me352_hw6_soln - 1 ME 352 System Dynamics and Control...

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Unformatted text preview: 1 ME 352 System Dynamics and Control Homework #6 – Solutions s Solutions given for the following ID 2 5 0 7 0 5 0 0 5 6 5 5 5 = = ⇒ = = = b a z y x [1]. Unit-step response is obtained, on the s-shaped response curve R and L values are calculated. Homework #6 -- PID Tuning Step Scope (s+a)(s+b) [1]*z_vec(s) Plant PID PID Controller cl Gain 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.01 0.02 0.03 0.04 0.05 0.06 time (s) y(t) Ziegler-Nichols Process Reaction Curve, R=0.0668, L=0.05 s. Optimal P, PI, and PID parameters are calculated and their closed-loop responses are obtained. 2 0.5 1 1.5 2 2.5 3 3.5 4 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 time (s) y(t) Homework #6 Solution -- PID Control, Ziegler-Nichols Process Reaction Method P Control, Kp=293.50 PI Control, Kp=264.15, Ki=1554.15 PID Control, Kp=352.20, Ki=3453.66, Kd=8.98 We observe that P control results in steady-state error. PI cancels the steady-state error but exhibits oscillations for some 4-5 cycles. PID yields faster decaying oscillations and no steady-state error. Among oscillations for some 4-5 cycles....
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me352_hw6_soln - 1 ME 352 System Dynamics and Control...

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