Planar linear systems with single saturated feedback

Suárez, Rodolfo; Álvarez, Jesús

doi:10.1016/0167-6911(93)90009-u

Cited by 33 publications

(35 citation statements)

References 9 publications

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“…In [1], it was shown that the boundary of S, denoted by @S, is a closed orbit, but no method to find this closed orbit is provided. Generally, only a subset of S lying between fx = 1 and fx = 01 is detected as a level set of some Lyapunov function (see, e.g., [5]).…”

Section: Results On the Null Controllable Regionmentioning

confidence: 99%

“…In this latter case, an important feature of the overall system is its hybrid continuous/discrete nature. It has been shown that when a LPTV system is controllable, the whole "monodromy matrix" is assignable by periodic feedback gains with sampled state or sampled output feedback [6], [1]. In [4], a further step has been taken by arguing that the characteristic exponents are all relocated with this feedback scheme.…”

Section: Joseph J Yamé and Raymond Hanusmentioning

confidence: 99%

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Practical stabilization of exponentially unstable linear systems subject to actuator saturation nonlinearity and disturbance

Lin

2001

Intl J Robust & Nonlinear

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Abstract-We study the problem of stabilizing exponentially unstable linear systems with saturating actuators. The study begins with planar systems with both poles exponentially unstable. For such a system, we show that the boundary of the domain of attraction under a saturated stabilizing linear state feedback is the unique stable limit cycle of its time-reversed system. A saturated linear state feedback is designed that results in a closed-loop system having a domain of attraction that is arbitrarily close to the null controllable region. This design is then utilized to construct state feedback laws for higher order systems with two exponentially unstable poles.Index Terms-Actuator saturation, domain of attraction, null controllable region, semiglobal stabilization.

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Section: Results On the Null Controllable Regionmentioning

confidence: 99%

Section: Joseph J Yamé and Raymond Hanusmentioning

confidence: 99%

Practical stabilization of exponentially unstable linear systems subject to actuator saturation nonlinearity and disturbance

Lin

2001

Intl J Robust & Nonlinear

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“…[7, Chapter 2] [8, Chapter 2] [9, Chapter 2]. Related literature on constrained planar systems include [10], [11].…”

Section: Introductionmentioning

confidence: 99%

Gradient Projection Anti-windup Scheme on Constrained Planar LTI Systems

Teo¹,

How²

2010

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Abstract-The gradient projection anti-windup (GPAW) scheme was recently proposed as an anti-windup method for nonlinear multi-input-multi-output systems/controllers, the solution of which was recognized as a largely open problem in a recent survey paper. This paper analyzes the properties of the GPAW scheme applied to an input constrained first order linear time invariant (LTI) system driven by a first order LTI controller, where the objective is to regulate the system state about the origin. We show that the GPAW compensated system is in fact a projected dynamical system (PDS), and use results in the PDS literature to assert existence and uniqueness of its solutions. The main result is that the GPAW scheme can only maintain/enlarge the exact region of attraction of the uncompensated system.

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“…the region in state space from which the closed-loop system asymptotically reaches the origin [1,5]) to the null controllable region (i.e. the region in state space where there exists an open-loop input that can steer the system to the origin [1,5,6,7]). In a former work [3] we considered a system with a single unstable pole and a single stable pole.…”

Section: Introductionmentioning

confidence: 99%

“…The aim is to use the reference controller proposed by [2] and to enlarge its region of attraction (i.e. the region in state space from which the closed-loop system asymptotically reaches the origin [1,5]) to the null controllable region (i.e. the region in state space where there exists an open-loop input that can steer the system to the origin [1,5,6,7]).…”

Section: Introductionmentioning

confidence: 99%

Improving the region of attraction of ITER in the presence of actuator saturation

Favez

Mulhaupt

Srinivasan

et al.

42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)

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The control of the ITER tokamak unstable vertical position is considered in the presence of actuator saturation. Linearised models of the ITER system all share the feature of a single unstable pole (attributable to the vertical instability) and a large number of stable poles. The aim of this work is to improve the existing controller in the sense of increasing the region of attraction while retaining the local performance around the origin. For second order systems with one unstable and one stable pole under saturated input, it has been shown that these requirements can be achieved using an additional nonlinear term in the existing linear control law. In this work, we discuss the extension to this nonlinear control law for higher order systems like the ITER tokamak. The validation of this new controller is done via simulations.

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Planar linear systems with single saturated feedback

Cited by 33 publications

References 9 publications

Practical stabilization of exponentially unstable linear systems subject to actuator saturation nonlinearity and disturbance

Practical stabilization of exponentially unstable linear systems subject to actuator saturation nonlinearity and disturbance

Gradient Projection Anti-windup Scheme on Constrained Planar LTI Systems

Improving the region of attraction of ITER in the presence of actuator saturation

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