Robust controller synthesis with consideration of performance criteria

This paper presents interactive controller synthesis methods based on an inward approach and offers some advantages over the traditional loop gain shaping methods. The indirect use of weighting functions for the robustness controller tuning is introduced. Besides that, the method allows transparent closed‐loop pole placement to achieve desirable transient performance. The obtained controllers are of lower order for comparable performance than those synthesized with rmH₂, H_∞ or µ‐synthesis. The method is particularly well suited for robust control problems where frequency domain constraints emerge from the analyses of non‐parametric uncertainties and also for control problems where the frequency domain loop shaping is used to achieve time domain performance specifications. Copyright © 2010 John Wiley & Sons, Ltd.     

Delay‐dependent feedforward control of time‐delay systems with parametric uncertainties via dynamic IQCs

This paper studies the design problem of a robust delay‐dependent H _∞ feedforward controller design for a class of linear uncertain time‐delay system having state and control delays when the system is subject to ‐type disturbances. The proposed controller scheme involves two main controllers, which are static state‐feedback and dynamic feedforward controllers. The state‐feedback controller is used for stabilizing the delay and uncertainty‐free system, whereas the feedforward controller performs disturbance attenuation. Dynamic type integral quadratic constraints (IQCs), which consist of frequency‐dependent multipliers, have been introduced to represent the delays and parametric uncertainties in the system where the degree of the multiplier used in IQC representation is in an adjustable nature. This scheme allows the designer to obtain less conservative controllers with increasing precision. Sufficient delay‐dependent criteria in terms of linear matrix inequalities are obtained such that the uncertain linear time‐delay system is guaranteed to be globally, uniformly, asymptotically stable with a minimum disturbance attenuation level. Several numerical examples together with the simulation studies provided at the end illustrate the usefulness of the proposed design. Copyright © 2012 John Wiley & Sons, Ltd.     

Fixed‐structure controller design for polytopic systems via LMIs

In this paper, a new approach for fixed‐structure H₂ controller design in terms of solutions to a set of linear matrix inequalities are given. Both discrete‐time and continuous‐time SISO time‐invariant systems are considered. Then the results are extended to systems with polytopic uncertainty. The presented methods are based on an inner convex approximation of the non‐convex set of fixed‐structure H₂ controllers. The designed procedures are initialized either with a stable polynomial or with a stabilizing controller. An iterative procedure for robust controller design is given that converges to a suboptimal solution. The monotonic decreasing of the upper bound on the H₂ norm is established theoretically for both nominal and robust controller design. Copyright © 2014 John Wiley & Sons, Ltd.     

ROBUST POWER SYSTEM LOAD-FREQUENCY CONTROLLER DESIGN BASED ON H∞ OPTIMIZATION APPROACH

An H_∞ controller based on the standard H_∞ control design approach is proposed for power system load-frequency control with system parametric uncertainties. The variation bounds of power system parameters are obtained by changing parameters by 30%-50% simultaneously from their typical values. The existing H_∞ control technique is applied to design a load-frequency controller for power systems. The design procedure is given. The proposed H_∞ controller is simple, effective and can ensure that the overall system is asymptotically stable for all admissible uncertainties. Our simulation results show that for the example system the proposed H_∞ load-frequency controller can achieve good performance even in the presence of generation rate constraint.     

Robust H∞ control for uncertain linear neutral delay systems

This paper deals with the problem of robust H_∞ control for uncertain linear neutral delay systems. The parameter uncertainty under consideration is assumed to be norm‐bounded time‐invariant and appears in all the matrices of the state‐space model. The problem we address is the design of memoryless state feedback controllers such that the closed‐loop system is asymptotically stable and the H_∞ norm of the closed‐loop transfer function from disturbance to the controlled output is strictly less than a prescribed positive scalar for all admissible uncertainties. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of the above problem is proposed. When this matrix inequality is feasible, an explicit expression for the desired state feedback controller is given. Furthermore, a numerical example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

