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Control of multiplicative discrete-time systems

El-Bialy, Ahmed Mohamed
http://rave.ohiolink.edu/etdc/view?acc_num=case1055262732

Abstract Details

1990, Doctor of Philosophy, Case Western Reserve University, Systems and Control Engineering.
In this research, new nonlinear controllers are going to be designed, based upon a combination of a recently developed technique called exact linearization and both state space optimal as well as classical control methods. The exact linearization technique is used to transform the nonlinear control problem into a linear one, through a nonlinear feedback and a change in the state coordinates. In this study, we derive the discrete time exact linearization, prove the required necessary and sufficient conditions, for its application, and apply it to the class of multiplicative systems. We then propose a family of objective functions that, under the exact linearization technique, yield easily computed optimal laws. Both finite and infinite time horizon optimal nonlinear compensators result for the class of multiplicative systems under consideration. We also consider the application of the classical linear control methods for the linearized models. This results in methods for the design of relatively robust nonlinear compensators. We introduce another two applications for the exact linearization technique. First, we apply the technique to solve the nonlinear first conditions of optimality of the quadratic nonlinear control problem. Second, we investigate problems involving the control of the n onlinear systems subject to equality and inequality constraints. Finally, these results are applied to the control of electrically stimulated muscles. A discrete time model is used to simulate a double-muscle joint system. For this system all of the controller designs developed here are tested and compared (via computer simulations). The controllers are tested in trials with and without input and output simulated noise, as well as in trials having parameters variations. In these simulations we tested three types of controllers; a PID, a linearized quadratic and an open loop controller. The results of these simulations indicate that the linearized quadratic controllers are less sensitive to environmental noise than the others. On the other hand, the results of testing the use of incorrect parameters for the controller design show that the open loop controllers are best if parameter variations are small, while for large parameter variations the linearized quadratic controllers are better. (Abstract shortened with permission of author.
Howard Chizeck (Advisor)
150 p.
Control multiplicative discrete-time systems

Recommended Citations

Citations

  • El-Bialy, A. M. (1990). Control of multiplicative discrete-time systems [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1055262732

    APA Style (7th edition)

  • El-Bialy, Ahmed. Control of multiplicative discrete-time systems. 1990. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1055262732.

    MLA Style (8th edition)

  • El-Bialy, Ahmed. "Control of multiplicative discrete-time systems." Doctoral dissertation, Case Western Reserve University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=case1055262732

    Chicago Manual of Style (17th edition)

case1055262732
823
© 1990, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.