This chapter has introduced the design of PID position control, including elementary path planning. Both root locus and automated design methods have been explored. The main points are as follows:
Derivative compensation provides an additional degree of freedom to bend the root locus through the control design point, thereby achieving the transient response goal.
For many systems, a proportional-integral-derivative (PID) controller allows a design that meets the requirements for both overshoot and settling time, with zero steady-state error for a step input.
The root locus PID design method first establishes a design point based on the required transient response. The design proceeds in three steps: First, a proportional controller is designed to meet the percent overshoot requirement. Second, the position of the zero and the gain for a derivative controller are found. And third, the gain and zero for an integral controller are selected such that the already established transient response is not disrupted.
The choice of amplifier (voltage or current) determines the dynamic character of the DC motor model. Proportional-integral-derivative controller designs based on root locus methods are considered for both amplifiers.
The concept of automatic design of controllers was introduced. In this lab, we design a position controller for the DC motor powered by the current amplifier. The PID controller is designed using MATLAB's pidtune() tool, based on the motor/amplifier transfer function, and the desired closed-loop bandwidth.
A common task for a positioning system is to start from a stationary position, move to a new location, and then stop. In this lab, a path-planning algorithm is introduced that computes the reference input, as a function of time, applied to the closed-loop position control system. The motor/load moves to the new position in minimum time, subject to specified limits on the maximum acceleration and velocity, while avoiding discontinuities in the position slope.
The lab exercise organizes elements from previous chapters into a multithread program in which one thread exchanges set point and control parameters with the user, while the other thread seamlessly controls the motor/load position.