FDP on Electronic Design Tools Matlab for Control System Modeling 13/12/2017. A hands-on training session on

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1 A hands-on training session on MATLAB for Control System Modeling in connection with the FDP on Electronic Design GCE Kannur December 2017 Resource Person : Dr. A. Ranjith Ram Associate Professor, ECE Dept. Govt. College of Engineering Kannur Cell : arr@gcek.ac.in Objective : Familiarization with Control System Toolbox in MATLAB 21 Slides & 60 Minutes Outline The Symbolic Math Toolbox Laplace Transform Control System Models & Model Conversions Partial Fraction Expansion Impulse Response, Step Response & Frequency Response Root Locus Method Closed-loop Systems Matlab for Control System Modeling 2 Dr. A. Ranjith Ram arr@gcek.ac.in 1

2 A. Symbolic Math Toolbox 15 Minutes The Symbolic Math Toolbox In MATLAB, symbolic variables are also possible, which do not possess any values, but only symbolic in nature Symbolic Math Toolbox provides functions for solving and manipulating symbolic math expressions and performing variable-precision arithmetic One can analytically perform differentiation, integration, simplification, transforms, and equation solving. Also, one can generate code for MATLAB and Simulink from symbolic math expressions. >> syms x >> diff(sin(x^2)) >> ans = 2*x*cos(x^2) Matlab for Control System Modeling 4 Dr. A. Ranjith Ram arr@gcek.ac.in 2

3 Laplace Transform The Laplace Transform gives the representation of a continuous time signal/system in s domain Laplace Transform : laplace(); Inverse LT : ilaplace() Laplace Transformation does not need any numerical computation, but an integration/summation of a signal/sequence To cope with such a situation, MATLAB supports symbolic variables >> syms t a b; >> f = t^2; >> F = laplace(f) >> fhat = ilaplace(f) >> x = a*sin(b*t); >> X = laplace(x) >> xhat = ilaplace(x) Matlab for Control System Modeling 5 B. Control System Models 15 Minutes Dr. A. Ranjith Ram arr@gcek.ac.in 3

4 Control System Models Transfer Function Model >> num = [ 1 0]; >> den = [1 2 10]; >> H = tf(num,den) Zero-Pole-Gain Model >> z = 0; >> p = [2 i+1 i-1]; >> k = -2; >> H = zpk(z,p,k) Matlab for Control System Modeling 7 Control System Models (Contd ) State Space Model >> A = [ 0 1; -5-2]; >> B = [0; 3]; >> C = [1 0]; >> D = 0; >> H = ss(a, B, C, D) Matlab for Control System Modeling 8 Dr. A. Ranjith Ram arr@gcek.ac.in 4

5 Model Conversions >> num = [ ]; >> den = [ ]; >> [z p k] = tf2zp(num, den) >> z = [-1; -3]; >> p = [0; -2; -4; -6]; >> k = 4; >> [num den] = zp2tf(z,p,k); >> printsys(num, den, s ) >> [A B C D] = tf2ss(num, den) Matlab for Control System Modeling 9 Partial Fraction Expansion The Matlab function is residue >> num = [ ]; >> den = [ ]; >> [r p k] = residue(num, den) The inverse function is also residue >> [num den] = residue(r,p,k); >> printsys(num, den, s ) Matlab for Control System Modeling 10 Dr. A. Ranjith Ram arr@gcek.ac.in 5

6 C. System Responses 15 Minutes Impulse Response of Systems The Matlab function for impulse response is impulse >> b = [1]; >> a = [1 2 4]; >> sys = tf(b,a); % transfer function >> impulse(sys); % Response, h(t) >> grid on Matlab for Control System Modeling 12 Dr. A. Ranjith Ram arr@gcek.ac.in 6

7 Step Response of Systems The Matlab function for step response is step >> num = [1]; >> den = [1 2 4]; >> step(num, den); >> grid on; Matlab for Control System Modeling 13 Frequency Response of Systems The Matlab function for frequency response is freqs and bode >> num = [10]; >> den = [ ]; >> w = logspace(-1, 4, 100); >> freqs(num, den, w); >> figure; >> bode(num, den, w); Gain and Phase Margins is through margin >> margin(num, den); Matlab for Control System Modeling 14 Dr. A. Ranjith Ram arr@gcek.ac.in 7

8 Frequency Response Plots >> freqs(num, den, w); Magnitude (db) Phase (degrees) Magnitude Phase (deg) >> bode(num, den, w); Matlab for Control System Modeling 15 D. Root Locus Plots 15 Minutes Dr. A. Ranjith Ram 8

9 Root Locus Method The Matlab function for root locus creation is rlocus >> k1 = 0:2:10; >> k2 = 11:0.5:90; >> k3 = 91:10:500; >> k = [k1 k2 k3]; >> rlocus(num, den, k); The Matlab function for manually obtaining poles, gain etc., form a root locus, by a mouse click is rlocfind >> [k poles] = rlocfind(num,den) Matlab for Control System Modeling 17 E. Closed Loop Systems 15 Minutes Dr. A. Ranjith Ram arr@gcek.ac.in 9

10 Closed Loop Response The function to get the closed loop transfer function is feedback >> num = [1]; >> den = [ ]; >> G = tf(num, den); >> T = feedback(g,1) >> step(t) Matlab for Control System Modeling 19 Summary Familiarized with the Symbolic Math Toolbox Studied about Laplace Transform in MATLAB Learnt about Control System Models in MATLAB Performed Model Conversions Applied MATLAB for Partial Fraction Expansion Plotted Impulse Response, Step Response & Frequency Response Learnt how to plot Root Locus in MATLAB Studied about Closed-loop Systems and responses Matlab for Control System Modeling 20 Dr. A. Ranjith Ram arr@gcek.ac.in 10

11 Thanks Courtesy : 1. MathWorks Training & Services, Bengaluru 2. TEQIP Project Phase-II, GCE Kannur arr@gcek.ac.in Mob : Matlab for Control System Modeling 21 Dr. A. Ranjith Ram arr@gcek.ac.in 11