INFT 940 -- Design Project #1

Simultaneous Stabilization of 3 Systems

INFT 940, Spring 1995.

  1. Shown below are the transfer functions representing three single-input, single-output systems. The overall objective is to determine a transfer function for a single compensator which will internally stabilize each of the three systems, while also satisfying specified performance requirements. The design procedure that you use to develop that compensator must follow the techniques discussed in this course.

  2. The final closed-loop systems must satisfy the following specifications:

    systems 1 and 3 must have steady-state errors for a step input of no more than 5%;

    systems 1 and 3 must have step response settling times, to within 2% of their final values, of no more than 10 seconds;

    systems 1 and 3 must have step response overshoots not exceeding 2%;

    system 2 must have all of its step response values lie in the range of -0.3 to +1.6;

    system 2 must have a step response settling time, to within an interval of ±0.05 about its final value, of no more than 60 seconds.

  3. Tasks:

    use the concepts of coprime factorization, strong stabilizability, etc. to analyze the simultaneous stabilizability of the three plants;

    use the coprime factorization approach to develop a compensator which will solve the simultaneous stabilization problem for the given three plant models;

    analyze the results of your design in terms of the performance specifications, modifying your compensator design as necessary;

    Document your efforts, including the following: (1) a description of your design and analysis procedures; a discussion of how your compensator design satisfies the simultaneous stabilization and performance requirements; and step response plots for the three closed-loop systems with the final compensator design; and (2) a discussion of what conditions would have to be satisfied by a parametrization of your compensator to generate all compensators which would guarantee simultaneous stabilization of all three of the given systems.

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Latest revision was made on 05/08/01 08:21 PM