Robust Stability Design Research Articles

Design of Robust Stabilization and Fault Diagnosis for an Auto-balancing Two-Wheeled Cart

This paper investigates robust fault diagnosis strategies for the auto-balancing of an ergonomically designed two-wheeled cart which is inherently unstable and has a non-minimum phase. To endow the rider with robust stabilization, the normalized coprime factorization for steering is employed for allowing maximum model uncertainties and the driving orientation is achieved with an electronic differential steering control. A model-based fault-detection filter is designed to detect sensor faults. The observer gain obtained by solving an algebraic Riccati equation in the normalized coprime factorization approach offers some design convenience associated with the fault diagnosis filter. In order to promptly alert the rider for safety purposes in the event of a malfunction, the decision-making process to identify a critical failure is also investigated. Finally, evaluation examples are given to illustrate the performance of the proposed robust fault diagnosis strategies.

New Robust Stability Conditions and Design of Robust Stabilizing Controllers for Takagi–Sugeno Fuzzy Time-Delay Systems

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.

The geometry and number of the root invariant regions for linear systems

The stability domain is a feasible set for numerous optimization problems. D-decomposition technique is targeted to describe the stability domain in the parameter space for linear parameter-dependent systems. This technique is very simple and efficient for robust stability analysis and design of low-order controllers. However, the geometry of the arising parameter space decomposition into root invariant regions has not been studied in detail; it is an objective of the present paper. We estimate the number of root invariant regions and provide examples, where this number is attained.

Improved robust stability criteria and design of robust stabilizing controller for uncertain linear time‐delay systems

AbstractIn this paper, an improved linear matrix inequality (LMI)‐based robust delay‐dependent stability test is introduced to ensure a larger upper bound for time‐varying delays affecting the state vector of an uncertain continuous‐time system with norm‐bounded‐type uncertainties. A quasi‐full‐size Lyapunov–Krasovskii functional is chosen and free‐weighting matrix approach is employed. Less restrictive sufficient conditions are derived for robust stability of time‐varying delay systems with norm‐bounded‐type uncertainties. Moreover, the investigation of the stabilization problem with memoryless state‐feedback control is presented such that the stabilizability criteria are obtained in terms of matrix inequalities, which can be solved via utilizing a cone complementarity minimization algorithm. Finally, the problem of output feedback stabilization for square systems is also taken into consideration. The output feedback stabilizability criteria are derived in the form of linear matrix inequalities, which are convex and can be easily solved using interior point algorithms. A plenty of numerical examples are presented indicating that the proposed stability and stabilization methods effectively improve the existing results. Copyright © 2006 John Wiley & Sons, Ltd.

LMI를 기반으로 한 퍼지 피드백 선형화 제어 시스템의 L2 강인 안정성 해석

This paper presents the robust stability analysis and design methodology of the fuzzy feedback linearization control systems. Uncertainty and disturbances with known bounds are assumed to be included Un the Takagi-Sugeno (TS) fuzzy models representing the nonlinear plants. robust stability of the closed system is analyzed by casting the systems into the diagonal norm bounded linear differential inclusions (DNLDI) formulation. Based on the linear matrix inequality (LMI) optimization programming, a numerical method for finding the maximum stable ranges of the fuzzy feedback linearization control gains is also proposed. To verify the effectiveness of the proposed scheme, the robust stability analysis and control design examples are given.

Optimal multiobjective design of robust power system stabilizers using genetic algorithms

Optimal multiobjective design of robust multimachine power system stabilizers (PSSs) using genetic algorithms is presented in this paper. A conventional speed-based lead-lag PSS is used in this work. The multimachine power system operating at various loading conditions and system configurations is treated as a finite set of plants. The stabilizers are tuned to simultaneously shift the lightly damped and undamped electromechanical modes of all plants to a prescribed zone in the s-plane. A multiobjective problem is formulated to optimize a composite set of objective functions comprising the damping factor, and the damping ratio of the lightly damped electromechanical modes. The problem of robustly selecting the parameters of the power system stabilizers is converted to an optimization problem which is solved by a genetic algorithm with the eigenvalue-based multiobjective function. The effectiveness of the suggested technique in damping local and interarea modes of oscillations in multimachine power systems, over a wide range of loading conditions and system configurations, is confirmed through eigenvalue analysis and nonlinear simulation results.

Robust controller design for automatic generation control based on Q-parameterization

This paper presents a robust controller design based on Q-parameterization theory for the automatic generation control problem of a power system. This controller is used in order to achieve both robust stability and good dynamic performance against the variation of system parameters. In the Q-parameterization method, the set of all stabilizing controllers of the power system is characterized by a free parameter Q. This free parameter is chosen to satisfy robust stability and other design requirements. Simulation results have confirmed the effectiveness of the proposed controller.

Observer-based robust control for uncertain systems with time-varying delay

This paper is concerned with the function observer-based stabilization for time-varying delay systems with parameter uncertainties. The uncertain systems tackled in this paper involve uncertainty in quadratic constrained form which includes the well-known normbounded time-varying uncertainty as a special case. In terms of Razumikhin-type stability theorem, we show that the feasibility of several matrix inequalities guarantees the solvability of the addressed problem. Furthermore, we propose a parametric approach for function observer-based robust stabilizer design.

Robust pole placement stabilizer design using linear matrix inequalities

This paper presents the design of robust power system stabilizers which place the system poles in an acceptable region in the complex plane for a given set of operating and system conditions. It therefore, guarantees a well damped system response over the entire set of operating conditions, The proposed controller uses full state feedback. The feedback gain matrix is obtained as the solution of a linear matrix inequality expressing the pole region constraints for polytopic plants. The technique is illustrated with applications to the design of stabilizers for a single machine and a 9 bus, 3 machine power system.

