300763: Advanced Dynamics - Matlab Assessment Answer

Subject Code: 300763 Internal Code: 1AICFG

300763: Advanced Dynamics - Matlab Assessment Answer

Assignment Task: 1. Use the model reduction techniques to make the block diagram in Figure 2 equivalent to the standard feedback system diagram with disturbance as shown in Figure 3, i.e., obtain the expression of G1(s) and G2(s) (1 Mark). Obtain the transfer functions X(s)/Xr(s) and X(s)/D(s) 2. Assuming the closed-loop system is stable, find the steady-state error if xr(t) = 0 and d(t) = 1(t). This means that inputs are zero reference displacement and a unit step disturbance, and then calculate the steady state error ex(?) = x(?) ? xr(?) = x(?) which is caused by the disturbance signal d(t) = 1(t) (1 Mark). If the controller Gcp(s) is replaced by a PD controller, i.e., Gcp(s) = Kp(1 + Tds), what is the steady-state error ex(?) with xr(t) = 0 and d(t) = 1(t) ? Explain why the steady state errors are different using PD and PID controller. 3. Determine the values of K? and K? such that in the inner attitude loop, ? can be controlled to respond to a unit step signal ?r = 1(t) with a maximum setting time 0.5 second (5% error criterion) and a maximum 10% percentage overshoot. 4. Using the value K? and K? obtained in (3), and assuming there is no disturbance, i.e., d(t) = 0, apply the root-locus method to design the PID controller Gcp(s) = Kp(1 + Tds + 1Tis) such that the overall closed-loop transfer function X(s)/Xr(s) has a pair of dominant poles at s = ?0.6 ± j0.8 and static acceleration error constant Ka = 9.275. 5. Assuming zero external disturbance, i.e., d(t) = 0, plot unit-step input response, unit-ramp step input response, and unit-parabolic step input response of your designed system using MATLAB codes. Calculate the steady-state errors of your designed system with unit-step input, unit-ramp step input, and unit-parabolic input (0.5 Mark). Also plot the trajectories of tracking errors with unit-step input, unit-ramp step input, and unit-parabolic input and check whether the results in your plots are consistent with your calculation.  6. In order to check the designed system robustness to constant disturbance, a Simulink model named as ‘AS2.slx’ is provided as shown in Figure 4. There is a unit-step disturbance occurs at 15 seconds by using the transport lag block. Fill your design parameters in the provided MATLAB script file ‘AS2_Setup.m’ and run the script file to obtain the system response. The parameters to be filled are b, J, K?, K?, Kp, Ti, Td, which are highlighted as shown in Figure 5. (The files ‘AS2_Setup.m’ and ‘AS2.slx’ should be under the same folder). 7. Use the MATLAB ‘bode’ command to obtain the Bode plots of your designed system. Find the gain margin and phase margin of the system based on the generated Bode plots (a rough estimate will be sufficient). Next, check your results with the MATLAB ‘margin’ command.

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