Structral–control optimization with H2- and H∞-norm bounds

An integrated approach to minimum weight structural design and robust control system design is presented. The controller is designed to tolerate both the structured real parameter uncertainty in the structural natural frequencies and the unstructured unmodelled dynamics due to model truncation. The control approach utilizes a mixed H₂–H_∞ LQG compensator with an H_∞-norm bound on the disturbance to the output transfer matrix in the closed-loop system and an upper bound on the H₂-norm signifying the maximum value of the quadratic control performance index for the uncertain system. In structural–control optimization problems, constraints are imposed on the fundamental structural frequency and on the dB gain separation between the open-loop and closed-loop singular values at prescribed frequencies. The method is demonstrated on a 48-state structural truth model of a three-dimensional tapered box truss with collocated actuators and sensors in which the control design model is eighth-order including the compensator dynamics. © 1997 John Wiley & Sons, Ltd.     

Delay‐dependent robust H ∞ control for uncertain singular time‐delay system with Markovian jumping parameters

The problem of robust H _∞ control for a class of uncertain singular time‐delay systems with Markovian jumping parameters is addressed in this paper. The considered Markovian jump singular systems involve constant time delay and norm‐bounded uncertainties. On the basis of LMI approach, a delay‐dependent condition is proposed, which ensures the nominal Markovian jump singular system to be regular, impulse‐free and stochastically stable. From the delay‐dependent condition, a sufficient condition leading to the existence of a state feedback controller that guarantees the robust admissibility and the H _∞ performance is also given. A numerical example is given to demonstrate the applicability of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust resilient H ∞ control for stochastic systems with Markovian jump parameters under partially known transition probabilities

In this paper, the robust resilient H _∞ control problem for a class of stochastic systems with partially known transition probabilities is investigated. The system under consideration finds extensive applications because of the uncertainties involved in the system matrices and the general assumption upon the transition probabilities. Attention is focused upon the design of a robust resilient H _∞ state feedback controller, which guarantees the stochastic stability of the closed‐loop system and a prescribed H _∞ disturbance attenuation level for all admissible uncertainties. Sufficient criteria ensuring the stochastic stability and stabilization of the underlying systems are presented via LMIs formulation. A numerical example is provided to demonstrate the effectiveness of all the results. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust H∞ control of stochastic time‐delay jumping systems with nonlinear disturbances

This paper deals with the problems of robust stabilization and H_∞ control for a class of uncertain stochastic jumping systems with nonlinear disturbances and time delays. The uncertain parameters are assumed to be norm‐bounded and mode dependent, and the time delays enter into the state matrix, the stochastic perturbation term, as well as the state feedback. The stochastic robust stabilization problem addressed in this paper is to design a state feedback controller with input delay such that, for all admissible uncertainties and the nonlinear disturbances, the closed‐loop system is robustly, stochastically, exponentially stable in the mean square. Moreover, the purpose of the robust H_∞ control problem is to guarantee a specified H_∞ performance index, while still achieving the mean‐square exponential stability requirement for the closed‐loop system. By resorting to the Itô's differential formula and the Lyapunov stability theory, sufficient conditions are derived, respectively, for the robust stabilization and the robust H_∞ control problems. It is shown that the addressed problems can be solved if a set of linear matrix inequalities (LMIs) are feasible. A numerical example is employed to illustrate the usefulness of the proposed LMI‐based design methods. Copyright © 2006 John Wiley & Sons, Ltd.     

H∞ control for sampled‐data linear systems with two Markov processes

This paper is concerned with the design problem of H_∞ digital switching control for linear continuous systems with Markovian jumping parameters. The controller is digital and monitored by the jumping parameters of the plant. The closed‐loop system is a hybrid one defined on a hybrid time space (composed of a continuous‐time and a discrete‐time) and a sample space. The sample space is specified by two separable continuous‐time discrete‐state Markov processes, one appearing in the open‐loop system, and the other appearing in control action, which is different with the traditional Markovian jumping process. Our attention is focused on designing digital output feedback controllers for the system with two Markovian jumping processes such that both stochastic stability and a prescribed H_∞ performance are achieved. The problem of robust H_∞ control for systems with parameters uncertainties is also studied. It is shown that the sampled‐data control problems for linear Markovian jumping systems with and without parameter uncertainties can be solved in terms of the solutions to a set of intercoupled matrix inequalities. Two numerical examples are given to show the design procedures. Copyright © 2005 John Wiley & Sons, Ltd.     

