Designed a PID controller and used different approaches to control and stabilize a Segway vehicle. Following are some of the steps that were taken to achieve this:
- The parameters which we wish to control are the tilt angle of the Segway "theta", and the linear velocity " x dot".
- First of all, the system was analyzed and was determined to be unstable.
- Using root locus and Routh's array, gain values were chosen and a PID controller was designed in an attempt to control the system.
- The response shows that the system was still unstable after the addition of the controller, which was restricted by a saturator.
- A high order compensator, with two zeros and two poles was designed and incorporated into the system to achieve stability. The poles, zeros and gain values were chosen using root locus analysis.
- As the images show, the response of theta and x dot become stable after adding the compensators, which gave the desired outcome and goal: stabilizing the system.
- The system was the rearranged in Simulink using state space representation to take advantage of Ackerman's algorithm in Matlab.
- The controllability and observability of the system was also determined.
- An observer was designed to predict the behavior of one state, with the knowledge of the data from the two other states.
- The predictions of the observer were almost identical to the actual response; in fact, it only took the observer less than one second to get back on track and correctly predict the behavior of the unknown state.