State Feedback Controller Design Method Research Articles

The design of nonovershooting and nonundershooting multivariable state feedback tracking controllers

We consider the use of linear multivariable feedback control to achieve a nonovershooting and nonundershooting step response. Recently, Schmid and Ntogramatzidis (2010) [13] introduced a linear state feedback controller design method to avoid overshoot. In this paper, we describe conditions under which the design method may be modified to avoid undershoot. The method is applicable to square and nonsquare systems, minimum and nonminimum phase systems, and also strictly proper and bi-proper systems.

Fuzzy Non-fragile H∞ Tracking Control for Flexible Air-breathing Hypersonic Vehicles

This paper proposed a fuzzy non-fragile tracking control design method for flexible air-breathing hypersonic vehicles (FAHVs). The T-S fuzzy set approach is applied to the modeling of the complex nonlinear dynamics of FAHVs, and a T-S fuzzy model is constructed, which can represent the nonlinear hypersonic vehicle system. Then, by considering the actuator controller coefficients uncertainties and disturbances, the fuzzy non-fragile H∞ tracking problem for FAHVs is proposed. A state-feedback controller design method is proposed to guarantee the tracking performance in the presence of actuator controller coefficients uncertainties. By a Lyapunov approach, the existence conditions for such a controller are established in terms of linear matrix inequalities (LMIs). An illustrative example is given to show the excellent tracking performance of the proposed controller design method.

Robust Controller Design for Sinusoidal PWM Inverters

This paper proposes a robust controller for sinusoidal PWM inverters, which can track a sinusoidal reference with zero steady-state error. A closed-loop system for single-phase full-bridge inverters is constructed on the basis of the internal model principle. The appropriate control gains of the constructed closed-loop system are determined using a state-feedback controller design method via linear matrix inequalities. The proposed controller can adapt to the uncertain variations in the load conditions. It is also shown that the pole-placement constraints and control performance indexes based on the H2 and H∞ norms as well as a standard quadric performance index in optimal control can be applied to the proposed robust controller. Digital computer simulation is implemented to confirm the validity of the proposed robust controller with the internal model principle. A prototype experimental model is constructed and tested. Experimental results demonstrate that an excellent and practical robust controller for sinusoidal PWM inverters is realized under uncertain and fluctuating load conditions, including the nonlinear loads such as diode rectifiers.

An impulse control approach to spacecraft autonomous rendezvous based on genetic algorithms

This paper proposes a novel approach to spacecraft impulse autonomous rendezvous by using genetic algorithms. Based on the Clohessy–Wiltshire (C–W) equations, the whole rendezvous process is described as a switching system composed of closed-loop system and open-loop system, which correspond to the impulse action phase and free motion phase during the rendezvous process. Based on Lyapunov theory, the autonomous rendezvous problem is regarded as an asymptotic stabilization problem. By introducing two virtual energy functions, the stability of the switching system is analyzed, and the duration of the impulse action and the thrust limitation are considered synthetically. Then, a state-feedback controller design method is proposed, and an approach based on linear matrix inequality and genetic algorithm (GA) is proposed to solve the controller design problem and the calculation steps are presented. With the designed controller, the impulse thrust which satisfies the given thrust constraint is determined according to the real-time relative state between two spacecraft at the impulse instant, and the impulse duration is kept as short as possible. The effectiveness of the proposed approach is illustrated by simulation examples.

Nonundershooting linear multivariable tracking controllers

AbstractWe consider the use of linear multivariable state feedback control to achieve a nonundershooting step response. The recently introduced nonovershooting linear state feedback controller design method of Schmid and Ntogramatzidis (2010) is here modified to yield a step response that is nonundershooting. The design method is applicable to square and non-square systems, minimum and nonminimum phase systems, and also strictly proper and bi-proper systems.

Delay-dependent robust control for discrete-time uncertain singular systems with interval time-varying delays in state and control input

Abstract The problem of the delay-dependent robust H ∞ controller design for discrete-time uncertain singular systems with interval time-varying delays in state and control input is investigated in this paper. A new delay-dependent bounded real lemma for singular systems with interval time-varying delays is derived and expressed in terms of LMI. Based on the result, the controller existence condition and robust H ∞ state feedback controller design method are proposed by linear matrix inequality (LMI) approach without any decompositions of system matrices and equivalent transformation. Also, the resulting criterion is extended to delayed discrete-time singular systems with polytopic uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

Robust H ∞ control for a class of uncertain mechanical systems

In this article, the problem of H ∞ control is investigated for a class of mechanical systems with input delay and parameter uncertainties which appear in all the mass, damping and stiffness matrices. Two approaches, norm-bounded and linear fractional transformation (LFT) uncertainty formulations, are considered. By using a new Lyapunov–Krasovskii functional approach, combined with the advanced techniques for achieving delay dependence, improved robust H ∞ state-feedback controller design methods are developed. The existence condition for admissible controllers is formulated in the form of linear matrix inequalities (LMIs), and the controller design is cast into a convex optimisation problem subject to LMI constraints. If the optimisation problem is solvable, a desired controller can be readily constructed. The result for the norm-bounded uncertainty case improves the existing ones in terms of design conservatism, and that for the LFT uncertainty case represents the first attempt in this direction. An illustrative example is provided to show the effectiveness and advantage of the proposed controller design methodologies.

