ECE 421 -- Design Project -- Spring 2000

The output of this block is the heading angle, psi, and the input to the block is the actual rudder angle, delta_r. In the absence of a disturbance, the actual and commanded rudder angles are equal.

TASKS:

1. Design a compensator G_c(s) such that the following specifications are all satisfied:

• when the reference input signal is a step function, and the disturbance signal is 0, the settling time of the actual heading angle must not exceed 200 seconds;
• when the reference input signal is a step function, and the disturbance signal is 0, the overshoot in actual heading angle must not exceed 15%;
• when the reference input signal is a unit ramp function, and the disturbance signal is 0, the steady-state error must not exceed 1;

2. Perform simulations in MATLAB with your compensator design to verify that all the specifications have been satisfied. Plots should be made that indicate the responses of the various signals are satisfactory. In addition to the plots that indicate the specifications have been satisfied, the following plots should also be made: 

   • step response from R(s) to U(s), with D(s) = 0;
   • step response from D(s) to C(s), with R(s) = 0 (if a "special" lag compensator was used to satisfy the steady-state error specification, step responses from D(s) to C(s) should be made both before and after the "special" lag compensator is designed).

3. This part of the project deals with the stability robustness of your design, that is, how much change can there be in the plant and/or controller models without losing closed-loop stability?  The Kharitonov functions that you used previously will be used for this analysis also. The closed-loop characteristic equation that is the result of your design in step 1 will be the nominal polynomial; perturbations will be with respect to that characteristic equation. The leading coefficient of the characteristic equation will be fixed at 1 throughout the analysis. All of the other coefficients will vary. Assume that each of those coefficients will vary from their nominal values by the same percentage, for example by +/- 10%. Using value sets and Kharitonov polynomials, determine the largest percentage (within 5%) perturbation to the nominal coefficients that can be tolerated without losing closed-loop stability.

REPORT:

You must provide a typed report that documents your design activity and provides plots that verify that all the specifications are satisfied. Handwritten reports will not be accepted. If you wish, you may produce your reports, including plots, in the form of web pages rather than in hardcopy form. In that case, you must provide me with the URL for your web pages by the time that the project report is due.

Your report must describe your design approach and explain how the approach is able to satisfy the design specifications. Your report must reference the plots that are included in it. The plots must clearly demonstrate that the specifications are satisfied, and the plots must be clearly labeled with axis labels and titles. Compare the step responses from D(s) to C(s) with and without the "special" lag compensator, and discuss why the differences appear. Justify the steady-state value of c(t) in both cases. Also justify the maximum value of the control signal u(t) in the step response from R(s) to U(s).

Include in the report your analysis of the robustness of your control system. Include plots of one stable and one unstable value set (zoomed in so that it can be identified).