Parametric Robust Control Research Articles

Frequency response computation of fractional order interval transfer functions

The paper present extensions of some results developed in the parametric robust control to fractional order interval control systems (FOICS). Computation of the Bode and Nyquist envelopes of FOICS are studied. Using the geometric structure of the value set of fractional order interval polynomials (FOIP), a technique is proposed for computing the Bode and Nyquist envelopes of transfer functions whose numerator and denominator polynomials are fractional order polynomials with interval uncertainty structure. The results obtained are useful for the analysis and design of FOICS. Numerical examples are included to illustrate the benefit of the method presented.

Performance of a grid-connected wind generation system with a robust susceptance controller

Wind turbine driven induction generators are vulnerable to transient disturbances like wind gusts and low voltages on the system. The fixed capacitor at the generator terminal or the limited support from the grid may not be able to provide the requisite reactive power under these abnormal conditions. This paper presents a susceptance control strategy for a variable speed wound-rotor induction generator which can cater for the reactive power requirement. The susceptance is adjusted through a robust feedback controller included in the terminal voltage driven automatic excitation control circuit. The fixed parameter robust controller design is carried out in frequency domain using multiplicative uncertainty modeling and H ∞ norms. The robustness of the controller has been evaluated through optimally tuned PID controllers. Simulation results show that the robust controller can effectively restore normal operation following emergencies like sudden load changes, wind gusts and low voltage conditions. The proposed robust controller has been shown to have adequate fault ride through capabilities in order to be able to meet connection requirements defined by transmission system operators.

Design and Analysis of Robust SMES Controller for Stability Enhancement of Interconnected Power System Taking Coil Size Into Consideration

In power applications, efficiency and effectiveness of SMES with proper control are promising and highly remarkable, however, quite costly. Accordingly, optimum design and utilization are essentially needed. This paper presents the design and analysis of robust SMES controller for stability enhancement of interconnected power system taking coil size into consideration. With lead/lag controller structure, parameters of robust SMES controller can be optimized by a metaheuristic method; meanwhile, a multiplicative uncertainty is included in the design to cope with system uncertainties. Lastly, aiming at achieving optimum design and utilization, robust controllers for SMES with different coil sizes are examined to investigate performance and robustness under different situations via simulation studies.

Solving and visualizing nonlinear parametric constraints in control based on quantifier elimination

We present a new method with a software tool for parametric robust control synthesis by symbolic-numeric computation. The method is a parameter space approach and it is especially effective for analysis and design of fixed-structure controllers of rational type, which encompass PI and PID controllers. The real quantifier elimination (QE), which is one of the recent progresses in the symbolic computation, plays a key role in our development. The QE-based approach can uniformly deal with a lot of important design specifications for robust control such as frequency restricted H ∞ norm constraints, stability (gain/phase) margin and stability radius specifications, and pole location requirement by reducing such specifications to a particular type of formulae called a “sign definite condition (SDC)”. This is also useful for improving the efficiency of QE computations since we can utilize an efficient QE algorithm specialized to the SDC using the Sturm-Habicht sequence. We have developed a MATLAB toolbox for robust parametric control based on a parameter space approach accomplished by QE. The QE-based parameter space approach and numerical simulation of performances for specific controller parameter values taken from a controller parameter space are integrated conveniently in our toolbox with the assistance of a graphical user interface (GUI). With our toolbox the feasible regions of controller parameters are visualized in a parameter space for the controllers with three or two parameters. This enables control engineers to achieve multi-objective robust controller synthesis smoothly. We also discuss how to merge the numerical computation and the symbolic operation to make our new design methods more efficient in practical control design.

A Robust STATCOM Controller for a Multi-Machine Power System Using Particle Swarm Optimization and Loop-Shaping

Design of a fixed parameter robust STATCOM controller for a multi-machine power system through an H-∞ based loop-shaping procedure is presented. The trial and error part of the graphical loop-shaping procedure has been eliminated by embedding a particle swarm optimization (PSO) technique in the design loop. Robust controllers were designed considering the detailed dynamics of the multi-machine system and results were compared with reduced order models. The robust strategy employing loop-shaping and PSO algorithms was observed to provide very good damping profile for a wide range of operation and for various disturbance conditions.

Tuning of Robust Distant Downstream PI Controllers for an Irrigation Canal Pool. II: Implementation Issues

Based on the companion paper results, this paper presents a robust tuning method to tune a proportional integral (PI) controller that fulfills the design requirements for a single pool with different hydraulic conditions. The robust PI controller parameters are obtained analytically as a function of the physical parameters of the canal pool. Important implementation issues are also considered. Rules are provided for the sampling time selection in order to recover the continuous-time performance. When the sampling time is imposed, it has to be included in the controller design, by modifying the delay of the system. A simple way is proposed to take account of the gate opening as control action variable, instead of the upstream discharge. This robust PI tuning method is evaluated by simulation on a full nonlinear model of two different canal pools for different flow conditions and different implementations: continuous-time control, discrete-time control, using the discharge or the gate opening as control action variable. Simulation results show that the method leads to efficient realistic PI controllers for a canal pool.