Robust design and coordination of multiple damping controllers using nonlinear constrained optimization

This paper proposes a design approach for power system stabilizing controllers based on parameter optimization of compensators with generalized structures. It shows that a selective modal performance index is an improved measure of the stabilizing effect of a given design, although its blind minimization can end in a useless local minimum. Adding stability, sensitivity and robustness constraints greatly improve the engineering significance of the resulting design. The development is fully multivariable and remains sufficiently general to apply equally well to a feedback or cascade stabilizer, with any type of input signal or transfer function structure. Three examples are used: a robust PSS design for a single machine-infinite bus system with multiple operating points; multiple PSS coordination for a large system; and a coordinated design of four PSSs for the Kundur's two-area test system. All results show good prospects for the constrained optimization based approach to the design of robust stabilizers.

Robust stability analysis and design method for the fuzzy feedback linearization regulator

A robust stability analysis and design method for a fuzzy feedback linearization regulator is presented. The well-known Takagi-Sugeno fuzzy model is used as the nonlinear plant model. Uncertainties and disturbance are assumed to be included in the model structure with known bounds. For these structured uncertainties, stability robustness of the closed system is analyzed in both input-output sense and Lyapunov sense. The robust stability conditions are proposed using multivariable circle criterion and the relationship between input-output stability and Lyapunov stability. Also, based on the stability analysis, a systematic design procedure for the fuzzy feedback linearization regulator is provided. The effectiveness of the proposed analysis and design method is illustrated by a simple example.

Robust Stability and Integrity Control Design for Uncertain Singular Systems

A control law that maintains the closed-loop singular system regular, impulse free and asymptotically stable against arbitrary sensor failures is proposed. Synthesis method for a set of linear state feedback controllers is derived by utilizing the properties of spectral radius and matrix inequalities. In addition, the integrity design is further extended to the uncertain singular systems and to the study of retaining the stability characteristics of the given open loop system. In both cases, the tolerable perturbation bounds are all expressed explicitly.

Computational Issues in the Robust Stability Analysis and Design of Interval Paramater Systems

This paper addresses the computational issues related to computing a bound on the size of structured real parameter perturbations under which a nominally stable matrix remains stable. First, a computationally more efficient method is presented for computing existing bounds, requiring less time and storage than other methods. Then the possibility of obtaining an extreme point solution for the case of checking the robust stability of 'Interval Matrices' is explored and the associated computational implications are discussed.

Design and analysis of an adaptive fuzzy power system stabilizer

Power system stabilizers (PSS) must be capable of providing appropriate stabilization signals over a broad range of operating conditions and disturbances. Traditional PSS rely on robust linear design methods. In an attempt to cover a wider range of operating conditions, expert or rule-based controllers have also been proposed. Fuzzy logic as a novel robust control design method has shown promising results. The emphasis in fuzzy control design centers around uncertainties in system parameters and operating conditions. Such an emphasis is of particular relevance as the difficulty of accurately modelling the connected generation is expected to increase under power industry deregulation. Fuzzy logic controllers are based on empirical control rules. In this paper, a systematic approach to fuzzy logic control design is proposed. Implementation for a specific machine requires specification of performance criteria. This performance criteria translates into three controller parameters which can be calculated off-line or computed in real-time in response to system changes. The robustness of the controller is emphasized. Small signal and transient analysis methods are discussed. This work is directed at developing robust stabilizer design and analysis methods appropriate when fuzzy logic is applied.

Closest bifurcation analysis and robust stability design of flexible satellites

We consider the design of a satellite to ensure robust stability in a high-dimensional parameter space. Starting with a given nominal design that is stable, we compute instabilities that are locally closest to the nominal design in the design parameter space. If these worst-case instabilities are too close, we compute a design that is sufficiently far from the worst-case instabilities and hence sufficiently robust. The methods are based on computations from bifurcation theory and are considerably simplified by our assumption of a Hamiltonian satellite, which includes spin-stabilized satellites, dual-spin-stabilized satellites, and gravity-gradient-stabilized satellites. The Hamiltonian assumption is then relaxed to allow the inclusion of damping terms. We illustrate the computations by ensuring the robust stability of a flexible dual-spin satellite with six design parameters.

Continuity of optimal robustness and robust stabilization in slowly varying systems

Continuity properties of the optimal design of robust stabilization in the gap metric are investigated. In general the optimal design in the gap metric lacks continuity properties required for certain H ∞ adaptation schemes for slowly varying systems. On the other hand, the δ-suboptimal central design is shown to be Lipschitz continuous. Applications of the continuity properties and frozen-time stability analysis lead to a suboptimal design for robust stabilization in slowly time-varying plants which are represented by local normalized coprime factorizations.

Loop shaping based robust control of a magnetic bearing

H/sub infinity / robust control design of a magnetic bearing is considered. In particular, the design of a control system using the loop shaping design procedure (LSDP) is presented. After the introduction of the experimental machine and digital controller, model uncertainty and performance of the magnetic bearing are discussed. The performance and robust stability design objectives are specified as the requirements for particular closed loop transfer functions with the weighting functions. The frequency responses of these closed loop transfer functions are approximated by that of the open loop transfer function in a certain frequency band. Experimental results are presented to illustrate the robust stability and good performance of the designed control system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust stabilization of systems with multiple real pole uncertainties

The robust stabilization of systems with several uncertain real poles is discussed. Necessary and sufficient conditions of existence of a controller in terms is obtained of an interpolation problem are given. The interpolating function is obtained directly for a particular case. Two examples are shown for the synthesis of a controller. An explicit solution of the controller for plants without zeros in the right hand plane (RHP) and without known poles in the RHP is given. This shows the practical utility of the method to the design of robust stabilizers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>