The University of Asia Pacific Department of Electrical and Electronic Engineering EEE 318: Control Systems I Sessional Experiment No: _ _ Experiment Date: _ _ _ _ _ _ _ _ Name of the Experiment: Study of the effect of third pole and a zero in 2nd order system using MATLAB. Objectives: A. To study the effect of 3rd pole in 2nd order system with complex poles. B. To study the effect of an additional zero in 2nd order system with complex poles. Theory: Let us consider a 2nd order system with complex poles: 9 G1 s   2 s  2s  9 The poles are: -1±j√8 Now consider an additional pole at the real axis at -2. For this additional pole the denominator of the G1(s) becomes, (s+2)(s2+2s+9) = s3+4s2+13s+18. Then the new transfer function: 9 . G2 s   3 2 s  4s  13s  18 Again, let us consider another additional pole with the system G1(s) at -10 on the real axis. In this case the denominator will be, (s+10)(s2+2s+9) = s3+12s2+29s+90. Then the new transfer function: 9 . G3 s   3 2 s  12s  29s  90 Let us plot these three transfer functions using MATLAB and observe the effect of additional pole. Procedure to perform objective A: Write the following program using MATLAB: 1. Sample MATLAB program: clf clear all num1 = [9]; num2 = [9]; num3 = [9*10]; den1 = [1 2 9]; den2 = [1 4 13 18]; den3 = [1 12 29 90];

% Define numerator of G1(s) % It will keep all Css in the same level % Define denominator of of G1(s)

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t = 0 : 0.01 : 5; sys1 = tf(num1, den1); sys2 = tf(num2, den2); sys3 = tf(num3, den3); y1 = step(sys1, t); y2 = step(sys2, t); y3 = step(sys3, t); plot(t, y1, ‘r’, t, y2, ‘c’, t, y3, ‘b’) grid

% Define the transfer function of G1(s)

Report A: 1. State the effect of additional pole near the two complex poles on step response of the system. 2. If the additional third pole is far away from the complex poles then state its effect on step response. Explain your answer comparing it with the step response of 2nd order system. Procedure to perform objective B: Let us consider a 2nd order system with complex poles: 1 G1 s   2 s  2s  9 The poles are: -1±j√8 Now consider an additional zero at the real axis closer to the complex poles at -1.5. Then the new transfer function: s  1.5 . G2 s   2 s  2s  9 Again, let us consider another additional zero at real axis far away from the complex poles, say at -10. Then the new transfer function: s  10 . G3 s   2 s  2s  9 Let us simulate these three transfer functions using MATLAB and observe the effect of additional zero. Note: For additional zero s = -1.5, set numerator num2 = [-1 1.5]; To keep the Css of the step responses in the same level, you may change num2 as, num2 = (1/1.5)*[-1 1.5];

Report B: 1. If the zero is located at the right hand side of the s-plane, what would be the step response? 2. If such a control system represents a motor cycle steering system, then how it would respond?

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