Home About us Contact
|
Home About us Contact | ||
|
|
||
Feedback Law (feedback + law)
Selected AbstractsDiscontinuous feedbacks, discontinuous optimal controls, and continuous-time model predictive controlINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 3-4 2003Fernando A. C. C. Fontes Abstract It is known that there is a class of nonlinear systems that cannot be stabilized by a continuous time-invariant feedback. This class includes systems with interest in practice, such as nonholonomic systems, frequently appearing in robotics and other areas. Yet, most continuous-time model predictive control (MPC) frameworks had to assume continuity of the resulting feedback law, being unable to address an important class of nonlinear systems. It is also known that the open-loop optimal control problems that are solved in MPC algorithms may not have, in general, a continuous solution. Again, most continuous-time MPC frameworks had to artificially assume continuity of the optimal controls or, alternatively, impose some demanding assumptions on the data of the optimal control problem to achieve the desired continuity. In this work we analyse the reasons why traditional MPC approaches had to impose the continuity assumptions, the difficulties in relaxing these assumptions, and how the concept of ,sampling feedbacks' combines naturally with MPC to overcome these difficulties. A continuous-time MPC framework using a strictly positive inter-sampling time is argued to be appropriate to use with discontinuous optimal controls and discontinuous feedbacks. The essential features for the stability of such MPC framework are reviewed. Copyright © 2003 John Wiley & Sons, Ltd. [source] Practical stabilization of exponentially unstable linear systems subject to actuator saturation nonlinearity and disturbanceINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2001Tingshu Hu Abstract This paper investigates the problem of practical stabilization for linear systems subject to actuator saturation and input additive disturbance. Attention is restricted to systems with two anti-stable modes. For such a system, a family of linear feedback laws is constructed that achieves semi-global practical stabilization on the asymptotically null controllable region. This is in the sense that, for any set ,0 in the interior of the asymptotically null controllable region, any (arbitrarily small) set ,, containing the origin in its interior, and any (arbitrarily large) bound on the disturbance, there is a feedback law from the family such that any trajectory of the closed-loop system enters and remains in the set ,, in a finite time as long as it starts from the set ,0. In proving the main results, the continuity and monotonicity of the domain of attraction for a class of second-order systems are revealed. Copyright © 2001 John Wiley & Sons, Ltd. [source] Virtual passive control of flexible arms with collocated and noncollocated feedbackJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 11 2001Shang-Teh Wu A novel approach to the control of flexible manipulators is proposed. The controller includes both joint-variable and tip-deflection feedback. It is shown that tip-deflection feedback transforms the original structure into new system in which the structure parameters are virtually scaled up or down. The new system can hence be easily stabilized via a strictly passive feedback law. A co-hub, lumped-parameter structure with multiple massless links is first investigated and stability conditions are developed. The results are then applied to a distributed-parameter flexible arm, which is decomposed into an equivalent lumped-parameter structure via a set of modal functions normalized in a particular way. Tip-deflection feedback is shown to be capable of enhancing control performance on a flexible arm, and stability is ensured as long as the gain associated with the noncollocated feedback satisfies a simple inequality. The stability criteria re valid independent of high-order flexible modes. © 2001 John Wiley & Sons, Inc. [source] Optimal control of non-linear chemical reactors via an initial-value Hamiltonian problemOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 1 2006V. Costanza Abstract The problem of designing strategies for optimal feedback control of non-linear processes, specially for regulation and set-point changing, is attacked in this paper. A novel procedure based on the Hamiltonian equations associated to a bilinear approximation of the dynamics and a quadratic cost is presented. The usual boundary-value situation for the coupled state,costate system is transformed into an initial-value problem through the solution of a generalized algebraic Riccati equation. This allows to integrate the Hamiltonian equations on-line, and to construct the feedback law by using the costate solution trajectory. Results are shown applied to a classical non-linear chemical reactor model, and compared against suboptimal bilinear-quadratic strategies based on power series expansions. Since state variables calculated from Hamiltonian equations may differ from the values of physical states, the proposed control strategy is suboptimal with respect to the original plant. Copyright © 2005 John Wiley & Sons, Ltd. [source] State and output feedback design for robust tracking of linear systems with rate limited actuatorsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 1 2002Zongli Lin Abstract A design technique (Control of Uncertain Systems with Bounded Inputs, Tarbouriech S, Garcia G, (Eds), Lecture Notes in Control and Information Sciences, vol. 227, Springer: Berlin, 1997; 173,186) recently proposed for stabilization of a linear system with rate-limited actuators is utilized to design feedback laws that cause the system output to track a desired command signal. This design technique combines two design techniques recently developed for linear systems with position limited actuators, piecewise-linear LQ control (Automatica, 1994; 30: 403,416) and low-and-high gain feedback (IEEE Trans. Automat. Control, 1996; 41: 368,378), and hence takes advantage of both design techniques, while avoiding their disadvantages. In the case