{i,\\,j} = \\frac{1}{\\left(n\_i-j \\right) ! }\\, \\lim\_{s \\to p\_i} \\left\\{ \\frac{d^{(n\_i-j)}\\,}{d \\, s^{(n\_i-j)}} \\left\[ F(s) \\left(s-p\_i\\right)^{n\_i}\\right\] \\right\\}$ %[text] %[text] Can we compute such a sum of partial fractions using MATLAB? %[text] Use the MATLAB function `partfrac` help partfrac %[output:1564962f] %[text] Example: clear variables syms t s Ys = 1/(s^2+2*s) %[output:2c686ba5] Ys_PartFrac_Expansion = partfrac(Ys,s) %[output:150531b9] %[text] In fact, it is true that %[text]{"align":"center"} $\\begin{array}{rclcl} \n\\frac{1}{s^2+2\\,s} &=& \\frac{1}{s\\,\\big(s+2 \\big)} &=& \\frac{C\_1}{s}+\\frac{C\_2}{s\n+2} \\\\\nC\_1 &=& \\lim\_{s \\to 0} \\;\\frac{1}{s \\big(s+2 \\big)} \\cdot s &=& \\frac{1}{2}\\\\\nC\_2 &=& \\lim\_{s \\to -2} \\; \\frac{1}{s\\,\\big(s+2 \\big)} \\cdot \\big(s+2 \\big) &=& -\\,\\frac{1}{2}\n\\end{array} \\quad \\Longrightarrow \\quad \\frac{1}{2} \\cdot \\frac{1}{s^2+2\\,s} = \\frac{1}{s}-\\frac{1}{2} \\cdot \\frac{1}{s+2}$ %[text]{"align":"center"} %[text:anchor:H_91a6] %% %[text] %[text:anchor:H_15f3] ### The Inverse Laplace Transform using MATLAB: Examples %[text] %[text] %[text:anchor:H_606e] #### A First Example %[text] Given the Laplace transform %[text]{"align":"center"} $F(s) = \\displaystyle \\frac{5\\,s+3}{s^3+5\\,s^2+8\\,s+4}$ %[text] determine the corresponding causal function $f(t)$ (i.e., the inverse Laplace transform) clear variables syms t s F(s) = (5*s+3)/(s^3+5*s^2+8*s+4) %[output:5b4e9a94] %[text] We can simplify and factorize the rational expression, by applying the command **`simplify`** F(s) = simplify(F) %[output:3c1f561d] %[text] The inverse Laplace transform can be determined as follows: f(t) = ilaplace(F, s, t) %[output:54bb7372] %[text] %[text:anchor:H_9068] #### Important Remark on Notation %[text] As pointed out [previously in this live script](internal:H_14d3), often the symbolic math engine does not insert any Heaviside function in the evaluation of Laplace transforms and inverse transforms . %% %[text] %[text:anchor:H_8639] #### More Examples %[text] %[text] Given the Laplace transform %[text]{"align":"center"} $F(s) = \\frac{2}{s^2 + 2 s + 2}\\cdot e^{-2\\,s}$ %[text] determine the corresponding causal function $f(t)$ (i.e., the inverse Laplace transform). %[text] **Note**: According to the Laplace transform properties, this is the Laplace transform of a [delayed causal function](internal:H_2417). clear variables syms t s F(s) = (2/(s^2+2*s+2))*exp(-2*s) %[output:583ddb0f] f(t) = ilaplace(F, s, t) %[output:0eb97976] %[text] **Note**: This time the Heaviside function is needed! %% %[text] Given the Laplace transform %[text]{"align":"center"} $F(s) = \\frac{\\left(2\\,\\sqrt{3}+4\\right)\\,s^3+\\left(6\\,\\sqrt{3}+20 \\right)\\,s^2+\\left(14\\,\\sqrt{3}+92\\right)\\,s+ \\left(10\\,\\sqrt{3}+108 \\right)}{s^4+4\\,s^3+26\\,s^2+44\\,s+85}$ %[text] determine the corresponding causal function $f(t)$ clear variables syms t s F(s) = (sym(2*sym(sqrt(3))+4)*s^3+sym(6*sym(sqrt(3))+20)*s^2+sym(14*sym(sqrt(3))+92)*s + ... %[output:group:49f1bfab] %[output:85aa8db5] sym(10*sym(sqrt(3))+108))/(s^4+4*s^3+26*s^2+44*s+85) %[output:group:49f1bfab] %[output:85aa8db5] f(t) = ilaplace(F, s, t) %[output:445c69a7] ft1 = simplify(ilaplace(F, s, t), 10) %[output:3adec1fa] ft2 = simplify(ilaplace(F, s, t), 100) %[output:7447b5f8] %% %[text] %[text:anchor:H_0bb2] ### Zeros and Poles of a Rational Laplace Transform %[text] %[text] Consider a Laplace transform that is a rational function of the complex variable $s$ as, for example $F(s) = \\displaystyle \\frac{5\\,s+3}{s^3+5\\,s^2+8\\,s+4}$ %[text] How to determine **zeros** and **poles** of the rational function in MATLAB? clear variables syms t s F(s) = (5*s+3)/(s^3+5*s^2+8*s+4) %[output:50c806b0] %[text] To find the poles of $F(s)$ simply sue the command **`poles`**: pSET = poles(F, s) %[output:163f0be1] %[text] What about the **order** of each **pole**? [pSET, Np_SET] = poles(F, s) % %[output:6239607e] %[output:9d419188] %[text] How to determine the **zeros of a rational Laplace transform**? There is no devoted command. You have to use the **`solve`** command: zSET = solve(F, s) %[output:44d0d119] %[text] Thus you obtain a symbolic vector containing the zeros, each one with its multiplicity. %[text] %[text] %[text:anchor:H_959d] #### Important Remark on Zeros of a Rational Laplace Transform %[text] Pay attention: the command **`solve`** provides explicit solution usually for polynomial equations up to the degree $2$. If you want an explicit solution of a polynomial equation with higher degree, you have to use the following syntax for the command solve: G(s) = 3*((s+3)^3*(s-1))/((s+10)^2*(s-5)^3) %[output:6fdcf502] [pSET, nSET] = poles(G, s) %[output:97641729] %[output:1ef4f229] zSET = solve(G, s, "MaxDegree",4) %[output:5c36eea4] %[text] For details, refer to doc sym/solve %% %[text] %[text:anchor:H_129d] ## Theorems on the Laplace Transform %[text] %[text:anchor:H_782f] - Can we determine the **initial** **value** of a time-domain function **from** its **Laplace** **transform**? %[text] - Can we determine the **steady-state value** of a time-domain function **from** its **Laplace** **transform**? \ %[text] %% %[text] %[text:anchor:H_807e] ### Initial Value Theorem %[text] %[text:anchor:H_7717] Given a Laplace transform $F(s)$ that is a strictly proper rational function, the following property holds %[text]{"align":"center"} $\\lim\_{t \\to 0} f(t) = \\lim\_{s \\to +\\infty} s\\,F(s)$ %[text] - You can analyse the time behaviour of $f(t)$ at $t=0$ directly from its Laplace transform $F(s)$, without computing the inverse Laplace transform! \ %[text] %[text:anchor:H_9818] #### An Application Example %[text] Given the Laplace transform $F(s) = \\displaystyle \\frac{5\\,s+3}{(s+1)\\,(s+2)^2}$, determine $f(0)$ without computing the inverse Laplace transform: clear variables syms s t F(s) = (5*s+3)/(s+1)/(s+2)^2 %[output:0b0a7705] f0 = limit(s*F, s, +Inf) %[output:1dab16ba] %[text] Let's verify: f(t) = ilaplace(F,s, t) %[output:0d30e6a0] f(0) %[output:3424f1f6] %% %[text] %[text:anchor:H_2ed7] ### Final Value Theorem %[text] Given a Laplace transform $F(s)$ that is a rational function, %[text] - if all the **poles** of $F(s)$ are in the **left open half-plane**, with at most one simple pole in the origin, then the following identity holds and the two limits assume the same finite value. \ %[text]{"align":"center"} $\\lim\_{t \\to +\\infty} f(t) = \\lim\_{s \\to 0} s \\cdot F(s)$ %[text] %[text:anchor:H_13cf] #### Important Remark %[text] Pay attention to the assumptions about the poles of the Laplace transform! They are crucial! %[text] %[text] %[text:anchor:H_4353] #### Application Example %[text] Given the Laplace transform $F(s) = \\displaystyle \\frac{5\\,s+3}{s\\,(s+1)\\,(s+2)^2}$, determine, if possible, $f\_{\\infty} = \\lim\_{t \\to +\\infty} f(t) $ clear variables syms s t F(s) = (5*s+3)/s/(s+1)/(s+2)^2; %[text] Let's verify if the Final Value Theorem's assumptions are met: %[text] - determine the poles of $F(s)$; %[text] - verify that all the poles belong to the left open half-plane, with at most one simple pole at the origin. \ [pF, n_pF] = poles(F, s) % poles and corresponding multiplicity %[output:3c223836] %[output:6f8c8117] % --- 1st check: is there a pole at s=0? --- pole0ID = isAlways(pF==sym(0)); if any(pole0ID) pole0 = true; p0M = isAlways(n_pF(pole0ID)==1); else pole0 = false; p0M = false; end if (pole0 && p0M) || ~(pole0) p0OK = true; else p0OK = false; end % --- 1st check: is there a pole at s=0? --- % ---- 2nd check: Do all the remaining poles have negative real part? ---- if pole0 poles2analyse = not(pole0ID); else poles2analyse = true(size(pF)); end pN_OK = all(isAlways(real(pF(poles2analyse))sym\/piecewise<\/strong> ---\n\n sym\/piecewise<\/strong> - Conditionally defined expression or function\n This MATLAB function returns the piecewise expression or function pw\n whose value is val1 when condition cond1 is true, is val2 when cond2 is\n true, and so on.\n\n Syntax\n pw = piecewise<\/strong>(cond1,val1,cond2,val2,...)