ITEC40081 Digital Control.
Assessment Details
This exercise shows the PID Controller tuning in MATLAB and Simulink, for DC Motor control. Download this Simulink file "dcintrocomplete.mdl" form the contents in NOW.
Then, open the PID tuner AutotunerPID to tune the controller parameters.
Change the parameters until you achieve the following performance specifications:
? Maximum overshoot ? 6%
? Maximum rise time < 0.35s
? Maximum setting time < 1.10s
? Gain margin > 25 dB
? Phase margin ? 45
? Explain the differences between the outputs of the initial and the modified system.
? Define the steady state error for control systems. Then, find the steady state error for the following system (Figure 2) when the input is (a) unit step, (b) ramp function, and (c) parabola.
? A typical hard disk drive actuator can be modelled quite accurately as a double integrator:
G(s) = Y(s)/U(s) = 6 107/S2
where y is the displacement of the read/write head in micrometre and u is the actuator input in volts. The sampling used in a typical hard disk drive servo system is 10 kHz. It is required to design an appropriate controller so the resulting closed-loop system has an overshoot less than 25% and a settling time less than 8 milliseconds as the response to a step reference of 1 micrometer. Design a digital PD, PI, or PID controller to meet the above design specifications using the emulation based method. Show all the detailed design procedure and the results of your simulations using MATLAB and Simulink.
4 (a) Convert (manually) the following digital transfer function into its state space representation:
G(z) = 0.8z2- 1.2z + 0.4/z2 - 1.2z + 0.4
Provide the detail derivations and the values of state space parameter matrices.
(b) Use MATLAB to find the state space model and compare it with your manual achievement.
? (a) Explain what Gain (GM) and Phase (PM) Margins are, what they should be to ensure stability of the control system, and how they can be adjusted or compensated for the overall system to be stable.
? Plot and use Bode diagram to find the GM and PM for the following control system (Figure 3).
? Design and use a suitable compensator to have a phase margin of more than 50 degree. Plot the Bode diagram of the compensator separately and also the final Bode diagram of the compensated system.
? Use "feedback" command in Matlab to find the closed loop transfer function of the compensated system. Provide the overall closed loop transfer function.