State feedback ℋ∞-suboptimal control of arigid spacecraft

A state feedback ℋ_∞-suboptimal control problem on TSO(3) for a rigid spacecraft with three control torques and disturbances is addressed, the Hamilton-Jacobi inequality associated with a corresponding state feedback ℋ_∞-suboptimal control problem on TS³ is solved globally. The ℋ_∞-suboptimal state feedback on TS³ involves the Euler parameters and solves the original problem on TSO(3) when the initial values of the Euler parameters are appropriately chosen     

混合灵敏度问题的鲁棒H-/LTR设计方法

本文对具有输出乘型不确定性的Ｈ∞混合灵敏度问题进行了研究，提出了一种新的鲁棒Ｈ∞／ＬＴＲ设计方法。这种设计方法由三部分组成：首先针对偶系统设计一个Ｈ∞全状态反馈控制，使得系统满足性能和鲁棒性要求。其次设计一个全状态观测器，使得上述状态反馈的特性得以恢复，最后综合出满足原系统性能和鲁棒性要求的输出反馈动态控制律。     

l/sup /spl infin//-bounded robustness for nonlinear systems: analysis and synthesis

The purpose of this paper is to describe systematic analysis and design tools for robust control problems with l/sup /spl infin// criteria. We first generalize the Hill-Moylan-Willems framework for dissipative systems to accommodate l/sup /spl infin// criteria, and then derive state feedback and measurement feedback synthesis procedures for l/sup /spl infin// robust control problems. The information state framework is used for the measurement feedback robust control problem. Necessary and sufficient conditions are proved, and new synthesis procedures using dynamic programming are presented.     

State feedback performance recovery via an observer in H∞ robust control

The paper is concerned with H_∞ robust suboptimal control problem for linear time-invariant systems with structural uncertainties. The main result shows that if there exists a state feedback gain matrix which ensures H_∞robust suboptimally of the closed-loop system, then the robust performance achieved by the state feedback can be asymptotically recovered by a controller with high-gain observer.     

H∞ and positive-real control for linear neutraldelay systems

This note is concerned with the H_∞ and positive-real control problems for linear neutral delay systems. The purpose of H_∞ control is the design of a memoryless state feedback controller which stabilizes the neutral delay system and reduces the H_∞ norm of the closed-loop transfer function from the disturbance to the controlled output to a prescribed level, while the purpose of positive-real control is to design a memoryless state feedback controller such that the resulting closed-loop system is stable and the closed-loop transfer function is extended strictly positive real. Sufficient conditions for the existence of the desired controllers are given in terms of a linear matrix inequality (LMI). When this LMI is feasible, the expected memoryless state feedback controllers can be easily constructed via convex optimization     

Robust H∞ output feedback control for nonlinearsystems

In this paper we present a new approach to the solution of the output feedback robust H_∞ control problem. We employ the recently developed concept of information state for output feedback dynamic games and obtain necessary and sufficient conditions for the solution to the robust control problem expressed in terms of the information state. The resulting controller is an information state feedback controller and is intrinsically infinite dimensional. Stability results are obtained using the theory of dissipative systems, and our results are expressed in terms of dissipation inequalities     

H∞ state feedback control for discrete singularsystems

Deals with the problem of state feedback H_∞ control for discrete singular systems. It is not assumed that the singular system under consideration is necessarily regular. The problem we address is the design of a state feedback controller, such that the resulting closed-loop system is not only regular, causal, and stable, but also satisfies a prescribed H_∞-norm-bound condition. In terms of certain matrix inequalities, a necessary and sufficient condition for the solution to this problem is obtained, and a suitable state feedback-control law is also given     

Simultaneous H2/H∞ optimal control The state feedback case

A simultaneous H₂/H_∞ control problem is considered. This problem seeks to minimize the H₂ norm of a closed-loop transfer matrix while simultaneously satisfying a prescribed H_∞ norm bound on some other closed-loop transfer matrix by utilizing dynamic state feedback controllers. Such a problem was formulated earlier by Rotea and Khargonekar (Automatica, 27, 307–316, 1991) who considered only so called regular problems. Here, for a class of singular problems, necessary and sufficient conditions are established so that the posed simultaneous H₂/H_∞ problem is solvable by using state feedback controllers. The class of singular problems considered have a left invertible transfer function matrix from the control input to the controlled output which is used for the H₂ norm performance measure. This class of problems subsumes the class of regular problems.     

Optimal state feedback controller for three tank cylindrical interacting system using Grey Wolf Algorithm

This article presents, optimal state feedback controller for three tank cylindrical interacting system was proposed to maintain set point in the tank. Grey Wolf Optimization Algorithm used to describe the optimal tuning of state feedback controller. Generally, optimal state feedback controller reduces fluctuation state with lowest control energy. Gain of the optimal state feedback controller used to reduce the fluctuation state to minimum value. By adding integrator, the measured value of the tank moves towards set point. Linear quadratic regulator is a multivariable state feedback control and it depends on the state of the system. The controller performance enhanced by suitable range of Q and R value. The proposed technique uses heuristic algorithm for tuning the state feedback gain directly. The results show that the developed control technique given better performance.     

Disturbance attenuation andH^{∞}optimization: A design method based on the algebraic Riccati equation

This note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system. The problem under consideration involves attenuating the disturbances to a prespecified level. The construction of the state feedback control law requires the solution of a certain algebraic Riccati equation. By applying the procedure with successively smaller values of the prespecifled disturbance level, the result also provides an approach to theH^{infty}optimization problem for the state feedback case.     

