Assignment
The mechanical system shown below is to be controlled by controlling its displacement, xi(t), for set-point step commands using the applied force, f(t). The TF, X1(s)/F(s) of the plant is provided:
X1 (s) / F(s) = [0.25 * (s/1.67 + 1)] / [(s/4.81 + 1)(s/2.18 + 1) (s2/0.95 + 1.51s/0.95 + 1)]
The force is applied via an actuator that has (say) the following TF, with an actuator speed limit of 10 units/s or a cross over frequency limit of 10 rad/s.
GA (s) = 1 / (s/5 + 1)
Design feedback controllers based 1) on the Root Locus (RL) method learned in class- 2) the PID method- 3) the Loop shaping method learned in class- 3a - using plant pole-zero cancelation approach & 3b- by matching the desired with the actual controller-plant OL TFs step-by-step (show steps). The control designs should take maximum advantage of the speed of the actuator (as much as possible - fast response), with good disturbance rejection required: approximately 20 dB gain at mid-frequency, with an overshoot of less than 20%, and with PM & GM of greater than 50° and 10 dB, respectively.
For the RL design, show the plot with the point on the RL selected for the closed loop pole placement...showing the gain and other values for the selected datatip. For the LS control design, see if the settling time will improve by placing the zero of the desired open loop TF, above the recommended Veto 'A the pole frequency (but still below the pole frequency).
The figures should include bode plots for each of the designed OL TF, displaying data points with the values of PM & GM, and mid frequency gain. For each design write down a proper controller TF, and over-plot this final OL design on the original bode plot to compare (clearly show legends on overplots). For each design show the step response, x1(t), of the feedback control system and place a cursor point to show the settling time. Also, show the Nyquist for each design, and finally, have a short discussion that compares the designs/methods. Notice for the step responses, you may need to specify the time duration of the simulation (i.e., step (G, time), or MATLAB may not carry the simulation to the end, and the response may look that it has an offset.
The control designs need to be briefly described and presented, including all MATLAB code used and figures that show the work. Note this is a project and the write-up should reflect that - be brief but comprehensive, clear, and organized as this will also be reflected on your grade. A better job on the project is expected from Graduate students and grading will be accordantly.