that only the output is available for feedback, the performance of the state feedback law is preserved by the use of a fast observer. An open-loop exponentially unstable fighter aircraft is used to demonstrate the effectiveness of the proposed control design method. Copyright © 2002 John Wiley & Sons, Ltd. [source] Properties of parameter-dependent open-loop MPC for uncertain systems with polytopic description,ASIAN JOURNAL OF CONTROL, Issue 1 2010Baocang Ding Abstract This paper investigates the parameter-dependent open-loop model predictive control (PDOLMPC) scheme for systems with a polytopic uncertainty description. PDOLMPC parameterizes the infinite horizon control moves into a number of free control moves followed by a single state feedback law. The free control moves (excluding the first one) are parameter dependent and constructed upon all of the extreme realizations of the uncertainty before the switching horizon N. Our primary contribution is to point out that this PDOLMPC is a relaxed version of the feedback MPC. Thus, some properties of nominal MPC, such as enhancement of optimality and enlargement of region of attraction by increasing the switching horizon, can be inherited in PDOLMPC. These properties are theoretically important for robust MPC and a simulation example is given for demonstration. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Feedback stabilization of bifurcations in multivariable nonlinear systems,Part II: Hopf bifurcationsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 4 2007Yong Wang Abstract In this paper we derive necessary and sufficient conditions of stabilizability for multi-input nonlinear systems possessing a Hopf bifurcation with the critical mode being linearly uncontrollable, under the non-degeneracy assumption that stability can be determined by the third order term in the normal form of the dynamics on the centre manifold. Stabilizability is defined as the existence of a sufficiently smooth state feedback such that the Hopf bifurcation of the closed-loop system is supercritical, which is equivalent to local asymptotic stability of the system at the bifurcation point. We prove that under the non-degeneracy conditions, stabilizability is equivalent to the existence of solutions to a third order algebraic inequality of the feedback gains. Explicit conditions for the existence of solutions to the algebraic inequality are derived, and the stabilizing feedback laws are constructed. Part of the sufficient conditions are equivalent to the rank conditions of an augmented matrix which is a generalization of the Popov,Belevitch,Hautus (PBH) rank test of controllability for linear time invariant (LTI) systems. We also apply our theory to feedback control of rotating stall in axial compression systems using bleed valve as actuators. Copyright © 2006 John Wiley & Sons, Ltd. [source] Practical stabilization of exponentially unstable linear systems subject to actuator saturation nonlinearity and disturbanceINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2001Tingshu Hu Abstract This paper investigates the problem of practical stabilization for linear systems subject to actuator saturation and input additive disturbance. Attention is restricted to systems with two anti-stable modes. For such a system, a family of linear feedback laws is constructed that achieves semi-global practical stabilization on the asymptotically null controllable region. This is in the sense that, for any set ,0 in the interior of the asymptotically null controllable region, any (arbitrarily small) set ,, containing the origin in its interior, and any (arbitrarily large) bound on the disturbance, there is a feedback law from the family such that any trajectory of the closed-loop system enters and remains in the set ,, in a finite time as long as it starts from the set ,0. In proving the main results, the continuity and monotonicity of the domain of attraction for a class of second-order systems are revealed. Copyright © 2001 John Wiley & Sons, Ltd. [source] State and output feedback design for robust tracking of linear systems with rate limited actuatorsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 1 2002Zongli Lin Abstract A design technique (Control of Uncertain Systems with Bounded Inputs, Tarbouriech S, Garcia G, (Eds), Lecture Notes in Control and Information Sciences, vol. 227, Springer: Berlin, 1997; 173,186) recently proposed for stabilization of a linear system with rate-limited actuators is utilized to design feedback laws that cause the system output to track a desired command signal. This design technique combines two design techniques recently developed for linear systems with position limited actuators, piecewise-linear LQ control (Automatica, 1994; 30: 403,416) and low-and-high gain feedback (IEEE Trans. Automat. Control, 1996; 41: 368,378), and hence takes advantage of both design techniques, while avoiding their disadvantages. In the case that only the output is available for feedback, the performance of the state feedback law is preserved by the use of a fast observer. An open-loop exponentially unstable fighter aircraft is used to demonstrate the effectiveness of the proposed control design method. Copyright © 2002 John Wiley & Sons, Ltd. [source] Stabilization of uncertain chained nonholonomic systems using adaptive output feedback,ASIAN JOURNAL OF CONTROL, Issue 6 2009Z. P. Yuan Abstract In this paper, adaptive output feedback control is presented to solve the stabilization problem of nonholonomic systems in chained form with strong nonlinear drifts and uncertain parameters using output signals only. The objective is to design adaptive nonlinear output feedback laws which can steer the closed-loop systems to globally converge to the origin, while the estimated parameters remain bounded. The proposed systematic strategy combines input-state scaling with backstepping technique. Motivated from a special case, adaptive output feedback controllers are proposed for a class of uncertain chained systems. The simulation results demonstrate the effectiveness of the proposed controllers. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] | ||||||||||