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Electrical Engineering Assignment:
Task:
Description of Assignment
Using MATLAB and/or SIMULINK(Control system Tool box) compute anwers for the following questions.Show the results to your lecturer and document them in the assignment report.
1. A process control system is shown in Figure 1. The system is regulated by a conventional PID or three-term controller.
(a) If , determine analytically the closed-loop transfer function, . Using Matlab/Simulink, plot the unit step response of the function and determine rise time, settling time, overshoot and the steady state error.
(b) Show analytically that the steady state error, for a unit step input, if the integrator coefficient, K i ? 0 If K P = K d = 1, find a value of K i required to cancel the open loop pole at s = -0.3.
(c)With the coefficient values given in (b), above, obtain a Bode plot for the open loop system, and determine the phase margin (PM) and cross-over frequency.
2. For each of the following open-loop transfer functions (OLTF) and gain settings, use Matlab to obtain the Bode plot, using the margin statement, and determine the phase margin and gain margin. Predict whether the resultant closed-loop system will be stable, critically stable, or unstable.
Derive the closed-loop transfer functions and the unit step response plots using Matlab. Assume unity feedback in all cases. Confirm your predictions of relative stability.
(a) G(s) =
(b) G(s) =
(a) G(s) =
With gain values:
(i) K = 0.25
(ii) K = 0.5
(iii)K=1
(iv) K=2
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