Answer Happy

DESIGN PROBLEM: The open-loop transfer function of the DC motor is given in Figure 1 as follows: T,(s) Armature Electromagnetic force effect Mechanic U,G) 1,(s) K, L₂s+R, Js+ B Induced electromotive force effect K, Figure 1: The block diagram of a DC motor controller plant W C(s) P(s) Figure 2: Unity feedback system with a PID controller Parameters are given below: 0.01 kg.m² 0.1 N.m.s J: moment of inertia of the rotor B: motor viscous friction constant K: electromotive force constant motor torque constant R electric resistance L, K 0.01 V/rad/sec 0.01 N.m/A 1.0 Ohm electric inductance 0.5 H Design Criteria: The output should follow the input with the following time-domain specs Settling time less than 1 seconds Overshoot less than 4% Steady-state error less than 0.5% T_() D()
5. Do you think the response of the open-loop system you find in the question 3 satisfies the given design criteria? (10p) 6. If not, use a PID controller as shown in Figure 2 and tune gains of the controller using PID tuner of Matlab a. Use only proportional controller with a gain of Kp =75 and obtain the unit step response of the feedback system. What is the effect of the proportional controller on the percentage overshoot, settling time and the steady-state value of the system response? (15 p) b. Use PID controller with gains of Kp -75, Ko=1.0, and Ki-150 and obtain the unit step response of the feedback system. What is the effect of the PID controller on the percentage overshoot, settling time and the steady-state value of the system response? (15 p) C. Are the design criteria satisfied? If not, tune the gains of the PID controller using Matlab/pidTuner such that design criteria are satisfied (20 p).