Feedback controllers for a wind tunnel model involving a delay: Analytical design and numerical simulation

An application of a finite spectrum assignment method for time-delay systems to a feedback control of Mach number in a wind tunnel is presented. The linearized model of Mach number control is a system of three state equations with a delay in one of the state variables. The proposed feedback is a linear combination of state variables and weighted integrals of some of the state variables over a period equal to time delay. The spectrum of the closed-loop system is finite and consists of three eigenvalues that can be placed arbitrarily. Four possible variants of the feedback control law are presented. The calculation of feedback coefficients is very simple, which makes it possible to update the controller's parameters on-line with the changes of the operating point. An extensive numerical simulation of the system dynamics and the feedback controllers was done and led to several conclusions. In particular, a very good settling time under problem constraints has been obtained, and several nice features of the proposed feedback controller have been demonstrated.     

An H∞/MinMax periodic control in a two-dimensionalstructural acoustic model with piezoceramic actuators

A feedback control computational methodology for reducing acoustic sound pressure levels in a two-dimensional cavity with a flexible boundary (a beam) is investigated. The control is implemented in this model through voltages to piezoceramic patches on the beam which are excited in a manner (out-of-phase) so as to produce pure bending moments. The incorporation of the output feedback control in this system leads to a problem with unbounded input and output terms. By writing the resulting system as an abstract Cauchy equation, the problem of reducing interior pressure levels can be posed in the context of an H_∞ /MinMax time-domain state-space formulation. A summary of extensive computational efforts comparing output feedback to full state feedback and investigating the effect of the number and location of sensors on performance of the control is presented     

Robust H∞-output feedback control of decoupledautomobile active suspension systems

H^∞-output feedback control is applied to the control of automobile active suspensions based on a dynamic model of the full vehicle. The output feedback control is desirable from the viewpoint of implementation in the sense that it reduces the number of measurements drastically compared with state feedback used currently in suspension control. In this paper, the authors show that a linearized model can be block-decoupled by a similarity transformation, which reduces the controller complexity significantly. The uncertainties of the vehicle model are properly taken into account in the derivation of the H^∞ controller. The controller is actually implemented in a commercial car, and the performance is evaluated both by simulations and experiments. The performance obtained proves to be quite satisfactory     

Reduced-complexity nonlinear H/sup /spl infin// control of discrete-time systems

In this note, we describe a reduced-complexity solution to the nonlinear H/sup /spl infin// control problem. This reduction applies to systems where some of the states are perfectly known, and is an intermediate problem between full state feedback and the standard measurement feedback problem. The reduction of computational complexity is significant and of practical importance. Online implementation is feasible with 2003 computer technology for a range of practical engineering design problems.     

On the relation between state feedback and full informationregulators in nonlinear singular H∞ control

In this paper the relationship between state feedback control laws and full information control laws, i.e. control laws which make explicit use of the disturbance signals, is discussed in the framework of nonlinear singular H_∞ control. In particular, it is shown that any (polynomial) full information control law can always be approximated by a state feedback control law, provided that a certain (arbitrarily small) amount of performance is sacrificed. Moreover, the obtained result is used to give alternative proofs and generalizations to some existing results in the area of global disturbance attenuation for nonlinear systems and to establish some new and interesting results regarding the problem of approximate model matching     

H∞ control for more general nonlinear systems

The authors consider the standard H^∞-control problem for more general nonlinear systems modeled by equations in which the penalty output and the measured output are, in general, functions of the state, the exogenous input, and the control input. In particular, we characterize a family of H^∞ controllers via output feedback as well as state feedback, solving the problem. The results obtained generalize some recent results in the literature     

On the limit cycle stabilization of a DC/DC three-cell converter

This paper investigates a new state feedback controller design for DC/DC three-cell converter. The high dynamic performances of the converter have been translated into a desired limit cycle stabilization problem. The state feedback is established using hybrid automaton formalism, which allows us to design independently a transitory state and steady state control schemes. Finite-time convergence of the trajectory to the steady state and the local asymptotic stability of the desired limit cycle under the proposed controller are proved analytically. Simulation and experimental results confirm the theoretical results and show the effectiveness and robustness of the hybrid controller in spite of load variations.     

State and Mode Feedback Control for Discrete-time Markovian Jump Linear Systems With Controllable MTPM

In this note, the state and mode feedback control problems for a class of discrete-time Markovian jump linear systems (MJLSs) with controllable mode transition probability matrix (MTPM) are investigated. In most achievements, controller design of MJLSs pays more attention to state/output feedback control for stability, while the system cost in practice is out of consideration. In this paper, we propose a control mechanism consisting of two parts: finite-path-dependent state feedback controller design with which uniform stability of MJLSs can be ensured, and mode feedback control which aims to decrease system cost. Differing from the traditional state/output feedback controller design, the main novelty is that the proposed control mechanism not only guarantees system stability, but also decreases system cost effectively by adjusting the occurrence probability of system modes. The effectiveness of the proposed mechanism is illustrated via numerical examples.      

Internal behaviour provided by nonlinear l1-optimal controllers

An l₁-optimal linear time-invariant (LTI) compensator may have an order significantly higher than that of the plant, even when the state is measurable. Recently there has been work exploring the use of nonlinear static feedback controllers which provide near optimal performance. Here we consider a class of nonlinear state feedback controllers and derive superposition-like bounds on both the plant state and the controlled output in the event that the plant initial condition, the disturbance, and the noise are all non-zero.