This section covers my work in the field of controls:
Design of state-space controller for inverted pendulum
The inverted pendulum is an excellent lab experiment to practice controller design. This is because the inverted pendulum is inherently unstable when no controller feedback is used, similar to what occurs when you try to balance a stick on your hand at arm’s length without moving. Shown below is the general setup for the problem, which I analyze using Ackerman’s state-space controller theory.
The equation to solve these matrices is shown below, followed by the alpha-d quadratic equation.
After setting up the problem, I used the Ackermann command in MATLAB to solve the equations to produce the necessary gain values. I then plugged the gain values into the experimental test stand and simulated the different initial pole values with their respective K values. The response of the experimental setup with respect to the K values is shown below. As seen in the data, the pole values have a marked effect on the settling time and the percent overshoot of the experimental setup. Also shown below are the pole values used.
Design of P, PD, and PID controller
To gain a better understanding of the types of controllers and their strengths and weakness, I subjected P, PD, and PID controllers of a frictionless cart to a step input. The FBD of this system is shown below, along with the motion of the cart that I derived through conservation of linear momentum and the transfer function that will be simulated.
The following Simulink diagram shows how the code will be implemented for P, PD, and PID control.
I developed MATLAB and Simulink programs to simulate this diagram. Below are the respective plots for each controller setup. The differences in steady-state error, settling time, peak time, and percent overshoot are clearly visible with the different types of controllers.
