for a Ship's Heading Angle

2 Weeks

**OBJECTIVE:** To analyze the effects of nonlinearities and changes in the ship's
open-loop model on closed-loop stability and performance.

**OVERVIEW:** The controller that you designed in section C.1 was based on the
linear ship model with nominal values for all the parameters. The actual ship has a
nonlinear mechanism that moves the rudder in response to the control signal. This
steering mechanism has several nonlinear effects (saturation, deadzone, hysteresis,
and rate limiting). In addition, certain parameters in the ship may be subject to
change or to uncertainty. Each of these factors means that the controller has to
control a different system than the one for which it was designed.

This lab experiment will allow you to see the differences in performance that can occur when the system model is different than the design model. The simulations will be performed in SIMULINK. The block that implements the nonlinear steering mechanism and a data file that has three transfer functions for the ship are in a .zip file that should be downloaded. The two files can be extracted from the .zip file and should be stored in your MATLAB working directory.

The two perturbed system models are given by the following transfer functions. They will be used along with the nominal model given in C.1 and the compensator that you designed in C.1.

**TASKS:**

- Download and extract the .zip file mentioned above. Store the two files in your MATLAB working directory.
- Create a SIMULINK model that will allow you to simulate the closed-loop system. The forward path
should consist of one transfer function block for your compensator, one transfer function block for the
ship model, and the nonlinear steering mechanism. The steering mechanism block goes between the other
two blocks. The reference input (ordered heading angle) should be a step of amplitude 10.
The simulation should be run for 1200 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): - Simulate the system using the nominal ship model from C.1. Compare the responses from this simulation with the results that you obtained in C.1 without the steering mechanism in terms of overshoot, settling time, and oscillations. Compare the commanded and actual rudder signals to see the effects of the nonlinearities.
- Using the transfer function
*G*to model the ship, perform the simulation of the closed-loop system. Compare the results of this simulation with those obtained from the nominal model._{p_min} - Repeat the previous step using
*G*to model the ship._{p_max} - Produce Bode plots for your compensator with each of the ship models. Determine the gain and phase margins and the
maximum allowed pure time delay for each of these configurations.
- Write a report documenting your analyses. Plots from each of the simulations should be included. Discuss the effects that the nonlinear steering mechanism has on the closed-loop performance. Discuss the robustness of your compensator design to system changes as illustrated by the results of the simulations and the Bode plot analyses.

**REPORT:**

Write a report documenting your analyses. Plots from each of the simulations should be included. Discuss the effects that the nonlinear steering mechanism has on the closed-loop performance. Discuss the robustness of your compensator design to system changes as illustrated by the results of the simulations and the Bode plot analyses.

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*Latest revision on
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