05/02514 A robust damping controller for SMES using loop-shaping technique

A robust damping controller for a power system installed with super-conducting magnetic energy storage (SMES) has been designed using a simple graphical loopshaping technique. The graphical method starts by selection of a nominal plant function satisfying the robust stability and performance criterion. The variations in operating conditions from the nominal values are modeled as multiplicative structured uncertainty. The generator-SMES system has been represented with a detailed dynamic model for the control design. The robust design, with generator speed variation as the controller input, was tested for a range of operating points considering various disturbances. It is observed that the fixed parameter robust controller provides very good damping for a wide range of operating conditions. COPY; 2005 Elsevier Ltd. All rights reserved.

A robust damping controller for SMES using loop-shaping technique

A robust damping controller for a power system installed with super-conducting magnetic energy storage (SMES) has been designed using a simple graphical loop-shaping technique. The graphical method starts by selection of a nominal plant function satisfying the robust stability and performance criterion. The variations in operating conditions from the nominal values are modeled as multiplicative structured uncertainty. The generator-SMES system has been represented with a detailed dynamic model for the control design. The robust design, with generator speed variation as the controller input, was tested for a range of operating points considering various disturbances. It is observed that the fixed parameter robust controller provides very good damping for a wide range of operating conditions.

On the synthesis of robust PID controllers for plants with structured and unstructured uncertainty

AbstractIn this paper, we consider the problems of synthesizing PID controllers for robust stability and performance for a given linear time‐invariant plant subject to both parametric and H∞‐norm‐bounded perturbations. Using results from the area of parametric robust control, synthesis problems are converted into simultaneous stabilization of a family of complex segment polynomials. The results on H∞ PID synthesis are then used to devise a design procedure for determining the admissible PID gain values. One of the important features of the proposed method is that it constructively characterizes the approximated set of all admissible PID controllers. This characterization can facilitate the optimal design of any additional design requirements. Copyright © 2005 John Wiley & Sons, Ltd.

시변시간지연을 가지는 네트워크기반 제어시스템의 H2제어기 설계

H₂ controller is proposed for networked control systems with time-varying delay. The time-varying network delay is assumed to be unknown, but its lower and upper bounds are assumed to be known. The time-varying delay is treated like a parameter variation and robust control technique is used to deal with the time-varying delay. The proposed controller can be computed by solving linear matrix inequalities. Through numerical simulations, the proposed controller is verified.

Parameter robust control design using bimatrix co-evolution algorithms

The parameter robust controller design problem is often expressed as a game between the controller and uncertain parameters. The game is expressed as a constrained minimax problem if design requirements are treated as the constraints, but the saddle-point solution of the constrained minimax problem is difficult to obtain by using conventional methods. This paper proposes a new method of designing parameter robust controllers by introducing a bimatrix co-evolution algorithm which solves the constrained minimax problem. The proposed algorithm approximates the problem as a bimatrix game between two groups having independent fitness measures and finds the saddle-point solution through successive bimatrix games. The resulting controller guarantees robustness against bounded parameter uncertainties and satisfies the design requirements. The performance of the proposed algorithm is verified by its application to a satellite attitude control problem.

Sensitivity study of the control loops of DC-DC converters by means of robust parametric control theory

Robust parametric control theory is a powerful tool for the research of linear control systems robustness against simultaneous changes in the parameters that define the plant and controller transfer functions. The purpose of this paper is to show how those techniques can be applied to the sensitivity study of DC-DC power converters control loops with respect to simultaneous variations of all the parameters defining the power stage: line voltage, load, and passive elements of the power stage.

Robust Assignment of Poles in Large-Scale Interval Systems

Controls ensuring given limits of variation of direct quality indexes for large-scale interval systems are designed. The robust controller parameters are determined from the Sylvester interval equation. A decomposition procedure for the Sylvester equation for reducing the computational requirements of design is elaborated.

An LMI Approach to H.INF. PI Controller Design.

A Linear Matrix Inequality (LMI) approach for designing the H∞ Proportional-Integral (PI) controller for a nonlinear dynamic system is studied. A local linear model containing time-varying norm-bounded uncertain parameters is identified at first. The robust PI control design problem based on the norm-bounded uncertain linear model is then transformed into a standard H∞ control problem, where the latter is further formulated as LMIs. By adopting the LMI expression, a symmetric positive definite matrix P with guaranteed overall system’s quadratic stability can be easily determined. The matrix P can finally be used to infer the robust PI controller parameters. One chemical process, a non-isothermal continuous-stirred-tank reactor (CSTR) with a first-order exothermic reaction, is illustrated to demonstrate the effectiveness of the proposed LMI-based H∞ PI controller design method for nonlinear dynamic processes.