Analytical design of stable delta‐domain generalized predictive control

This paper addresses certain fundamental issues related to the discrete‐time design problem of the delta‐domain generalized predictive control (δ‐GPC) for both minimum phase and non‐minimum phase linear SISO plants including nominal stability and nominal performance of the closed‐loop system. The approach being presented is completely analytical, and the nominal performance of the control system is directly achieved by a prototype design of the closed‐loop system characteristics resulting in definite time‐domain specifications. Two design methods are offered in which a model‐based prediction paradigm is applied to achieve the future output and the future filtered output trajectory of the plant. Prediction of the first type is based on suitable emulations of the output δ‐derivatives and is used in the GPC controller design for minimum‐phase models of the plant. Prediction of the second type utilizes emulation of derivatives of the output filtered by the numerator polynomial of the transfer function of the controlled part of the plant. It can be employed both for minimum phase and non‐minimum phase plants. A numerical example is given that illustrates the δ‐GPC method for controller design. Copyright © 2002 John Wiley & Sons, Ltd.     

Robust continuous‐time controller design via structural Youla–Kučera parameterization with application to predictive control

This paper addresses the continuous‐time control of uncertain linear SISO plants and its nominal and robust stability and nominal and robust performance objectives. A specific application of the Youla–Ku?era (Q) parameterization concept leads to a new development of observer‐like controller structures. This method is combined with a nominal design of continuous‐time generalized predictive control suitable for both minimum‐phase and non‐minimum‐phase plants. The subsequent design procedure consists of two steps. Firstly, the nominal stability and nominal performance of the control system are established by using an analytical design methodology, based on a collection of closed‐loop prototype characteristics with definite time‐domain specifications. And secondly, a generic structure of the controller is enhanced by suitable Q‐parameters guaranteeing that the control system has the required robustness properties. The proposed structural (reduced‐order) Q‐parameterization relies on an observer structure of controllers, which can be easily enhanced with certain filters necessary for control robustification. To reduce the complexity of the resulting robust controllers, we suggest using a structural factorization, which allows for simple forms of robustifying (phase‐lag) correctors of low order, easy for implementation, and convenient for optimization and tuning. Two numerical examples are given to illustrate the composed technique and its practical consequences. Copyright © 2004 John Wiley & Sons, Ltd.     

The advantages of robust control of pulse amplitude modulation series–parallel load induction heating inverters

The goal of this paper is to present to the research community the benefit of utilizing advanced control methods for induction heating inverters in comparison with the existing classical control methods and to promote their application. For this purpose, a robust controller and a classical PI controller for application in a high‐power series–parallel load induction heating inverter has been designed. For the robust controller designed, the series–parallel load inverter model is augmented with additive and multiplicative uncertainties for nonmagnetic material heating, and the H_∞ algorithm is utilized. To highlight the advantages of the robust controller designed in this research study, a comparison is made with the classical PI controller system. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust ℋ︁2 static output feedback design starting from a parameter‐dependent state feedback controller for time‐invariant discrete‐time polytopic systems

This paper investigates the problem of computing robust ??₂ static output feedback controllers for discrete‐time uncertain linear systems with time‐invariant parameters lying in polytopic domains. A two stages design procedure based on linear matrix inequalities is proposed as the main contribution. First, a parameter‐dependent state feedback controller is synthesized and the resulting gains are used as an input condition for the second stage, which designs the desired robust static output feedback controller with an ??₂ guaranteed cost. The conditions are based on parameter‐dependent Lyapunov functions and, differently from most of existing approaches, can also cope with uncertainties in the output control matrix. Numerical examples, including a mass–spring system, illustrate the advantages of the proposed procedure when compared with other methods available in the literature. Copyright © 2009 John Wiley & Sons, Ltd.     

