Research: Near Time Optimal Controllers with Integral Action

Motivation:

Efficient design of automatic control systems is extremely important for the performance of complex high technology systems and for their cost-effective development. To get the best cost-to-performance ratio one would like to be able to design a controller that takes full advantage of actuator capabilities, but this might lead to non-linear control due to actuator saturation. The saturation nonlinearities in the system may have severe effects on the system performance due, for example to integral-windup. The traditional approach to deal with saturation nonlinearities is to use a linear design technique for the unsaturated plant and then use ad-hoc modifications to overcome the effects of the saturation non-linearities. The disadvantage of this traditional approach is that one has no assurance that actuator capabilities are being used optimally and one does not know how much saturating can be tolerated before the behavior starts to deteriorate. Consequently time-consuming trial and error design might be necessary even for an experienced control engineer (see question posed in the ASME Dynamic Systems and Control Division newsletter).The motivation for this research is to come up with a simple design procedure that incorporates the actuator constraints directly in the design of a controller with integral action, and make sure that we take full advantage of actuator capabilities to achieve the desired behavior.

Purpose and scope

The purpose of the research is to come up with a simple design procedure for single-input single-output (SISO) linear systems that leads to a near time optimal controller with integral action by taking advantage of the saturation characteristics of the actuator. The design should take the following into account:

  • 1) Actuator limitations.
  • 2) Parameter uncertainty.
  • 3) Measurement noise.
  • 4) Disturbances.
  • 5) Unmodeled dynamics.
    To make the design easy, software should be developed that makes it possible for someone with limited experience in control design to use the design approach that has been developed. The software should also tell the control designer when criteria are impossible to meet and what needs to be changed in the system or in the specifications.

    • Design example: Position control of a DC Motor.

    DESIGN

    EXAMPLE

    		 Values used in the

    design procedure

    		 Values used in

    simulation
    M 1-1.5 1.4
    B 0.3-0.6 0.4
    Disturbance input 0.1-0.2 0.1
    Max actuator output 1 1
    Reference input 1 1
    Measurement noise for y and dy/dt 0.001/0.002 0.001/0.002

    Simulation result:

    Last update: March 20, 1997 by T. Larsson: tlarsson@engin.umich.edu.