Analyze a Control System Application


In this project you will try to analyze a control system application, response of open-loop system and evaluate the performance of the feedback controllers to satisfy the desired control objectives such as rise time, settling time, overshoot, steady state error, noise/disturbance rejection, etc. For this purpose, you should do the following steps and submit your results by the end of day of the final exam.
1. Choose a system that is of interest to you. We will also post some systems that you may choose. A good source is also Your textbook has numerous excellent examples as well. But we encourage you to chooses something that interests you.
2. Start with the linearized differential equation describing the system behavior. (If you start with a nonlinear system and linearize it, you may obtain 10 points extra credit.) Single input-single output systems are highly recommended.
3. Define its open loop and closed loop systems and determine the system transfer function for closed-loop system with unit feedback. Figure 1 (next page) shows A closed-Loop feedback Control System with a unit feedback loop.
4. Determine the poles of the transfer function (or equivalently, the eigenvalues of the A matrix).
5. Determine the transient response of the system.
6. Generate the phase variable (controllable) and observer canonical state space representations.
7. Determine whether the system is controllable and observable.
8. If necessary (and controllable), stabilize the system using state feedback.
9. If controllable and observable, design a controller and observer for the system, and demonstrate the performance of the combined system.
10. Define a PID controller for the system and demonstrate its performance
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