OBJECTIVES:  

To design a compensator for the given system such that the closed-loop system satisfies a set of time-domain performance objectives;

To become familiar with SIMULINK.

TASKS:

The system to be controlled is the heading angle of a ship. The input to the system is the rudder angle, and the output is the heading angle.  The transfer function for a linear model of the Mariner-class cargo ship with nominal parameter values is shown below.

The closed-loop response for a unit step input must satisfy the following specifications:

• the settling time (2%) must be less than 125 seconds;

• the overshoot must be less than 25%; and

• the maximum absolute value of the rudder angle must be less than 3.

Design a compensator which accomplishes this. Use SIMULINK (see below) to evaluate the design. 

Develop a SIMULINK model for this system. The forward path should consist of one transfer function block for your compensator and one transfer function block for the ship model. The reference input (ordered heading angle) should be a step of amplitude 10. In addition to the transfer function blocks, you will need blocks for the summing junction, for the reference input, and for storing the output either in the MATLAB workspace or in a disc file.

The simulation should be run for 500 seconds. A variable-step integration time should be used. Choose a numerical integration method such as the ode23s (stiff/Mod. Rosenbrock) method. The following variables should be returned to the MATLAB workspace by the simulation (a time vector tout is automatically returned):

reference input (ordered heading angle);

actual heading angle;

commanded rudder angle (output of your compensator).

Determine the actual closed-loop step response overshoot and settling time for the compensated system and also for the uncompensated system (closed-loop and with a gain of -1 in series with the uncompensated system's transfer function).  Determine the rudder angle for the compensated system.

REPORT:

Write a report which documents your design process.  Discuss how satisfying the performance specifications is related to the locations of the closed-loop poles.  Include time domain plots, and other plots if appropriate (such as root locus), to illustrate and justify your work. Discuss the ease or difficulty of developing a SIMULINK model for evaluating the response relative to writing code directly in MATLAB.