Complete the following tasks before the lab session: 1. Lead compensator design by the root locus...

  

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Complete the following tasks before the lab session: 1. Lead compensator design by the root locus method Consider the feedback control system in Figure 1. + 1 0.48s +1 PET G.(s) Figure 1 4 S a) Plot the unit step response for G (s) = 1. What is the overshoot and settling time? b) Design a lead compensator to achieve less than 5% overshoot and less than 1 sec settling time. 2. Lead compensator design by the frequency response method Read the Lead Compensation - Control System Analysis and Design by the Frequency Response Method in the textbook by Ogata. Write down the design steps. 3. Control system design by the pole placement Method Consider the system shown in Figure 2. The system state space model is given: where Го A = 0 x = Ax + Bu y = Cx 1 0 0 -5 -6 1. Determine the stability of the uncompensated system. 2. Determine the controllability of uncompensated system. 3. Determine the state-feedback gain matrix K such that the closed-loop poles are located at s = -2±j4,s = -10. 0 0 1 B = 0 and C=[100] k₁ 11 x = AX + Bu ky ky Figure 2 X2 (1) y = Cx y=Xj Complete the following tasks before the lab session: 1. Lead compensator design by the root locus method Consider the feedback control system in Figure 1. + 1 0.48s +1 PET G.(s) Figure 1 4 S a) Plot the unit step response for G (s) = 1. What is the overshoot and settling time? b) Design a lead compensator to achieve less than 5% overshoot and less than 1 sec settling time. 2. Lead compensator design by the frequency response method Read the Lead Compensation - Control System Analysis and Design by the Frequency Response Method in the textbook by Ogata. Write down the design steps. 3. Control system design by the pole placement Method Consider the system shown in Figure 2. The system state space model is given: where Го A = 0 x = Ax + Bu y = Cx 1 0 0 -5 -6 1. Determine the stability of the uncompensated system. 2. Determine the controllability of uncompensated system. 3. Determine the state-feedback gain matrix K such that the closed-loop poles are located at s = -2±j4,s = -10. 0 0 1 B = 0 and C=[100] k₁ 11 x = AX + Bu ky ky Figure 2 X2 (1) y = Cx y=Xj