ECE 5470 Control Systems 2 Design Project

The goal of this project is to model a system and to design a controller for the system so that the closed-loop system performs satisfactorily. The system to be controlled is the ball-suspension system shown in the figure. The steel ball is suspended in the air by the electromagnetic force generated by the electromagnet. The control objective is to keep the metal ball suspended at the nominal equilibrium position by controlling the current in the magnet with voltage e(t). The resistance of the coil is R and the inductance is L(y)=L/y (depending on y). The force generated by the electromagnet is Ki2/y2.

1. Model the system by deriving the state equations.

2. Let E be the nominal value of e(t). Find the nominal values of y and dy/dt at equilibrium.

3. Linearize the system around its equilibrium. Assume R=1~2, L=0.4~0.6H, E=10~15V, K=1~2, g=9.8, M=0.2~0.3kg.

4. Assume that we can observe the position of the ball. Check if the system is controllable and observable.

5. Assume that we can measure all the states. Design a state feedback so that the closed-loop system performs satisfactory (you select the pole locations).

6. Assume that we can observe the position of the ball. Design a full-order observer. 7. Assume that we can observe the position of the ball. Design a reduced-order observer. 8. Assume that we can measure all the states. Design a state feedback so that the closed-

loop system achieves some optimality (you select the matrices Q and R). 9. Simulate the closed-loop systems of (5), (6), (7), and (8). 10. Simulate the closed-loop systems of (5), (6), and (8) using nonlinear plant. 11. Change M from its nominal value and simulate the closed-loop susyems to see if the

control is robust for (5) and (8). Each student should do his/her project independently. On the first page of your project, write the following statement: I have not received, nor have I given, any help and assistance on this project. Sign your name and date it.