The open-loop transfer function of a DC-motor is a second order transfer function, e() K P(s)...

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The open-loop transfer function of a DC-motor is a second order transfer function, e() K P(s) - V(o) (Ja+b)(La + R) + K² where the rotational speed è is considered the output, the armature voltage V is considered the input, the physical parameters for the considered DC motor are: 0.02 kg.m² (J) moment of inertia of the rotor (b) motor viscous friction constant 0.2 N.m.s 0.02 V/rad/sec 2 Ohm 1 H (K) static DC gain (R) electric resistance (L) electric inductance An automatic controller is used to control the DC-motor rotational speed, as shown the block diagram. controller C(s) 11 The transfer function for a PID controller is: K₁ C(s) = K₂ + + Kas plant P(s) Kas²+K₂s+Ki For a 1-rad/sec step reference, the design criteria are the following. • Settling time less than 2 seconds • Overshoot less than 5% Steady-state error less than 1% Use MATLAB to create a Simulink block diagram representing the closed-loop system shown in the block diagram. Obtain the response (t) to the unit step input for the following cases: • Use proportional controller with K, 10. (Simulate for 10 sec) • Use proportional controller with K, 100. (Simulate for 10 sec) • Use a PID controller with K, - 75, K-1 and K-1. (Simulate for 300 sec) • Use a PID controller with K, 100, K, • Use a PID controller with K, 100, K, 200 and Ka= 1. (Simulate for 10 sec) 200 and K-10. (Simulate for 10 sec) Z Then discuss the effect of the controller on the system response, taking into consideration the rise time, the overshot, the settling time and the steady state error. The open-loop transfer function of a DC-motor is a second order transfer function, e() K P(s) - V(o) (Ja+b)(La + R) + K² where the rotational speed è is considered the output, the armature voltage V is considered the input, the physical parameters for the considered DC motor are: 0.02 kg.m² (J) moment of inertia of the rotor (b) motor viscous friction constant 0.2 N.m.s 0.02 V/rad/sec 2 Ohm 1 H (K) static DC gain (R) electric resistance (L) electric inductance An automatic controller is used to control the DC-motor rotational speed, as shown the block diagram. controller C(s) 11 The transfer function for a PID controller is: K₁ C(s) = K₂ + + Kas plant P(s) Kas²+K₂s+Ki For a 1-rad/sec step reference, the design criteria are the following. • Settling time less than 2 seconds • Overshoot less than 5% Steady-state error less than 1% Use MATLAB to create a Simulink block diagram representing the closed-loop system shown in the block diagram. Obtain the response (t) to the unit step input for the following cases: • Use proportional controller with K, 10. (Simulate for 10 sec) • Use proportional controller with K, 100. (Simulate for 10 sec) • Use a PID controller with K, - 75, K-1 and K-1. (Simulate for 300 sec) • Use a PID controller with K, 100, K, • Use a PID controller with K, 100, K, 200 and Ka= 1. (Simulate for 10 sec) 200 and K-10. (Simulate for 10 sec) Z Then discuss the effect of the controller on the system response, taking into consideration the rise time, the overshot, the settling time and the steady state error.

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Here are the actual Simulink models and responses for each case 1 Proportional controller with Kp 10 ... View the full answer