ECE 421 -- Design Project -- Fall 1999

Ship Heading Control

Assigned 10/19/99
Due 4:00 p.m., Monday, 12/13/99.

INTRODUCTION:

This design project is to be an individual effort for each of the students. The George Mason University honor code applies to this project. Any questions concerning the project should be directed to Dr. Beale.

The block diagram for this project is seen to consist of the plant transfer function Gp(s), a compensator Gc(s), and a disturbance signal D(s). The plant model represents a linearization of the heading dynamics of a 250,000 ton tanker ship. The reference input signal R(s) is the desired heading angle for the ship, and the output signal C(s) is the actual heading angle. In this linear system, angles can be expressed in either radians or degrees. The output of the compensator, U(s), is the commanded rudder angle that is used to control the heading of the ship.

The transfer function for the open-loop ship model Gp(s) is given by

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

TASKS:

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

    • when the reference input signal is 0, and the disturbance signal is a step function, the steady-state value of the actual heading angle must be 0;
    • 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 250 seconds;
    • when the reference input signal is a step function, and the disturbance signal is 0, the actual heading angle must not exceed the desired heading angle by more than 15%;
    • when the reference input signal is a unit ramp function, and the disturbance signal is 0, the steady-state error must not exceed 3;
    • when the reference input signal is a step function equal to 10 degrees, and the disturbance signal is 0, the commanded control signal must not exceed 35 degrees in absolute value.

  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. It should be noted that there is not a settling time requirement for a step input at the disturbance signal, so that response might take much longer than the other responses. Ramp responses may be longer than step responses.

  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? My MATLAB function tsypkin.m can be used for this. The zipped version of this file should be downloaded and unzipped. (If you have trouble downloading the file, email me, and I will email it back to you). For your purpose in this project, the syntax for using the function can be

    rho = tsypkin(dcl, 0.1*dcl);

    where dcl is the closed-loop characteristic polynomial of your final compensated system. The function will create a figure with 3 plots on it, and will return a 3-element vector rho. A sample plot is shown for illustration. The elements in the rho vector are the maximum allowed perturbations to the coefficients of the closed-loop characteristic equation in terms of the 1-norm, 2-norm, and infinity-norm, respectively. The larger the values in rho, the more robust your control system is to changes in these coefficients. Evaluate your design using this function. It is hoped that all the values in rho will be greater than 1.

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.

Include in your report a discussion on why robustness of the control system should be included in your design process, or at least evaluated when the design is complete.

Click the icon to return to the Dr. Beale's home page

Lastest revision on Wednesday, June 7, 2006 9:15 PM