Static Output Feedback Controller Design Research Articles

Fault-Tolerant Controller Design for Uncertain Networked Control Systems Based on Static Output Feedback

The problem studied the robust fault-tolerant controller design for the uncertain networked control system, The considered system has actuator and sensor failures. Under the non-ideal network conditions such as time-delay, data packet dropout and mis-sequence, a model of the networked control systems is provided, The robust stability conditions are obtained in the situation of actuator and sensor failures based on Lyapunov Krsasovkii functional method and static output feedback by introducing some free-weighing matrices, Based on this sufficient condition, the static output feedback controller design method is deduced in terms of linear matrix inequalities. An illustrative example shows the effectiveness and feasibility of proposed method.

Robust static output‐feedback controller design against sensor failure for vehicle dynamics

This study deals with the design of a robust fault estimation and fault-tolerant control for vehicle lateral dynamics subject to external disturbance and unknown sensor faults. Firstly, a descriptor state and fault observer is designed to achieve the system state and sensor fault estimates simultaneously. Secondly, based on the information of on-line fault estimates, a robust fault-tolerant controller based on static output-feedback controller (SOFC) design approach is developed. To provide linear matrix inequalities of less conservatism, the results are conducted in the non-quadratic framework dealing with unmeasurable premise variables case. Simulation results show the effectiveness of the proposed control approach when the vehicle road adhesion conditions change and the sideslip angle is unavailable for measurement.

H∞ static output feedback controller design for continuous Markov jump systems with incomplete transition probabilities

The [Formula: see text] static output feedback control of continuous Markov jump systems with incomplete transition probabilities is investigated in this paper. Employing the property of continuous transition probabilities and a matrix transformation technique, relaxed sufficient conditions for the existence of a solution to the [Formula: see text] static output feedback control problem are established in terms of linear matrix inequalities. In addition, the obtained results are extended to Markov jump nonlinear systems. Numerical examples are provided to demonstrate the effectiveness of the derived results.

線形時変力学系のLMIを用いた静的出力フィードバック制御の<i>L</i><sub>2</sub>ゲイン性能最適設計

線形時変力学系のLMIを用いた静的出力フィードバック制御の<i>L</i><sub>2</sub>ゲイン性能最適設計

Recent Advances in Static Output-Feedback Controller Design with Applications to Vibration Control of Large Structures

Published version of an article in the journal: Modeling, Identification and Control. Also available from the publisher at: http://dx.doi.org/10.4173/mic.2014.3.4 Open Access

Static output feedback control design for linear MIMO systems with actuator dynamics governed by diffusion PDEs

This paper deals with the problem of static output feedback (SOF) control design for a class of diffusion partial differential equation (PDE) and ordinary differential equation (ODE) cascades, where the ODE model is used to describe the dynamics of the multi-input and multi-output (MIMO) plant and the diffusion PDE model is employed to represent the dynamics of actuators. The objective of this paper is to develop a simple as well as effective SOF controller via the Lyapunov's direct method such that the resulting closed-loop system is globally exponentially stable. By constructing a quadratic Lyapunov function, the sufficient condition on the globally exponential stability of the closed-loop cascaded system is presented in terms of linear matrix inequality (LMI). Then, an LMI-based design method of the SOF controller is developed on the basis of the obtained stability analysis result. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed design method.

Feasibility issues in static output-feedback controller design with application to structural vibration control

Recent results in output-feedback controller design make possible an efficient computation of static output-feedback controllers by solving a single-step LMI optimization problem. This new design strategy is based on a simple transformation of variables, and it has been applied in the field of vibration control of large structures with positive results. There are, however, some feasibility problems that can compromise the effectiveness and applicability of the new approach. In this paper, we present some relevant properties of the variable transformations that allow devising an effective procedure to deal with these feasibility issues. The proposed procedure is applied in designing a static velocity-feedback H∞ controller for the seismic protection of a five-story building with excellent results.

H∞ static output-feedback control design with constrained information for offshore wind turbine system

This paper deals with H∞ static output-feedback control design with constrained information for offshore wind turbines. Constrained information indicates that a special zero–nonzero structure is imposed on the static output-feedback gain matrix. A practical use of such an approach is to design a decentralized controller for a wind turbine. This will also benefit the controller in such a way that it is more tolerant to sensor failure. Furthermore, the model under consideration is obtained by using the wind turbine simulation software FAST. Sufficient conditions to design an H∞ controller are given in terms of Linear Matrix Inequalities (LMIs). Simulation results are given to illustrate the effectiveness of the proposed methodology for different cases of the control gain structures.