STABILITY MARGIN COMPUTATION FOR NONLINEAR SYSTEMS: A PARAMETRIC APPROACH

This paper studies the existence of limit cycles in a control system which contains nonlinearities and parametric uncertainties. The existence of limit cycles in a control system with a separable nonlinearity can be predicted using the describing function. In this paper, some of the well-known results developed in the area of parametric robust control are used together with the describing function method to analyze the stability problem of uncertain nonlinear systems. Based on the segment lemma, a stability result for a control system with an uncertain nonlinear element and a fixed linear element is first derived. Then, a polynomial method and a graphical method are proposed to determine how much one can perturb the coefficients of the linear element without causing the nonlinear system to have a limit cycle. Examples are given to illustrate the method presented.

Robust and non‐fragile PID controller design

AbstractThis paper provides a solution to the problem of robustly stabilizing a given interval plant family using P, PI and PID controllers. This solution is derived by combining some recent results on P, PI and PID stabilization of fixed plants with some standard results from the parametric robust control literature. The paper also develops a technique for designing PID controllers which are not only robust with respect to plant parameter perturbations but are also ‘non‐fragile’ in the space of the controller coefficients. Copyright © 2001 John Wiley & Sons, Ltd.

Mapping of Nyquist/Popov Theta-Stability Margins Into Parameter Space

The application of the parameter space method has proven to be useful for robustness analysis of uncertain parametric systems and robust control synthesis for quite a number of applications. However, it has been restricted to linear systems and the consideration of eigenvalue criteria. This paper enhances the application of the parameter space method to include various locus criteria. This allows not only for incorporation of linear criteria (e. g. gain and phase margin) but for nonlinear criteria as well (e.g. Popov- or circle criterion and the dual locus method).

Simultaneous parametric uncertainty modeling and robust control synthesis by LFT scaling

Given a set of experimental data points in the plant parameter space, the objective of this paper is to give a systematic method for designing a controller to achieve a prescribed level of robust performance for the closed-loop system. A standard procedure would be to model the data first and then to design a controller. Our focus here, instead, is to complete these two tasks simultaneously, eliminating the conservatism caused by the fact that the data is modeled independently of the closed-loop objective. To this end, integral quadratic constraints (IQCs) are used as a tool for uncertainty modeling. We propose the LFT scaling to integrate the IQC modeling with the control synthesis. It is shown that the LFT scaling provides a condition dual to the standard IQC for linear time-invariant systems, and this duality result is essential for solving the simultaneous modeling and synthesis problem. A solution is given in terms of matrix inequalities and its computational aspects are discussed. The proposed method is applied to the control design for an AC linear servo motor, and experimental results demonstrate that our method achieves the performance superior to that achieved by existing methods.

Composite Interval Control Systems: Some Strong Kharitonov-Like Properties

The interval model plays an important role in parametric robust control. This paper deals with the strict positive realness of a class of composite interval control systems, and establishes a strong Kharitonov-like extreme point criterion. We also discuss the robust strict positive realness of the shifted interval plant-controller family, and improve some previous results in the literature. Furthermore, for the collection of Popov plots of an interval transfer function family, we prove that a large portion of its outer boundary comes from the sixteen Kharitonov transfer functions. Finally, we study the beta boundedness of interval systems. A strong Kharitonov-like vertex result is established, namely, that all members in the interval system family are beta bounded if and only if the sixteen Kharitonov critical vertices are beta bounded.

Robust stability and performance with fixed-order controllers

This paper deals with the problem of synthesizing or designing a feedback controller of fixed dynamic order for a linear time-invariant plant for a fixed plant, as well as for an uncertain family of plants containing parameter uncertainty, so that stability, robust stability and robust performance are attained. The desired closed-loop specifications considered here are given in terms of a target performance vector representing a desired closed-loop design. In general, these point targets are unattainable with a fixed-order controller. By enlarging the target from a fixed-point set to an interval set the solvability conditions are relaxed and a solution is enabled. Results from the parametric robust control literature can be used to design the interval target family so that the poles and zeros of the closed-loop system are guaranteed to remain in a prescribed region of the complex plane, and closed-loop performance, measured for instance in the H ∞ norm are attained, even when plant uncertainty is present. It is shown that it is possible to devise a computationally simple linear programming approach that attempts to meet the desired closed-loop specifications. The approach developed here gives the entire set of controllers attaining the specifications as a convex set and also can be recast to give the lowest-order controller attaining specifications.