Question Control Systems Matlab Simulink The following open loop system is not stable. (s + 1000) Y(s) = 10 s (a) [4 marks] Use the bode () function in Matlab to draw the bode plot of the open loop transfer function. Using a gain margin of 0 dB and a phase margin of 135 degrees, identify the range of angular frequencies where the closed loop system is not stable. (b) [4 marks] Design a compensator (lead or lag) that makes the open loop system stable at all frequencies. Verify your design via. a Bode plot.

(a).   MatLab Code:   s = tf('s'); Ys = 10*(s+1000)/((s+1)*(s+5)); bode(Ys) grid       Output:                 (b).   Lead Compensator Design:   MatLab Code:   s = tf('s'); Ys = 10*(s+1000)/((s+1)*(s+5)); sisotool(Ys)       Output:         Click On:     Tuning Method    ===>   PID tuning:     PID TuningCompensatorC=0.037487 \times \frac{(1+0.069 \mathrm{~s})}{(1+0.00031 \mathrm{~s})}Select Loop to TuneLoopTransfer_CAdd new loop...SpecificationsTuning method: Robust response timeController Type: P 1 PI O PD PID\square pesign with first order derivative filterDesign mode: TimeUpdate CompensatorHelp       Export the Compensator:   C =     8.3606 (s+14.58)   ----------------       (s+3251)   Name: C Continuous-time zero/pole/gain model.       Verification:   s = tf('s'); Ys = 10*(s+1000)/((s+1)*(s+5)); C = 8.3606 *(s+14.58)/(s+3251); margin(C*Ys)                 You can see, the bode plot of the compensated system has nonzero Gain margin and Phase Margin. So, the system is stable.       ...