A static output feedback control design for path following of autonomous underwater vehicle in vertical plane

This paper presents the design of an output feedback controller for an autonomous underwater vehicle to achieve the task of path following in vertical plane. Using vehicle kinematics, a reference frame is generated which provides desired orientation of the vehicle along the path. An error space is then defined using the reference trajectory and thereby linearized. Based on this linearized model, a static output feedback controller is designed and implemented on the nonlinear plant. Computer simulations have been used to verify the controller design.

Guaranteed cost control for bilinear systems by static output feedback

This paper proposes a static output feedback controller design technique for bilinear systems. Based on Lyapunov’s direct method, a nonlinear control law is derived to stabilize the system in the presence of external disturbances. Sufficient condition is derived in terms of a state-dependent nonlinear matrix inequality and then it is converted into a sum-of-squares (SOS) optimization problem. Semidefinite programming and SOS decomposition techniques are employed to solve the optimization problem. The obtained output feedback controller guarantees an upper bound of the performance index. The effectiveness of the proposed method is demonstrated through simulation results.

Robust Finite Frequency ℋ∞ Passive Fault Tolerant Static Output Feedback Control with Application to Active Vibration Attenuation

In this work, the robust finite frequency ℋ∞ passive fault-tolerant static output feedback controller design problem is investigated. The control law is a static output feedback control and the actuators are subject to faults. The fault matrix is described by a polytope with finite vertices. In order to attenuate the effect from the external disturbance to the controlled output, the finite frequency ℋ∞ control in which the Hamilton matrix is avoided is employed. The static output feedback gain is determined via a two-stage method. Then, an iterative algorithm is proposed to derive a smaller ℋ∞ performance index. The proposed algorithm is applied to an active control problem of a structural system under an earthquake excitation. Simulations and comparisons have shown that the designed fault-tolerant controller can significantly attenuate the vibration from the ground and protect the structural system even actuator faults occur.

Delay-dependent generalized H2 fuzzy static-output-feedback control for discrete T-S fuzzy bilinear stochastic systems with mixed delays

This paper is concerned with the delay-dependent generalized H2 fuzzy static out feedback control scheme for a class of nonlinear systems with mixed time delays. The nonlinear plant is represented by Takagi-Sugeno T-S fuzzy bilinear stochastic systems with time-varying and infinite-distributed delays. Firstly, a novel delay-dependent piecewise Lyapunov-Krasovskii functional DDPLKF is proposed, in which both the upper and the lower bound of delays are considered. Then, based on this DDPLKF, a new delay-dependent generalized H2 fuzzy static output feedback controller design approach is first derived for the fuzzy bilinear stochastic system, and two improved delay-dependent stochastic stability conditions are established. The solutions of the problem can be obtained by solving a set of nonlinear minimization problems involving linear matrix inequalities LMIs constraints. An iterative algorithm making use of sequential linear programming matrix method SLPMM is proposed to solve the nonlinear minimization problem. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approaches in this paper.

Robust non-quadratic static output feedback controller design for Takagi–Sugeno systems using descriptor redundancy

This work concerns robust static output feedback controller (SOFC) design for uncertain and disturbed Takagi–Sugeno (TS) systems using an H-infinity criterion. The main result is based on a descriptor formulation of the closed-loop dynamics. The proposed approach allows avoiding appearance of crossing terms between the controller’s and the TS system’s input matrices leading to easier LMI formulation than existing studies in the literature. Moreover, the proposed SOFC design conditions do not require any restrictions on the output equation and allow dealing with unmeasurable premise variables. Indeed, taking advantage of the uncertain TS modeling, nonlinearities associated to unmeasurable premises variables can be reported from the nominal part to the uncertainties. To provide LMIs of less conservatism, the results are conducted in the non-quadratic framework. Finally, two numerical examples and a benchmark of a crane system are proposed to illustrate the efficiency of the SOFC design methodology.

Delay-dependent fuzzy static output feedback control for discrete-time fuzzy stochastic systems with distributed time-varying delays

This paper is concerned with the delay-dependent H∞ fuzzy static output feedback control scheme for discrete-time Takagi–Sugeno (T–S) fuzzy stochastic systems with distributed time-varying delays. To begin with, the T–S fuzzy stochastic system is transformed to an equivalent switching fuzzy stochastic system. Then, based on novel matrix decoupling technique, improved free-weighting matrix technique and piecewise Lyapunov–Krasovskii function (PLKF), a new delay-dependent H∞ fuzzy static output feedback controller design approach is first derived for the switching fuzzy stochastic system. Some drawbacks existing in the previous papers such as matrix equalities constraint, coordinate transformation, the same output matrices, diagonal structure constraint on Lyapunov matrices and BMI problem have been eliminated. Since only a set of LMIs is involved, the controller parameters can be solved directly by the Matlab LMI toolbox. Finally, two examples are provided to illustrate the validity of the proposed method.

