The observer-based controller design of discrete-time singularly perturbed systems

Oloomi, Hossein M.; Sawan, M.E.

doi:10.1109/tac.1987.1104565

Cited by 40 publications

(12 citation statements)

References 8 publications

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“…Using typical discretization techniques, the linear shiftinvariant discrete-time singularly perturbed system can be ex pressed in a fast time scale as (1982) and Oloomi and Sawan (1987). The robustness of output feedback control to unmodelled dynamics was studied by Esfandiari and Khalil (1989).…”

Section: Robustness Analysismentioning

confidence: 99%

“…The stability issue of singularly perturbed systems has been extensively investigated i~the literature (Kokotovic and Khalil 1986). Recently there has great interest in discussing robust stability of the control of multiple-timescale continuous systems (Khalil 1981, O'Reilly 1986, Vidyasagar 1985 and discrete systems (Esfandiari and Khalil 1989, Litkouhi and Khalil 1985, Mahmoud 1982, Mahmoud 1985, Oloomi and Sawan 1987. For the discrete-time case, general discussions for stability of observer-based control were considered by Mahmoud …”

Section: Robustness Analysismentioning

confidence: 99%

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Stabilizing control of discrete-time singularly perturbed systems

Lin

1996

International Journal of Systems Science

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Section: Robustness Analysismentioning

confidence: 99%

Section: Robustness Analysismentioning

confidence: 99%

Stabilizing control of discrete-time singularly perturbed systems

Lin

1996

International Journal of Systems Science

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“…The proposed controller is a 'Department of Engineering t Department of Electrical Engineering Technology two-timescale observer based controller and is based on the theory of singular perturbation [5]. In comparison to the PID and fuzzy controllers, we believe that the new controller is advantageous with respect to the following considerations.…”

Section: Ntroductionmentioning

confidence: 99%

“…Thus, using the results of [5], the controller and observer gains for the overall system are found to be G = [ 120.2707 19.808 0.8 1 ,…”

Section: Two Time Scale Observer Controller Designmentioning

confidence: 99%

“…The phenomenon of producing an unstable fast design stems from the fact that the singularly perturbed sampled data model in [5] always produces the poles of the fast subsystem outside of a circle of radius O(1) centered at the point z = 1. Therefore, it is never guaranteed aprzorz that the fast poles will be placed near the origin or even inside the unit disk in the z-plane unless the sampling is sufficiently small.…”

Section: Two Time Scale Observer Controller Designmentioning

confidence: 99%

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Two-time-scale digital controller design for a position servo system

Oloomi

Lin

Proceedings IEEE Conference on Industrial Automation and Control Emerging Technology Applications

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A b s t r a c tIn this paper we propose a new digital controller for a position servo system. 'The controller is an observerbased controller which takes advantage of the twotime-scale structure of the motor. Only some knowledge, of the mechanical and electrical time constants, and not a detailed mathematical model or exact parameter values, are required t o implement the controller and that the closed loop system performance specifications can be met reasonably well under the lack of detailed modeling. The transient mismatch phenomenon which occurs for this class of designs is fully discussed and a sufficient condition is obtained to guarantee that such a mismatch will not occur. 1NTR.ODUCTIONPosition servo systems have been used extensively throughout the industry [l], [2]. A position servo system is a feedback system whose primary objective is to keep the angular displacement of the shaft, or more often a mechanical load driven by the motor, within an acceptable range of a given set point. PI, PD, and PID controllers have been the most popular controllers for this class of applications. Simplicity of the hardware and the tuning procedures have been among the key factors for making these controllers popular.To cope with the problem of parameter variation and model uncertainty, several authors have proposed fuzzy logic controllers for the position servo systems and have drawn comparison between the performance of these controllers and the more traditional PI, PD, and PID controllers [3],[4]. It has been claimed that a fuzzy controller can out-perform a digitally tuned PID controller [4].In this paper we propose yet another controller for the position servo system. The proposed controller is a 'Department of Engineering t Department of Electrical Engineering Technology two-timescale observer based controller and is based on the theory of singular perturbation [5]. In comparison to the PID and fuzzy controllers, we believe that the new controller is advantageous with respect to the following considerations.1. The proposed controller operates on the basis of the full state variables and not just the position measurements as is the case for the PID and fuzzy controllers. However, only one additional potentiometer is needed to acquire the armature current. Since state variables are reconstructed by the use of the observer, accuracy of these measurements are not as crucial in comparison to other design methods. Reconstructing the full set of the states provides additional flexibility in monitoring armature current and angular velocity without requiring a tachometer.2. The problem of high dimensionality associated with the use of the observer is resolved by incorporating the two-timescale structure that is inherited in the system. That is, while the use of the observer increases the dimension of the system from three to six, exploiting the two-timescale structure of the system allows the system to be separated into two lower dimensional subsystems, one with the dimension of four and one with the dimension of two. Thus, ...

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Nonlinear observer design for two‐time‐scale systems

Duan

Kravaris

2020

AIChE Journal

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A two-time-scale system involves both fast and slow dynamics. This article studies observer design for general nonlinear two-time-scale systems and presents two alternative nonlinear observer design approaches, one full-order and one reduced-order.The full-order observer is designed by following a scheme to systematically select design parameters, so that the fast and slow observer dynamics are assigned to estimate the corresponding system modes. The reduced-order observer is derived based on a lower dimensional model to reconstruct the slow states, along with the algebraic slow-motion invariant manifold function to reconstruct the fast states. Through an error analysis, it is shown that the reduced-order observer is capable of providing accurate estimation of the states for the detailed system with an exponentially decaying estimation error. In the last part of the article, the two proposed observers are designed for an anaerobic digestion process, as an illustrative example to evaluate their performance and convergence properties.

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The observer-based controller design of discrete-time singularly perturbed systems

Cited by 40 publications

References 8 publications

Stabilizing control of discrete-time singularly perturbed systems

Stabilizing control of discrete-time singularly perturbed systems

Two-time-scale digital controller design for a position servo system

Nonlinear observer design for two‐time‐scale systems

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