Time-Domain Synthesis of Dual-Range Controller For Use With Nonlinear Systems
21 Jun 1989-pp 1734-1738
TL;DR: A new procedure for synthesis of dual-range linear controllers for use with nonlinear systems as well as linear systems with integrity is presented, which uses a factorization approach coupled with non linear optimization.
Abstract: In this paper we present a new procedure for synthesis of dual-range linear controllers for use with nonlinear systems as well as linear systems with integrity. The procedure uses a factorization approach coupled with nonlinear optimization. The procedure is demonstrated by solving an example problem.
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08 Oct 2007
TL;DR: In this paper, the authors focus on the problem of fault tolerant control for a Maglev suspension system based on simultaneous stabilization theory and propose a fault tolerant controller for highly nonlinear plants.
Abstract: This paper focuses on the problem of fault tolerant control for maglev suspension system based on simultaneous stabilization theory. Given two plants which are linear models of suspension system before and after the electromagnet failure respectively, we seek for a single compensator that stables both of them simultaneously. A systematic and simple linear control system design method for highly nonlinear plants is adopted. The simulation for the single magnet model shows that the designed fault tolerant controller has a better static and dynamic performance compared with a conventional PID controller. The method may provide valuable experience to the research on maglev suspension control system with more failures.
13 citations
TL;DR: The method of simultaneous stabilization is used to design a single linear compensator that stabilizes a servo valve with significant nonlinear dynamics and the minimum gas flow rate achievable is improved by a factor of five when compared to conventional PI control.
Abstract: The method of simultaneous stabilization is used to design a single linear compensator that stabilizes a servo valve with significant nonlinear dynamics. The servo valve is part of an automotive exhaust gas recirculation system. Linear models of the response of a servo valve at distinct operating points are developed using the actual hardware. A simultaneous stabilizing compensator (c/sub ss/) is designed based on these models and implemented as an analog controller. The performance of the compensator is compared to results previously achieved using a conventional PI control scheme. As a result of the c/sub ss/ control's ability to stabilize the plant for small valve openings, the minimum gas flow rate achievable is improved by a factor of five when compared to conventional PI control, and valve response at high flows does not deteriorate. Several techniques for applying the method of simultaneous stabilization to real problems are presented.
9 citations
Cites methods from "Time-Domain Synthesis of Dual-Range..."
...The method of simultaneous stabilization has been applied to the control of two discrete linear systems, specifically the use of the same propulsion system in two airframes [18] and has been used to develop a multirange controller for a simulation of a nonlinear robotic manipulator [ 191, [ 20 ]....
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References
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TL;DR: In this paper, the problem of simultaneously stabilizing l + 1 plants using a stable compensator is reduced to a purely algebraic problem, which can be expressed as follows: given a plant G, we would like to know whether or not there exists a single compensator C that stabilizes G ; if not, what is the smallest number of right half-place poles (counted according to their McMillan degree) that any stabilizing compensator must have?
Abstract: In this paper we study two problems in feedback stabilization. The first is the simultaneous stabilization problem, which can be stated as follows. Given plants G_{0}, G_{1},..., G_{l} , does there exist a single compensator C that stabilizes all of them? The second is that of stabilization by a stable compensator, or more generally, a "least unstable" compensator. Given a plant G , we would like to know whether or not there exists a stable compensator C that stabilizes G ; if not, what is the smallest number of right half-place poles (counted according to their McMillan degree) that any stabilizing compensator must have? We show that the two problems are equivalent in the following sense. The problem of simultaneously stabilizing l + 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator, which in turn can be stated as the following purely algebraic problem. Given 2l matrices A_{1}, ..., A_{l}, B_{1}, ..., B_{l} , where A_{i}, B_{i} are right-coprime for all i , does there exist a matrix M such that A_{i} + MB_{i} , is unimodular for all i? Conversely, the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l + 1 plants. The problem of determining whether or not there exists an M such that A + BM is unimodular, given a right-coprime pair ( A, B ), turns out to be a special case of a question concerning a matrix division algorithm in a proper Euclidean domain. We give an answer to this question, and we believe this result might be of some independent interest. We show that, given two n \times m plants G_{0} and G_{1} we can generically stabilize them simultaneously provided either n or m is greater than one. In contrast, simultaneous stabilizability, of two single-input-single-output plants, g 0 and g 1 , is not generic.
403 citations
22 Jun 1983
TL;DR: In this paper, the authors provide an overview of one school of thought in this area, typified by the following key ideas: 1. Quasilinear models of the nonlinear system that account for the operating range of system variables must be more realistic than conventional linear models. 2. The designer should be led to a nonlinear controller design if and only if it is really required.
Abstract: Recent research in the area of describing function approaches (both random-input and sinusoidal-input) has laid the foundation for a systematic approach to designing controllers for nonlinear plants. This paper provides an overview of one school of thought in this area, typified by the following key ideas: 1. Quasilinear models of the nonlinear system that account for the operating range of system variables must be more realistic than conventional linear models. 2. A staged design approach that applies more power to "difficult" nonlinear plants than to "easy" ones is more sensible than a single design method. 3. The designer should be led to a nonlinear controller design if and only if it is really required. These points will be developed, illustrated and justified in this presentation.
53 citations
TL;DR: In this article, a solution to the problem of simultaneously stabilizing m single-input-single-output (SISO) plants by one dynamic compensator with the constraint that each closed-loop system has the same characteristic polynomial is given.
Abstract: A solution is given to the problem of simultaneously stabilizing m single-input-single-output plants by one dynamic compensator with the constraint that each closed-loop system has the same characteristic polynomial.
42 citations
33 citations
06 Jun 1984
TL;DR: In this paper, the authors report on recent progress in developing nonlinear control system design techniques based on sinusoidal-input describing function (SIDF) methods and illustrate a fundamental difference between SIDF and RIDF models of nonlinear systems.
Abstract: In this paper, we report on recent progress in developing nonlinear control system design techniques based on sinusoidal-input describing function (SIDF) methods. Primarily, this involves illustrating a fundamental difference between SIDF and random-input describing function (RIDF) models of nonlinear systems, developing the nonlinear controller design method more fully, and demonstrating it by applying it to a significant nonlinear control design problem in robotics. Based on these results, the use of this nonlinear controller design method should be substantially better understood.
32 citations