Bifurcation control of rotating stall with actuator magnitude and rate limits: Part II—control synthesis and comparison with experiments

Yong, Wang; Yeung, S.; Murray, Richard M.

doi:10.1016/s0005-1098(01)00241-2

Cited by 15 publications

(15 citation statements)

References 8 publications

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“…In [10], it is required that β|c 1 + 3c 3 | < 1, c 1 − 9c 3 > 0 and β 2 (c 1 + 3c 3 )(c 1 − 9c 3 ) < 1. Thus Theorem 2 applies to (33) [4,9]. The following theorem shows that (33) has bifurcation stabilizability by dynamic output feedback for a general cubic characteristic curve.…”

Section: Control Of Rotating Stall In Axial Flow Compressorsmentioning

confidence: 87%

“…There are many types of bifurcations such as stationary bifurcation, Hopf bifurcation and other more complex bifurcation [1][2][3][4][5]. Wang et al further considered the control effects of the bifurcation phenomena with actuator saturation [8,9]. Many significant results have been obtained in the area of stabilization of stationary bifurcation.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we deal with stabilization of stationary bifurcation and its application to rotating stall control. In applications of bifurcation control, the stall phenomena and their bifurcation-related control in axial flow compressors have been extensively studied [8][9][10][11][12][13]. Abed and his team dealt with different bifurcations in nonlinear control systems [1,2], while Kang et al provided a way to analyze and control bifurcation based on normal form [6,7].…”

Section: Introductionmentioning

confidence: 99%

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Bifurcation stabilization of nonlinear systems by dynamic output feedback with application to rotating stall control

Chen

Qin

Wang

et al. 2011

Sci. China Inf. Sci.

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The paper deals with the problem of stabilization of stationary bifurcation solutions of nonlinear systems via dynamic output feedback. It is emphasized that the parameter of the system is not directly available. We introduce the concepts of uniform observability of the inverse of a function of state and input and N -orderinput-to-state bifurcation stability. Based on the concepts, we propose a new method for designing dynamic compensators that guarantee bifurcation stability for the closed-loop system. As an example, we apply the general theory to active control of rotating stall in axial flow compressors by designing a stabilizing dynamic compensator for the three-state Moore-Greitzer model with a class of cubic compressor characteristics. CitationChen P N, Qin H S, Wang Y, et al. Bifurcation stabilization of nonlinear systems by dynamic output feedback with application to rotating stall control. 201via a dynamic output feedback. Washout filters and high-pass filters were used in [16] for bifurcation stabilization of nonlinear systems via dynamic output feedback. The methods presented in [5,10,11,16] are applicable to dynamic output feedback bifurcation stabilization only in the case where the dimension of the dynamic compensator is known. However, in general, the dimension of the dynamic compensator cannot be determined a priori. Thus, the theory on bifurcation stabilization via dynamic output feedback is far from complete. Moreover, even in the rotating stall control, the output feedback design for the compressor system with pressure rise as output measurement is still a challenging problem [10,11]. In the cases where some state variables are not measurable, output feedback control design of nonlinear systems becomes necessary and has been studied in different ways [17,18]. Center manifold and normal form theory provides an effective method for both nonlinear control and bifurcation analysis [19,20]. In the output feedback control design related to center manifold, two concepts of the approximation stability [18,21] and uniform observability [17,18] have often been used.In this paper, we propose a new method for dynamic output feedback stabilization of stationary bifurcation. Here the bifurcation parameters of the system are not available, and it is difficult to make conventional uniform observability of an input function and approximation stability applicable in this case. To deal with the difficulties, two generalized concepts are proposed. One is uniform observability of the inverse of a function of state and input as a generalization of uniform observability of a function of state, and the other is N -order-input-to-state bifurcation stability as an extension of approximation stability. Based on these two concepts, we provide an explicit procedure of constructing an dynamic compensator for bifurcation stabilization. As an application, we construct a dynamic compensator for the Moore-Greitzer model in active control of rotating stall for general cubic compressor characteristic curves with pressure-rise as ...

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Section: Control Of Rotating Stall In Axial Flow Compressorsmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bifurcation stabilization of nonlinear systems by dynamic output feedback with application to rotating stall control

Chen

Qin

Wang

et al. 2011

Sci. China Inf. Sci.

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“…Based on the above result, in our examples we will use LQR gains for v 1 designed based on the linear dynamics (26). Nevertheless different selections for K aw in (24), and of v 1 in general, aimed at inducing large stability regions and extreme performance from a nonlinear viewpoint in (25b) constitute an open research problem.…”

Section: Almost Anti-windup With Magnitude Rate and Curvature Samentioning

confidence: 99%

“…This context is especially relevant in a number of applications, including flight control, control of Tokamak plasmas with superconducting coils and many others where the request to the actuators is not allowed to change too fast (see, e.g., [4], [5], [26], [18], [19]). Anti-windup approaches for magnitude+rate saturated plants have been given in [27] and [25] where a plant-order and a static compensation scheme, respectively, are proposed and in [9] (further extended in [8]), where a static solution is given.…”

Section: Introductionmentioning

confidence: 99%

An almost Anti-Windup scheme for plants with magnitude, rate and curvature saturation

Forni

Galeani

Zaccarian

2010

Proceedings of the 2010 American Control Conference

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Abstract-We address the anti-windup augmentation problem for plants with saturations on the magnitude, rate and curvature of the control input. To this aim, given an unconstrained closed-loop, we generate a slightly modified strictly proper controller for which the derivatives of the control signal are available and we solve the anti-windup problem for this modified control scheme (namely, an almost anti-windup for the original closed-loop). Based on this "almost" approach, we revisit an existing Model Recovery anti-windup solution for rate and magnitude saturated plants and then we extend the results to the case of rate, magnitude and curvature saturation, by providing a Model Recovery solution to this additional problem. Several examples are used to illustrate the peculiarities and the effectiveness of the proposed solutions.

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Feedback stabilization of bifurcations in multivariable nonlinear systems—Part I: equilibrium bifurcations

Wang

Murray

2006

Intl J Robust & Nonlinear

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SUMMARYUnder certain non-degeneracy conditions, necessary and sufficient conditions for stabilizability are obtained for multi-input nonlinear systems possessing a simple equilibrium bifurcation with the critical mode being linearly uncontrollable. Stabilizability is defined as the existence of a sufficiently smooth state feedback such that the bifurcation of the closed-loop system is a supercritical pitchfork bifurcation, which is equivalent to local asymptotic stability of the system at the bifurcation point. Stabilizability is reduced to the existence of solutions to a third order algebraic inequality, coupled with a quadratic algebraic equation, with the unknowns being the feedback gains. Explicit conditions for the existence of solutions to the algebraic equation and the inequality are derived. Part of the sufficient conditions are equivalent to the rank conditions of augmented matrices. Conditions under which there exists a stabilizing linear feedback law are also derived. The theoretical results are applied to active control of rotating stall in axial compressors using bleed valve as actuator.

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Bifurcation control of rotating stall with actuator magnitude and rate limits: Part II—control synthesis and comparison with experiments

Cited by 15 publications

References 8 publications

Bifurcation stabilization of nonlinear systems by dynamic output feedback with application to rotating stall control

Bifurcation stabilization of nonlinear systems by dynamic output feedback with application to rotating stall control

An almost Anti-Windup scheme for plants with magnitude, rate and curvature saturation

Feedback stabilization of bifurcations in multivariable nonlinear systems—Part I: equilibrium bifurcations

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