LPV Controller Design for Robot Manipulators Based on Augmented LMI Conditions with Structural Constraints

This paper addresses the Linear Parameter Varying (LPV) control of robot manipulators. The dynamical model of such mechanical systems, obtained by writing the Euler-Lagrange equations, is nonlinear. Based on the measured signals and some change of variables, the nonlinear model can lead to an equivalent LPV state-space representation of the system. In this paper, we present a design method of state-feedback and output-feedback LPV controllers for robot manipulators. This method uses structured parameter-dependent Lyapunov matrices and proposes augmented Linear Matrix Inequalities (LMI) conditions with structural constraints. These design conditions are given as a finite number of LMIs. The validity of the proposed approach is demonstrated through simulations.

A simple state feedback controller design method of networked control systems with time delay and packet dropout

This paper presents a simple yet effective method to design state feedback controller for networked control systems (NCSs). By introducing the lifting technique into NCSs and by considering the balance between effectiveness and simplicity, a novel discrete-time switch model is proposed with the consideration of time delay and packet dropout during the transmission of packets. In terms of the given model, we give sufficient conditions for the existence of state feedback controller such that the closed-loop NCSs are asymptotically stable. Based on the obtained stability conditions, a homotopy-based iterative LMI algorithm is developed to get the state feedback gain. Simulation and experimental results are given to demonstrate the effectiveness of the proposed approaches.

Improved stabilisation method for networked control systems

The controller design problem for networked control systems (NCSs) is investigated. By considering the relationship between the network-reduced delay and its upper bound, an improved stability criterion for networked closed-loop system is proposed without ignoring any terms in the derivative of Lyapunov–Krasovskii function. As a result, a state feedback controller design method is established using a modified cone complementary linearisation (CCL) algorithm with a new stopping condition. A numerical example is given to demonstrate the effectiveness and the benefits of the proposed method.

Stabilization of switched linear systems with time-delay in detection of switching signal

A feedback stabilization problem for switched linear systems with time-delay in detection of switching signal is formulated. First, online state feedback controller design method for asymptotic stability and exponential stability is given. Then, offline state feedback controller design method for asymptotic stability and exponential stability is given as well.

Controller Design for Linear Discrete-Time System with Band-Bounded Nonlinear Actuators and Additive Measurement Noise

A state feedback controller design method is proposed for linear discrete-time systems driven by actuators with certain types of nonlinearities. Bounded additive noises are assumed to exist when the state variables are measured for feedback. The controller is required to bring and confine all state trajectories to an ultimate boundedness region. The trade-off between getting a small ultimate boundedness region and tolerating large noises is formulated as an optimization problem under the framework of the linear matrix inequality approach.

H∞ state feedback control for generalized continuous/discrete time-delay system

In this paper, we consider the problem of designing H ∞ state feedback controller for the generalized time-delay systems with delayed states and control inputs in continuous and discrete time cases, respectively. The generalized time-delay system problems are solved on the basis of linear matrix inequality (LMI) technique considering time delays. The sufficient condition for the existence of controller and H ∞ state feedback controller design methods are presented. Also, using some changes of variables and Schur complements, the obtained sufficient condition can be rewritten as an LMI form in terms of transformed variables. The proposed controller design method can be extended into the problem of robust H ∞ state feedback controller design method easily.

Decentralized control of large flexible structures by joint decoupling

A decentralized control design method is presented for large complex flexible structures by using the idea of joint decoupling. The derivation is based on a coupled substructure state-space model, which is obtained from enforcing conditions of interface compatibility and equilibrium to the substructure state-space models. It is shown that by restricting the control law to be localized state feedback and by setting the joint actuator input commands to decouple joint 'degrees of freedom' (dof) from interior dof, the global structure control design problem can be decomposed into several substructure control design problems. The substructure control gains and substructure observers are designed based on modified substructure state-space models. The controllers produced by the proposed method can operate successfully at the individual substructure level as well as at the global structure level. Therefore, not only control design but also control implementation is decentralized. Stability and performance requirement of the closed-loop system can be achieved by using any existing state feedback control design method. A two-component mass-spring damper system and a three-truss structure are used as examples to demonstrate the proposed method.

Stability robustness bounds for discrete-time linear regulators

Stability robustness analysis and design for linear multivariable discrete-time systems with bounded uncertainties are discussed. Robust stability of the full-state feedback linear quadratic (LQ) regulator in the presence of perturbations (modelling errors) of the system matrices is investigated. These results are based on a recently developed bound on elemental (structured) time-varying perturbations of an asymptotically stable linear time-invariant discrete-time system. Lyapunov theory and singular value decomposition techniques are employed in deriving these bounds. Extensions of these results to linear stochastic systems with the Kalman filter as the stale estimator (LQG regulators) and to reduced-order dynamic compensator feedback are described. A state feedback control design method is presented for LQ regulators, using a quantitative measure called the Stability Robustness Index. Simple examples illustrate these new results.

State-feedback control of non-linear systems†

A design method for state-feedback controllers for single-input non-linear systems is proposed. The method makes use of the transformations of the non-linear system into ‘controllable-like’ canonical forms. The resulting non-linear state feedback is designed in such a way that the eigenvalues of the linearized closed-loop model are invariant with respect to any constant operating point. The method constitutes an alternative approach to the design methodology recently proposed by Baumann and Rugh. Also a review of different transformation methods for non-linear systems is presented. An example and simulation results of different control strategies are provided to illustrate the design technique.