\n pw = piecewise<\/strong>(cond1,val1,cond2,val2,...,otherwiseVal)\n\n Input Arguments\n cond<\/a> - Condition\n symbolic condition | symbolic variable\n val<\/a> - Value when condition is satisfied\n number | vector | matrix | multidimensional array |\n symbolic number | symbolic variable | symbolic vector |\n symbolic matrix | symbolic multidimensional array |\n symbolic function | symbolic expression\n otherwiseVal<\/a> - Value if no conditions are true\n number | vector | matrix | multidimensional array |\n symbolic number | symbolic variable | symbolic vector |\n symbolic matrix | symbolic multidimensional array |\n symbolic function | symbolic expression\n\n Output Arguments\n pw<\/a> - Piecewise expression or function\n symbolic expression | symbolic function\n\n Examples\n Define and Evaluate Piecewise Expression<\/a>\n Define Piecewise Function<\/a>\n Set Value When No Condition Is True<\/a>\n Plot Piecewise Expression<\/a>\n Assumptions and Piecewise Expressions<\/a>\n Differentiate, Integrate, and Find Limits of Piecewise Expression<\/a>\n Elementary Operations on Piecewise Expressions<\/a>\n Extract Expressions and Conditions from Piecewise<\/a>\n Modify or Extend Piecewise Expression<\/a>\n Solve System of Equations with Piecewise Expressions<\/a>\n\n See also and<\/a>, assume<\/a>, assumeAlso<\/a>, assumptions<\/a>, if<\/a>, in<\/a>, isAlways<\/a>, not<\/a>, or<\/a>\n\n Introduced in Symbolic Math Toolbox in R2016b\n Documentation for sym\/piecewise<\/a>\n\n","truncated":false}} %--- %[output:2c2d4341] % data: {"dataType":"text","outputData":{"text":" symfun<\/strong> - Create symbolic functions\n This MATLAB function creates the symbolic function f.\n\n Syntax\n f(inputs) = formula\n f = symfun<\/strong>(formula,inputs)\n f = symfun<\/strong>(fM)\n\n Input Arguments\n formula<\/a> - Function body\n symbolic expression | vector of symbolic expressions |\n matrix of symbolic expressions\n inputs<\/a> - Input argument or arguments of function\n symbolic variable | array of symbolic variables\n fM<\/a> - Symbolic matrix function to convert\n symbolic matrix function\n\n Output Arguments\n f<\/a> - Symbolic function\n symfun object\n\n Examples\n Create and Define Symbolic Functions<\/a>\n Return Body and Arguments of Symbolic Function<\/a>\n Combine Two Symbolic Functions<\/a>\n Convert Symbolic Matrix Function to Symbolic Function<\/a>\n\n See also argnames<\/a>, formula<\/a>, matlabFunction<\/a>, sym<\/a>, syms<\/a>, symvar<\/a>\n\n Introduced in Symbolic Math Toolbox in R2012a\n Documentation for symfun<\/a>\n\n","truncated":false}} %--- %[output:84419513] % data: {"dataType":"symbolic","outputData":{"name":"Xs","value":"\\frac{s^2 -2\\,s+3}{4\\,s^3 +6\\,s^2 +8\\,s}"}} %--- %[output:69b79159] % data: {"dataType":"symbolic","outputData":{"name":"Xderiv","value":"-\\frac{s^4 -4\\,s^3 +4\\,s^2 +9\\,s+6}{s^2 \\,{{\\left(2\\,s^2 +3\\,s+4\\right)}}^2 }"}} %--- %[output:6f99a961] % data: {"dataType":"symbolic","outputData":{"name":"p","value":"2"}} %--- %[output:1a4ca2ef] % data: {"dataType":"symbolic","outputData":{"name":"Xpow","value":"\\frac{133\\,{{\\left(s-2\\right)}}^2 }{7776}-\\frac{s}{54}-\\frac{119\\,{{\\left(s-2\\right)}}^3 }{8748}+\\frac{17}{216}"}} %--- %[output:09ff1afc] % data: {"dataType":"symbolic","outputData":{"name":"Fs","value":"\\frac{1}{s-1}"}} %--- %[output:58a12bb2] % data: {"dataType":"symbolic","outputData":{"name":"Hs","value":"\\frac{1}{s}"}} %--- %[output:5c05afee] % data: {"dataType":"symbolic","outputData":{"name":"ft1(t)","value":"{\\mathrm{e}}^t \\,\\mathrm{h}\\mathrm{e}\\mathrm{a}\\mathrm{v}\\mathrm{i}\\mathrm{s}\\mathrm{i}\\mathrm{d}\\mathrm{e}\\left(t\\right)"}} %--- %[output:3a94a861] % data: {"dataType":"symbolic","outputData":{"name":"ft2(t)","value":"{\\mathrm{e}}^t"}} %--- %[output:8dd3f121] % data: {"dataType":"symbolic","outputData":{"name":"Fs1","value":"\\frac{1}{s-1}"}} %--- %[output:2bb7fbf7] % data: {"dataType":"symbolic","outputData":{"name":"Fs2","value":"\\frac{1}{s-1}"}} %--- %[output:8bdef976] % data: {"dataType":"symbolic","outputData":{"name":"omogeneityL","value":"a\\,\\mathrm{l}\\mathrm{a}\\mathrm{p}\\mathrm{l}\\mathrm{a}\\mathrm{c}\\mathrm{e}\\left(f\\left(t\\right),t,s\\right)"}} %--- %[output:097dda95] % data: {"dataType":"symbolic","outputData":{"name":"omogeneityL","value":"a\\,F\\left(s\\right)"}} %--- %[output:4b6fb331] % data: {"dataType":"symbolic","outputData":{"name":"superpositionl","value":"F\\left(s\\right)+G\\left(s\\right)"}} %--- %[output:5a5d3b42] % data: {"dataType":"symbolic","outputData":{"name":"","value":"\\left(\\begin{array}{cc}\n\\frac{1}{s} & \\frac{1}{s-1}\n\\end{array}\\right)"}} %--- %[output:53511389] % data: {"dataType":"symbolic","outputData":{"name":"L(s)","value":"\\frac{2}{s-1}+\\frac{3}{s}"}} %--- %[output:86b60f23] % data: {"dataType":"symbolic","outputData":{"name":"L(s)","value":"\\frac{5\\,s-3}{s^2 -s}"}} %--- %[output:015c3e2b] % data: {"dataType":"symbolic","outputData":{"name":"L(s)","value":"\\frac{5\\,s-3}{s\\,\\left(s-1\\right)}"}} %--- %[output:6d4d8700] % data: {"dataType":"text","outputData":{"text":" subs<\/strong> - Symbolic substitution\n This MATLAB function returns a copy of s, replacing all occurrences of\n match with replacement, and then evaluates s.\n\n Substitute Symbolic Scalar Variables and Functions\n snew = subs<\/strong>(s,match,replacement)\n snew = subs<\/strong>(s,replacement)\n snew = subs<\/strong>(s)\n\n Substitute Symbolic Matrix Variables and Functions\n sMnew = subs<\/strong>(sM,matchM,replacementM)\n sMnew = subs<\/strong>(sM,replacementM)\n sMnew = subs<\/strong>(sM)\n\n Input Arguments\n s<\/a> - Symbolic input\n symbolic scalar variable | symbolic expression | symbolic equation |\n symbolic function | symbolic array | symbolic matrix | structure\n match<\/a> - Scalar variable to substitute\n symbolic scalar variable | symbolic function | symbolic expression |\n symbolic array | cell array\n replacement<\/a> - New replacement value\n number | symbolic number | symbolic scalar variable |\n symbolic function | symbolic expression | symbolic array |\n structure | cell array\n sM<\/a> - Symbolic input\n symbolic matrix variable | symbolic matrix function |\n symbolic expression | symbolic equation | symbolic condition\n matchM<\/a> - Matrix variable or function to substitute\n symbolic matrix variable | symbolic matrix function |\n symbolic expression | cell array\n replacementM<\/a> - New replacement value\n number | symbolic number | symbolic matrix variable |\n symbolic matrix function | symbolic expression | symbolic array |\n cell array\n\n Examples\n Single Substitution<\/a>\n Default Substitution Variable<\/a>\n Evaluate Expression with New Values<\/a>\n Multiple Substitutions<\/a>\n Substitute Scalars with Arrays<\/a>\n Substitute Symbolic Scalar Variables in Structure Array<\/a>\n Substitute Multiple Scalars with Arrays<\/a>\n Substitutions in Equations<\/a>\n Substitutions in Functions<\/a>\n Substitute Variables with Corresponding Values from Structure<\/a>\n Substitution Involving First-Order and Second-Order Derivatives<\/a>\n Substitute Symbolic Matrix Variables with Arrays<\/a>\n Characteristic Polynomial of Matrix<\/a>\n Substitute Variables in Symbolic Matrix Function<\/a>\n Substitute Symbolic Matrix Variables and Matrix Functions in Equation<\/a>\n Evaluate Expression Involving Symbolic Matrix Variables<\/a>\n\n See also double<\/a>, lhs<\/a>, rhs<\/a>, simplify<\/a>, subexpr<\/a>, vpa<\/a>\n\n Introduced in Symbolic Math Toolbox before R2006a\n Documentation for subs<\/a>\n\n","truncated":false}} %--- %[output:42dbd8e4] % data: {"dataType":"text","outputData":{"text":" sym\/collect<\/strong> - Collect coefficients of identical powers\n This MATLAB function collects the coefficients of identical powers of\n the default variable in the symbolic input P.