Controller Design
After a mathematical model for the system is made, a controller may be designed. For this project, a state space model was used.
State Space System Block Diagram
Synthesizing Velocity
The Sensors used in the design only provide information about the system's current position, not on the system's velocity. This requires that the velocity is synthesized from the rate of change of, or the derivative of, said position measurements. However, in practice this derivative action will amplify any noise that exists, as it is reiterated too frequency. To prevent this, the following control loop will be implemented to be a working average.
Designing "K" Matrix
Once The system has been properly modeled, the next step is to Start Designing the feedback gains which make up the "K" Matrix, shown in the state space block diagram above. This is accomplished in several steps, first determining the eigenvalues for the system as it stands without any control, or the eigenvalues of the "A" matrix. In this example, we find that the system has positive eigenvalues, casing it to be unstable, and there for a feedback controller is required. Now, using MatLab, the eigenvalues of the system may be changed to be anything. The image bellow demonstrates these steps.
