Consider a permanent magnet DC motor that has the following parameters: {R = 3.5[2], L =...

           

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Consider a permanent magnet DC motor that has the following parameters: {R₁ = 3.5[2], L = 0.0432[H], K₂=0.253[N·m / A], Kµ = 0.253[V / rad / s], Jm = 0.0017[Kg ·m²]} The load inertia and the motor inertia are matched J₁ = J, and the connection between the two m inertias is by direct drive. Note that in this problem t >>t and also TL = 0 (no counter load m torque). In the following block diagram G(s) may stand for either the simplified armature voltage to speed 1 KE 1+ TS transfer function Q(s) U (S) (in speed control problems) or as the simplified armature voltage 1 Ⓒ(s) KE U (s) s(1+Ts) Ge(s) represent the controller, feedback sensor gain and the power amplifier gain. to angle transfer function Ge(s) in position control problems. The transfer function G(s) 2.1) In Position Control, if we want the output angle to track the input angle step commands with zero steady-state error, is it okay to use a proportional control Ge(s) = K, a positive gain? Explain why this is so. Demonstrate in MATLAB CST or in Simulink. Also show and explain how changes in K affect the shape of the closed-loop step response. 2.2) In Speed Control, if we want the output angular velocity to track speed step commands with zero steady-state error, which of the following four controllers are ones that can do the job? a) A P controller G (s) = K₂ b) A I controller: G (s) = K₁ - S b) A PI controller: G. (s) = K₂ +K₁ 1 == S Kps + K, S c) A PD controller: G (s) = K + KDs. For the controllers that can do the job, find the range of parameters needed to guarantee closed- loop stability. Demonstrate using CST or Simulink. 2.3) Back to position control, but this time the motor angle must track a ramp input with zero steady-state error. Which of the above four controllers is the only one that can meet the requirement? Explain your answer. Be sure that the closed-loop system is stable. Demonstrate using CST or Simulink. Consider a permanent magnet DC motor that has the following parameters: {R₁ = 3.5[2], L = 0.0432[H], K₂=0.253[N·m / A], Kµ = 0.253[V / rad / s], Jm = 0.0017[Kg ·m²]} The load inertia and the motor inertia are matched J₁ = J, and the connection between the two m inertias is by direct drive. Note that in this problem t >>t and also TL = 0 (no counter load m torque). In the following block diagram G(s) may stand for either the simplified armature voltage to speed 1 KE 1+ TS transfer function Q(s) U (S) (in speed control problems) or as the simplified armature voltage 1 Ⓒ(s) KE U (s) s(1+Ts) Ge(s) represent the controller, feedback sensor gain and the power amplifier gain. to angle transfer function Ge(s) in position control problems. The transfer function G(s) 2.1) In Position Control, if we want the output angle to track the input angle step commands with zero steady-state error, is it okay to use a proportional control Ge(s) = K, a positive gain? Explain why this is so. Demonstrate in MATLAB CST or in Simulink. Also show and explain how changes in K affect the shape of the closed-loop step response. 2.2) In Speed Control, if we want the output angular velocity to track speed step commands with zero steady-state error, which of the following four controllers are ones that can do the job? a) A P controller G (s) = K₂ b) A I controller: G (s) = K₁ - S b) A PI controller: G. (s) = K₂ +K₁ 1 == S Kps + K, S c) A PD controller: G (s) = K + KDs. For the controllers that can do the job, find the range of parameters needed to guarantee closed- loop stability. Demonstrate using CST or Simulink. 2.3) Back to position control, but this time the motor angle must track a ramp input with zero steady-state error. Which of the above four controllers is the only one that can meet the requirement? Explain your answer. Be sure that the closed-loop system is stable. Demonstrate using CST or Simulink.