\n\n Syntax\n C = collect<\/strong>(P)\n C = collect<\/strong>(P,expr)\n\n Input Arguments\n P<\/a> - Input expression\n symbolic expression | symbolic function | symbolic vector |\n symbolic matrix\n expr<\/a> - Expression in terms of which you collect coefficients\n symbolic number | symbolic variable | symbolic expression |\n symbolic function | symbolic vector | string array |\n character vector | cell array of character vectors\n\n Examples\n Collect Coefficients of Identical Powers of Default Variable<\/a>\n Collect Coefficients of Identical Powers of Specified Variable<\/a>\n Collect Coefficients in Terms of i and pi<\/a>\n Collect Coefficients in Terms of Symbolic Expressions and Functions<\/a>\n Collect Coefficients for Each Element of Matrix<\/a>\n Collect Coefficients in Terms of Function Calls<\/a>\n Collect Coefficients of Rational Function<\/a>\n\n See also combine<\/a>, expand<\/a>, factor<\/a>, horner<\/a>, numden<\/a>, rewrite<\/a>, simplify<\/a>,\n simplifyFraction<\/a>, symvar<\/a>\n\n Introduced in Symbolic Math Toolbox before R2006a\n Documentation for sym\/collect<\/a>\n\n","truncated":false}} %--- %[output:547714bd] % data: {"dataType":"text","outputData":{"text":" sym\/simplify<\/strong> - Algebraic simplification\n This MATLAB function performs algebraic simplification of expr.\n\n Syntax\n S = simplify<\/strong>(expr)\n S = simplify<\/strong>(expr,Name=Value)\n\n Input Arguments\n expr<\/a> - Input expression\n symbolic expression | symbolic function | symbolic vector |\n symbolic matrix\n\n Name-Value Arguments\n All<\/a> - Option to return equivalent results\n false (default) | true\n Criterion<\/a> - Simplification criterion\n \"default\" (default) | \"preferReal\"\n IgnoreAnalyticConstraints<\/a> - Simplification rules\n false (default) | true\n Seconds<\/a> - Time limit for the simplification process\n Inf (default) | positive number\n Steps<\/a> - Number of simplification steps\n 1 (default) | positive number\n\n Examples\n Simplify Expressions<\/a>\n Simplify Matrix Elements<\/a>\n Get Simpler Results for Logarithms and Powers<\/a>\n Get Simpler Results Using More Simplification Steps<\/a>\n Get Equivalent Results for Symbolic Expression<\/a>\n Separate Real and Imaginary Parts<\/a>\n Avoid Imaginary Terms in Exponents<\/a>\n Simplify Units<\/a>\n Get Simpler Result by Expanding Expression<\/a>\n\n See also collect<\/a>, combine<\/a>, expand<\/a>, factor<\/a>, horner<\/a>, numden<\/a>, rewrite<\/a>,\n simplifyFraction<\/a>, Simplify Symbolic Expression<\/a>\n\n Introduced in Symbolic Math Toolbox before R2006a\n Documentation for sym\/simplify<\/a>\n\n","truncated":false}} %--- %[output:032b39ac] % data: {"dataType":"symbolic","outputData":{"name":"Dot_F(s)","value":"s\\,\\mathrm{l}\\mathrm{a}\\mathrm{p}\\mathrm{l}\\mathrm{a}\\mathrm{c}\\mathrm{e}\\left(f\\left(t\\right),t,s\\right)-f\\left(0\\right)"}} %--- %[output:5769dbf1] % data: {"dataType":"symbolic","outputData":{"name":"Dot_F(s)","value":"s\\,F\\left(s\\right)-f\\left(0\\right)"}} %--- %[output:1b5ce807] % data: {"dataType":"symbolic","outputData":{"name":"f0left","value":"0"}} %--- %[output:7e6c361e] % data: {"dataType":"symbolic","outputData":{"name":"f0right","value":"0"}} %--- %[output:86567dd4] % data: {"dataType":"symbolic","outputData":{"name":"ans","value":"0"}} %--- %[output:19f6fc47] % data: {"dataType":"symbolic","outputData":{"name":"F(s)","value":"\\frac{2}{s-1}-\\frac{2}{s}"}} %--- %[output:74e21690] % data: {"dataType":"symbolic","outputData":{"name":"dot_f(t)","value":"2\\,{\\mathrm{e}}^t"}} %--- %[output:5e165995] % data: {"dataType":"symbolic","outputData":{"name":"DotF(s)","value":"\\frac{2}{s-1}"}} %--- %[output:5e8549f0] % data: {"dataType":"symbolic","outputData":{"name":"DotF_ALT(s)","value":"\\frac{2}{s-1}"}} %--- %[output:6eec2fe6] % data: {"dataType":"symbolic","outputData":{"name":"DotF_ALT2(s)","value":"\\frac{2}{s-1}"}} %--- %[output:5bd0d790] % data: {"dataType":"text","outputData":{"text":"--- help for diff<\/strong> ---\n\n diff<\/strong> - Differences and approximate derivatives\n This MATLAB function calculates differences between adjacent elements of\n X.