Optimal trajectory generation and robust flatness–based tracking control of quadrotors

This work proposes an optimal trajectory generation and a robust flatness–based tracking controller design to create a new performance guidance module for the quadrotor in dense indoor environments. The properties of the differential flatness, the B‐spline, and the direct collocation method are exploited to convert the constrained optimization problem into a nonlinear programming one, which can be easily resolved by a classic solver. After that, the obtained optimal reference trajectory is applied to the dynamic quadrotor model and two different flatness‐based controllers, namely, one based on feedback linearization and one based on feedforward linearization, are developed and compared to ensure the trajectory tracking despite the existence of disturbances and parametric uncertainties. Numerical simulation is executed to evaluate the proposed optimal trajectory generation approach and the robust tracking strategies. It turns out that the controller based on feedforward linearization outperforms the feedback linearization one in robustness and permits obtaining a performance guidance law for an uncertain quadrotor system.     

Multiobjective fault‐tolerant fixed‐order/PID control of multivariable discrete‐time linear systems with unmeasured disturbances

In this paper, a multiobjective fault‐tolerant fixed‐order output feedback controller design technique is proposed for multivariable discrete‐time linear systems with unmeasured disturbances. Initially, a multiobjective fixed‐order controller is designed for the system by transforming the problem of tuning the parameters of the controller into a static output feedback problem and solving a mixed H₂/H_∞ optimization problem with bilinear matrix inequalities. Subsequently, the fixed‐order controller is used to construct the closed‐loop system and an active fault‐tolerant control scheme is applied using the input/output data collected from the controlled system. Motivated by its popularity in industry, the proposed method is also used to tune the parameters of proportional‐integral‐derivative controllers as a special case of structured controllers with the fixed order. Two numerical simulations are provided to demonstrate the design procedure and the flexibility of the proposed technique.     

Robust H∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay

This paper investigates the problem of control design for a class of uncertain switched singular systems with time‐varying delay. Under mode‐dependent average dwell time and using an appropriate Lyapunov‐Krasovskii functional, the exponential admissibility of the system is analyzed. In order to obtain less conservative conditions, the delay partitioning technique is adopted as well as the improved reciprocally convex approach. By means of the developed admissibility condition, a static output feedback controller is then designed using linear matrix inequality approach. Moreover, by solving an optimization convex problem with constraints, the switched controller is developed to ensure simultaneously the stability of the closed‐loop system and satisfy an optimized upper bound of both the linear quadratic guaranteed cost and the H_∞ norm. Numerical examples are proposed to verify the efficiency and the merits of the method proposed.     

Robust H∞ performance analysis for uncertain discrete‐time singular systems with time‐varying delays

This paper considers the problem of robust H∞ performance analysis for uncertain discrete‐time singular systems with time‐varying delays. Firstly, a delay‐dependent stability criterion under the H∞ performance index for the systems is given based on constructing a generalized Lyapunov–Krasovskii function and introducing a new difference inequality. Then, a sufficient condition ensuing the system to be regular, causal as well as stable for all admissible uncertainties is proposed in terms of a set of strict linear matrix inequalities (LMIs). Finally, we provide examples to show the reduced conservatism and effectiveness of the proposed conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

Design of robust nonfragile H∞ controller for uncertain nonlinear polynomial systems

This paper is concerned with the robust H_∞ nonfragile controller design for a particular class of nonlinear systems, namely, the perturbed polynomial systems, which are subject to unstructured bounded uncertainties in both the system model and the control law. Combining the Lyapunov stability theory, properties of linear matrix inequality, and Kronecker product properties, a sufficient condition of robust H_∞ nonfragile control design is proposed. More specifically, we propose a robust H_∞ controller of nonlinear polynomial systems with additive unstructured uncertainties and variation in the control law itself that guarantee the stability and the attenuation of external perturbations. Two examples are provided to illustrate the effectiveness of the proposed approach.