- Task 3 Choose Two Suitable Values For The Controller Gain K And Kn Such That The System Will Be Approximated By A D 1 (173.04 KiB) Viewed 12 times
- Task 3 Choose Two Suitable Values For The Controller Gain K And Kn Such That The System Will Be Approximated By A D 2 (173.04 KiB) Viewed 12 times
- Task 3 Choose Two Suitable Values For The Controller Gain K And Kn Such That The System Will Be Approximated By A D 3 (173.04 KiB) Viewed 12 times
- Task 3 Choose Two Suitable Values For The Controller Gain K And Kn Such That The System Will Be Approximated By A D 4 (197.28 KiB) Viewed 12 times
Task (3): Choose two suitable values for the controller gain, K and Kn, such that the system will be approximated by a dominant second order system with 0.6 < 5 <0.7 and 1.6 <0, < 1.8 rad/s. Plot the pole-zero map of the corresponding closed-loop system. In addition, run a statistical study to show both the average and the standard deviation of the: Maximum overshoot, Settling time when the gain of the open loop system changes from three to five (instead of exactly four) to check the effect of modeling inaccuracies. Task (4): Replace the controller gains of the original block diagram with a PD controller and try to find suitable values for the proportional and derivative gains such that the new response is very close to the one obtained in task (3). Compare between the two different control structures and report deviations in rise-time, maximum overshoot, and settling time. 1 Task (5): Develop a state space model of the servo system, assuming the position (output) and the velocity as two states for the system. Choose the third state to be the motor torque. You may rearrange the block diagram of the system to explicitly show the three states of the system. Prove that the transfer function of the state space model is equivalent to the one obtained in task (1). Hint: Find suitable values for the motor parameters that suit the block diagram. Adjust the open-loop block diagram to explicitly show the electrical and mechanical time constants. Change the mechanical time constant from its no-load value to 4-times as much and draw a relationship between the angular velocity vs. the torque, for both cases (use xy-graph in Simulink).
Task (3): Choose two suitable values for the controller gain, K and Kn, such that the system will be approximated by a dominant second order system with 0.6 < 5 <0.7 and 1.6 <0, < 1.8 rad/s. Plot the pole-zero map of the corresponding closed-loop system. In addition, run a statistical study to show both the average and the standard deviation of the: Maximum overshoot, Settling time when the gain of the open loop system changes from three to five (instead of exactly four) to check the effect of modeling inaccuracies. Task (4): Replace the controller gains of the original block diagram with a PD controller and try to find suitable values for the proportional and derivative gains such that the new response is very close to the one obtained in task (3). Compare between the two different control structures and report deviations in rise-time, maximum overshoot, and settling time. 1 Task (5): Develop a state space model of the servo system, assuming the position (output) and the velocity as two states for the system. Choose the third state to be the motor torque. You may rearrange the block diagram of the system to explicitly show the three states of the system. Prove that the transfer function of the state space model is equivalent to the one obtained in task (1). Hint: Find suitable values for the motor parameters that suit the block diagram. Adjust the open-loop block diagram to explicitly show the electrical and mechanical time constants. Change the mechanical time constant from its no-load value to 4-times as much and draw a relationship between the angular velocity vs. the torque, for both cases (use xy-graph in Simulink).
Problem: Design a closed-loop controller for a servo system (motor) with tachometer feedback. The output; (d), corresponds to the position of the motor, while the tachometer feedback provides a proportional signal to the velocity of the motor, Kn w(t). A proportional controller with gain K is inserted in the forward loop to adjust the transient performance of the system. A block diagram for this system is shown below: R(s) 1 C(s) K 4 (s + 1) (s+4) S Kh