\n\n Syntax\n Y = diff<\/strong>(X)\n Y = diff<\/strong>(X,n)\n Y = diff<\/strong>(X,n,dim)\n\n Input Arguments\n X<\/a> - Input array\n vector | matrix | multidimensional array | table | timetable\n n<\/a> - Difference order\n 1 (default) | positive integer scalar | []\n dim<\/a> - Dimension to operate along\n positive integer scalar\n\n Output Arguments\n Y<\/a> - Difference array\n scalar | vector | matrix | multidimensional array | table |\n timetable\n\n Examples\n Differences Between Vector Elements<\/a>\n Differences Between Matrix Rows<\/a>\n Multiple Differences<\/a>\n Differences Between Matrix Columns<\/a>\n Approximate Derivatives with diff<\/a>\n Differences Between Datetime Values<\/a>\n\n See also gradient<\/a>, prod<\/a>, cumsum<\/a>, sum<\/a>\n\n Introduced in MATLAB before R2006a\n Documentation for diff<\/a>\n Other uses of diff<\/a>\n\n","truncated":false}} %--- %[output:0e91bc61] % data: {"dataType":"symbolic","outputData":{"name":"Dot_F(s)","value":"s\\,\\mathrm{l}\\mathrm{a}\\mathrm{p}\\mathrm{l}\\mathrm{a}\\mathrm{c}\\mathrm{e}\\left(f\\left(t\\right),t,s\\right)-f\\left(0\\right)"}} %--- %[output:601da2c6] % data: {"dataType":"symbolic","outputData":{"name":"DDot_F(s)","value":"s^2 \\,\\mathrm{l}\\mathrm{a}\\mathrm{p}\\mathrm{l}\\mathrm{a}\\mathrm{c}\\mathrm{e}\\left(f\\left(t\\right),t,s\\right)-\\left({\\left(\\frac{\\partial }{\\partial t}\\;f\\left(t\\right)\\right)\\left|\\right.}_{t=0} \\right)-s\\,f\\left(0\\right)"}} %--- %[output:611c63af] % data: {"dataType":"symbolic","outputData":{"name":"f(t)","value":"2\\,{\\mathrm{e}}^{3\\,t} -2"}} %--- %[output:0974595f] % data: {"dataType":"symbolic","outputData":{"name":"dot_f(t)","value":"6\\,{\\mathrm{e}}^{3\\,t}"}} %--- %[output:7acee9c9] % data: {"dataType":"symbolic","outputData":{"name":"ddot_f(t)","value":"18\\,{\\mathrm{e}}^{3\\,t}"}} %--- %[output:873134f4] % data: {"dataType":"symbolic","outputData":{"name":"DDot_F(s)","value":"\\frac{18}{s-3}"}} %--- %[output:9f5645bb] % data: {"dataType":"symbolic","outputData":{"name":"DDotF_ALT(s)","value":"s^2 \\,\\left(\\frac{2}{s-3}-\\frac{2}{s}\\right)-6"}} %--- %[output:97b112d3] % data: {"dataType":"symbolic","outputData":{"name":"ans(s)","value":"\\frac{18}{s-3}"}} %--- %[output:857d5f8f] % data: {"dataType":"symbolic","outputData":{"name":"ans","value":"0\\le \\tau"}} %--- %[output:7f3f529a] % data: {"dataType":"symbolic","outputData":{"name":"F(s)","value":"\\frac{1}{s}"}} %--- %[output:2b876c5c] % data: {"dataType":"symbolic","outputData":{"name":"g(t)","value":"t"}} %--- %[output:78acb64b] % data: {"dataType":"symbolic","outputData":{"name":"G(s)","value":"\\frac{1}{s^2 }"}} %--- %[output:3a726a45] % data: {"dataType":"symbolic","outputData":{"name":"G(s)","value":"\\frac{1}{{\\left(s-1\\right)}^2 }"}} %--- %[output:32c9fdc7] % data: {"dataType":"symbolic","outputData":{"name":"G_ALT(s)","value":"\\frac{1}{{\\left(s-1\\right)}^2 }"}} %--- %[output:868fcd89] % data: {"dataType":"symbolic","outputData":{"name":"G1(s)","value":"\\frac{2}{{\\left(s-1\\right)}^3 }"}} %--- %[output:0d62e1ee] % data: {"dataType":"symbolic","outputData":{"name":"G1_ALT(s)","value":"\\frac{2}{{\\left(s-1\\right)}^3 }"}} %--- %[output:63a03cdc] % data: {"dataType":"symbolic","outputData":{"name":"G1_ALT_ALT(s)","value":"\\frac{2}{{\\left(s-1\\right)}^3 }"}} %--- %[output:136a23d2] % data: {"dataType":"symbolic","outputData":{"name":"f(t)","value":"\\cos \\left(\\omega \\,t\\right)"}} %--- %[output:4eea0856] % data: {"dataType":"symbolic","outputData":{"name":"g(t)","value":"{\\mathrm{e}}^{-t} \\,\\cos \\left(\\omega \\,t\\right)"}} %--- %[output:0eec2c77] % data: {"dataType":"symbolic","outputData":{"name":"F(s)","value":"\\frac{s}{\\omega^2 +s^2 }"}} %--- %[output:63568579] % data: {"dataType":"symbolic","outputData":{"name":"G(s)","value":"\\frac{s+1}{{\\left(s+1\\right)}^2 +\\omega^2 }"}} %--- %[output:43a15e3a] % data: {"dataType":"symbolic","outputData":{"name":"ans","value":"\\frac{s}{s^2 +1}"}} %--- %[output:1d9ef650] % data: {"dataType":"symbolic","outputData":{"name":"ans","value":"\\frac{s+1}{s^2 +2\\,s+2}"}} %--- %[output:76b427b7] % data: {"dataType":"symbolic","outputData":{"name":"f(t)","value":"\\mathrm{h}\\mathrm{e}\\mathrm{a}\\mathrm{v}\\mathrm{i}\\mathrm{s}\\mathrm{i}\\mathrm{d}\\mathrm{e}\\left(t-2\\right)-\\mathrm{h}\\mathrm{e}\\mathrm{a}\\mathrm{v}\\mathrm{i}\\mathrm{s}\\mathrm{i}\\mathrm{d}\\mathrm{e}\\left(t-5\\right)"}} %--- %[output:7a9a7687] % data: 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","height":337,"width":560}} %--- %[output:108100a7] % data: {"dataType":"symbolic","outputData":{"name":"F(s)","value":"\\frac{{\\mathrm{e}}^{-2\\,s} -{\\mathrm{e}}^{-5\\,s} }{s}"}} %--- %[output:5ac46136] % data: {"dataType":"symbolic","outputData":{"name":"f(t)","value":"3\\,\\sin \\left(16\\,t+\\frac{\\pi }{3}\\right)\\,{\\mathrm{e}}^{-\\frac{3\\,t}{4}} \\,\\mathrm{h}\\mathrm{e}\\mathrm{a}\\mathrm{v}\\mathrm{i}\\mathrm{s}\\mathrm{i}\\mathrm{d}\\mathrm{e}\\left(t\\right)"}} %--- %[output:187df4ac] % data: {"dataType":"symbolic","outputData":{"name":"g(t)","value":"3\\,\\mathrm{h}\\mathrm{e}\\mathrm{a}\\mathrm{v}\\mathrm{i}\\mathrm{s}\\mathrm{i}\\mathrm{d}\\mathrm{e}\\left(t-\\frac{3}{2}\\right)\\,\\sin \\left(16\\,t+\\frac{\\pi }{3}-24\\right)\\,{\\mathrm{e}}^{\\frac{9}{8}-\\frac{3\\,t}{4}}"}} %--- %[output:59e4a83f] % data: {"dataType":"symbolic","outputData":{"name":"g_ALT(t)","value":"3\\,\\mathrm{h}\\mathrm{e}\\mathrm{a}\\mathrm{v}\\mathrm{i}\\mathrm{s}\\mathrm{i}\\mathrm{d}\\mathrm{e}\\left(t-\\frac{3}{2}\\right)\\,\\sin \\left(16\\,t+\\frac{\\pi }{3}-24\\right)\\,{\\mathrm{e}}^{\\frac{9}{8}-\\frac{3\\,t}{4}}"}} %--- %[output:68d0a11e] % data: 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","height":337,"width":560}} %--- %[output:3fa42227] % data: {"dataType":"text","outputData":{"text":"--- help for sym\/ilaplace<\/strong> ---\n\n sym\/ilaplace<\/strong> - Inverse Laplace transform\n This MATLAB function returns the Inverse Laplace Transform of F.\n\n Syntax\n f = ilaplace<\/strong>(F)\n f = ilaplace<\/strong>(F,transVar)\n f = ilaplace<\/strong>(F,var,transVar)\n\n Input Arguments\n F<\/a> - Input\n symbolic expression | symbolic function | symbolic vector |\n symbolic matrix\n var<\/a> - Independent variable\n s (default) | symbolic variable | symbolic expression |\n symbolic vector | symbolic matrix\n transVar<\/a> - Transformation variable\n t (default) | x | symbolic variable | symbolic expression |\n symbolic vector | symbolic matrix\n\n Examples\n Inverse Laplace Transform of Symbolic Expression<\/a>\n Default Independent Variable and Transformation Variable<\/a>\n Inverse Laplace Transforms Involving Dirac and Heaviside Functions<\/a>\n Inverse Laplace Transform as Convolution<\/a>\n Inverse Laplace Transform of Array Inputs<\/a>\n Inverse Laplace Transform of Symbolic Function<\/a>\n If Inverse Laplace Transform Cannot Be Found<\/a>\n\n See also fourier<\/a>, ifourier<\/a>, iztrans<\/a>, laplace<\/a>, ztrans<\/a>, rewrite<\/a>\n\n Introduced in Symbolic Math Toolbox before R2006a\n Documentation for sym\/ilaplace<\/a>\n\n","truncated":false}} %--- %[output:1564962f] % data: {"dataType":"text","outputData":{"text":"--- help for sym\/partfrac<\/strong> ---\n\n sym\/partfrac<\/strong> - Partial fraction decomposition\n This MATLAB function finds the partial fraction decomposition of expr\n with respect to var.\n\n Syntax\n partfrac<\/strong>(expr,var)\n partfrac<\/strong>(expr,var,Name,Value)\n\n Input Arguments\n expr<\/a> - Rational expression\n symbolic expression | symbolic function\n var<\/a> - Variable of interest\n symbolic variable\n\n Name-Value Arguments\n FactorMode<\/a> - Factorization mode\n 'rational' (default) | 'real' | 'complex' | 'full'\n\n See also children<\/a>, coeffs<\/a>, collect<\/a>, combine<\/a>, compose<\/a>, divisors<\/a>, expand<\/a>,\n factor<\/a>, horner<\/a>, numden<\/a>, rewrite<\/a>, simplify<\/a>, simplifyFraction<\/a>\n\n Introduced in Symbolic Math Toolbox in R2015a\n Documentation for sym\/partfrac<\/a>\n\n","truncated":false}} %--- %[output:2c686ba5] % data: {"dataType":"symbolic","outputData":{"name":"Ys","value":"\\frac{1}{s^2 +2\\,s}"}} %--- %[output:150531b9] % data: {"dataType":"symbolic","outputData":{"name":"Ys_PartFrac_Expansion","value":"\\frac{1}{2\\,s}-\\frac{1}{2\\,\\left(s+2\\right)}"}} %--- %[output:5b4e9a94] % data: {"dataType":"symbolic","outputData":{"name":"F(s)","value":"\\frac{5\\,s+3}{s^3 +5\\,s^2 +8\\,s+4}"}} %--- %[output:3c1f561d] % data: {"dataType":"symbolic","outputData":{"name":"F(s)","value":"\\frac{5\\,s+3}{\\left(s+1\\right)\\,{\\left(s+2\\right)}^2 }"}} %--- %[output:54bb7372] % data: {"dataType":"symbolic","outputData":{"name":"f(t)","value":"2\\,{\\mathrm{e}}^{-2\\,t} -2\\,{\\mathrm{e}}^{-t} +7\\,t\\,{\\mathrm{e}}^{-2\\,t}"}} %--- %[output:583ddb0f] % data: {"dataType":"symbolic","outputData":{"name":"F(s)","value":"\\frac{2\\,{\\mathrm{e}}^{-2\\,s} }{s^2 +2\\,s+2}"}} %--- %[output:0eb97976] % data: {"dataType":"symbolic","outputData":{"name":"f(t)","value":"2\\,\\mathrm{h}\\mathrm{e}\\mathrm{a}\\mathrm{v}\\mathrm{i}\\mathrm{s}\\mathrm{i}\\mathrm{d}\\mathrm{e}\\left(t-2\\right)\\,\\sin \\left(t-2\\right)\\,{\\mathrm{e}}^{2-t}"}} %--- %[output:85aa8db5] % data: {"dataType":"symbolic","outputData":{"name":"F(s)","value":"\\frac{\\left(2\\,\\sqrt{3}+4\\right)\\,s^3 +\\left(6\\,\\sqrt{3}+20\\right)\\,s^2 +\\left(14\\,\\sqrt{3}+92\\right)\\,s+10\\,\\sqrt{3}+108}{s^4 +4\\,s^3 +26\\,s^2 +44\\,s+85}"}} %--- %[output:445c69a7] % data: {"dataType":"symbolic","outputData":{"name":"f(t)","value":"4\\,\\cos \\left(2\\,t\\right)\\,{\\mathrm{e}}^{-t} +2\\,\\sqrt{3}\\,{\\mathrm{e}}^{-t} \\,\\left(\\cos \\left(4\\,t\\right)+\\sin \\left(4\\,t\\right)\\,\\left(\\frac{\\sqrt{3}\\,\\left(2\\,\\sqrt{3}+8\\right)}{24}-\\frac{1}{4}\\right)\\right)"}} %--- %[output:3adec1fa] % data: {"dataType":"symbolic","outputData":{"name":"ft1","value":"2\\,{\\mathrm{e}}^{-t} \\,\\left(2\\,\\cos \\left(2\\,t\\right)+2\\,\\sin \\left(4\\,t+\\frac{\\pi }{3}\\right)\\right)"}} %--- %[output:7447b5f8] % data: {"dataType":"symbolic","outputData":{"name":"ft2","value":"4\\,{\\mathrm{e}}^{-t} \\,\\left(\\cos \\left(2\\,t\\right)+\\sin \\left(4\\,t+\\frac{\\pi }{3}\\right)\\right)"}} %--- %[output:50c806b0] % data: {"dataType":"symbolic","outputData":{"name":"F(s)","value":"\\frac{5\\,s+3}{s^3 +5\\,s^2 +8\\,s+4}"}} %--- %[output:163f0be1] % data: {"dataType":"symbolic","outputData":{"name":"pSET","value":"\\left(\\begin{array}{c}\n-2\\\\\n-1\n\\end{array}\\right)"}} %--- %[output:6239607e] % data: {"dataType":"symbolic","outputData":{"name":"pSET","value":"\\left(\\begin{array}{c}\n-2\\\\\n-1\n\\end{array}\\right)"}} %--- %[output:9d419188] % data: {"dataType":"symbolic","outputData":{"name":"Np_SET","value":"\\left(\\begin{array}{c}\n2\\\\\n1\n\\end{array}\\right)"}} %--- %[output:44d0d119] % data: {"dataType":"symbolic","outputData":{"name":"zSET","value":"-\\frac{3}{5}"}} %--- %[output:6fdcf502] % data: {"dataType":"symbolic","outputData":{"name":"G(s)","value":"\\frac{3\\,\\left(s-1\\right)\\,{\\left(s+3\\right)}^3 }{{\\left(s-5\\right)}^3 \\,{\\left(s+10\\right)}^2 }"}} %--- %[output:97641729] % data: {"dataType":"symbolic","outputData":{"name":"pSET","value":"\\left(\\begin{array}{c}\n-10\\\\\n5\n\\end{array}\\right)"}} %--- %[output:1ef4f229] % data: {"dataType":"symbolic","outputData":{"name":"nSET","value":"\\left(\\begin{array}{c}\n2\\\\\n3\n\\end{array}\\right)"}} %--- %[output:5c36eea4] % data: {"dataType":"symbolic","outputData":{"name":"zSET","value":"\\left(\\begin{array}{c}\n-3\\\\\n-3\\\\\n-3\\\\\n1\n\\end{array}\\right)"}} %--- %[output:0b0a7705] % data: {"dataType":"symbolic","outputData":{"name":"F(s)","value":"\\frac{5\\,s+3}{\\left(s+1\\right)\\,{\\left(s+2\\right)}^2 }"}} %--- %[output:1dab16ba] % data: {"dataType":"symbolic","outputData":{"name":"f0","value":"0"}} %--- %[output:0d30e6a0] % data: {"dataType":"symbolic","outputData":{"name":"f(t)","value":"2\\,{\\mathrm{e}}^{-2\\,t} -2\\,{\\mathrm{e}}^{-t} +7\\,t\\,{\\mathrm{e}}^{-2\\,t}"}} %--- %[output:3424f1f6] % data: {"dataType":"symbolic","outputData":{"name":"ans","value":"0"}} %--- %[output:3c223836] % data: {"dataType":"symbolic","outputData":{"name":"pF","value":"\\left(\\begin{array}{c}\n-2\\\\\n-1\\\\\n0\n\\end{array}\\right)"}} %--- %[output:6f8c8117] % data: {"dataType":"symbolic","outputData":{"name":"n_pF","value":"\\left(\\begin{array}{c}\n2\\\\\n1\\\\\n1\n\\end{array}\\right)"}} %--- %[output:8499ddc3] % data: {"dataType":"text","outputData":{"text":"The Final Value Theorem's assumptions are met!\n","truncated":false}} %--- %[output:7b092908] % data: {"dataType":"text","outputData":{"text":"You can apply the Final Value Theorem!\n","truncated":false}} %--- %[output:5fc91731] % data: {"dataType":"symbolic","outputData":{"name":"limf_infty","value":"\\frac{3}{4}"}} %--- %[output:3c8f5903] % data: {"dataType":"symbolic","outputData":{"name":"f2infty","value":"\\frac{3}{4}"}} %---