LMI Relaxations for Reduced-Order Robust ${\cal H}_{\infty}$ Control of Continuous-Time Uncertain Linear Systems

This technical note is concerned with the problem of reduced order robust <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> dynamic output feedback control design for uncertain continuous-time linear systems. The uncertain time-invariant parameters belong to a polytopic domain and affect all the system matrices. The search for a reduced-order controller is converted in a problem of static output feedback control design for an augmented system. To solve the problem, a two-stage linear matrix inequality (LMI) procedure is proposed. At the first step, a stabilizing state feedback scheduled controller with polynomial or rational dependence on the parameters is determined. This parameter-dependent state feedback controller is used at the second stage, which synthesizes the robust (parameter-independent) output feedback <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> dynamic controller. A homogeneous polynomially parameter-dependent Lyapunov function of arbitrary degree is used to assess closed-loop stability with a prescribed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> attenuation level. As illustrated by numerical examples, the proposed method provides better results than other LMI based conditions from the literature.

Nonlinear conjugate gradient methods for continuous-time output feedback design

In this paper, three nonlinear conjugate gradient methods are analyzed and studied for solving matrix optimization problem arising in the static output feedback control design for continuous-time systems. The problem structure is exploited and the methods are tested numerically on wide range of benchmark test problems.

Reduced-order dynamic output feedback control of continuous-time T–S fuzzy systems

The problem of reduced-order dynamic output feedback control design for continuous-time Takagi–Sugeno fuzzy systems with H∞ guaranteed cost is addressed. The proposed approach is based on a line-integral fuzzy Lyapunov function with arbitrary polynomial dependence on the premise variables, allowing the membership functions, modeled as multi-simplexes, to vary arbitrarily. The controller is obtained by transforming the problem into a static output feedback control design problem solved by means of a two-stages linear matrix inequality procedure. The main appeal of the approach is that the order of the output feedback controller as well as the dependence of the premise variables are customizable for control implementation purposes. Examples illustrate the flexibility of the method and also that the proposed strategy can provide less conservative results when compared to other methods for full order dynamic output feedback controllers from the literature of continuous-time Takagi–Sugeno fuzzy systems.

Improved resilient feedback stabilisation method for uncertain systems

The problem of resilient stabilisation for a class of continuous-time uncertain systems having norm-bounded parametric uncertainties is investigated. Both static and dynamic output-feedback resilient controller design is considered. The goal is to robustly quadratically stabilise the uncertain plant considering the controller gain perturbations. Sufficient conditions for the existence of static output feedback and dynamic output feedback resilient controllers are derived in terms of linear matrix inequalities. A numerical example for each type of controllers is illustrated to demonstrate their effectiveness.

Ptimal passive-damping design using a decentralized velocity-feedback H-Infinity approach

In this work, a new strategy to design passive energy dissipation systems for vibration control of large structures is presented. The method is based on the equivalence between passive damping systems and fully decentralized static velocity-feedback controllers. This equivalence allows to take advantage of recent developments in static output-feedback control design to formulate the passive-damping design as a single optimization problem with Linear Matrix Inequality constraints. To illustrate the application of the proposed methodology, a passive damping system is designed for the seismic protection of a ve-story

Robust Static Output Feedback Control and Remote PID Design for Networked Motor Systems

In this paper, we investigate the problem of robust static output feedback (SOF) control for networked control systems (NCSs) subject to network-induced delays and missing data. The uncertain system matrices are assumed to lie in a convex polytope. The network-induced delays are time varying but within a given interval. The random data missing is characterized by the Bernoulli random binary distribution. Delay-dependent conditions for the exponential mean-square stability are first established in terms of matrix inequalities. Then, for the robust stabilization problem, the design of an SOF controller is presented by solving bilinear matrix inequalities (BMIs). In order to efficiently solve a nonconvex BMI, we propose an approach based on the linear matrix inequality technique. Furthermore, the developed approach is employed to design the remote proportional–integral–derivative (PID) controller for NCSs. The design of a digital PID controller is formulated as a synthesis problem of the SOF control via an augmentation method. Simulation examples illustrate the effectiveness of the proposed methods.