A nonparametric approach to design robust controllers for uncertain systems: Application to an air flow heating system

This paper presents an approach to design robust fixed structure controllers for uncertain systems using a finite set of measurements in the frequency domain. In traditional control system design, usually, based on measurements, a model of the plant, which is only an approximation of the physical system, is first built, and then control approaches are used to design a controller based on the identified model. Errors associated with the identification process as well as the inevitable uncertainties associated with plant parameter variations, external disturbances, measurement noise, etc. are expected to all contribute to the degradation of the performance of such a scheme. In this paper, we propose a nonparametric method that uses frequency-domain data to directly design a robust controller, for a class of uncertainties, without the need for model identification. The proposed technique, which is based on interval analysis, allows us to take into account the plant uncertainties during the controller synthesis itself. The technique relies on computing the controller parameters for which the set of all possible frequency responses of the closed-loop system are included in the envelope of a desired frequency response. Such an inclusion problem can be solved using interval techniques. The main advantages of the proposed approach are: (1) the control design does not require any mathematical model, (2) the controller is robust with respect to plant uncertainties, and (3) the controller structure can be chosen a priori, which allows us to select low-order controllers. To illustrate the proposed method and demonstrate its efficacy, an application to an air flow heating system is presented.     

Robust stabilization of load frequency control system under networked environment

The deregulation of the electricity market made the open communication infrastructure an exigent need for future power system. In this scenario dedicated communication links are replaced by shared networks. These shared networks are characterized by random time delay and data loss. The random time delay and data loss may lead to system instability if they are not considered during the controller design stage. Load frequency control systems used to rely on dedicated communication links. To meet future power system challenges these dedicated networks are replaced by open communication links which makes the system stochastic. In this paper, the stochastic stabilization of load frequency control system under networked environment is investigated. The shared network is represented by three states which are governed by Markov chains. A controller synthesis method based on the stochastic stability criteria is presented in the paper. A one-area load frequency control system is chosen as case study. The effectiveness of the proposed method for the controller synthesis is tested through simulation. The derived proportion integration (PI) controller proves to be optimum where it is a compromise between compensating the random time delay effects and degrading the system dynamic performance. The range of the PI controller gains that guarantee the stochastic stability is determined. Also the range of the PI controller gains that achieve the robust stochastic stability is determined where the decay rate is used to measure the robustness of the system.     

The optimal projection equations with Petersen-Hollot bounds:robust stability and performance via fixed-order dynamic compensationfor systems with structured real-valued parameter uncertainty

A feedback control design problem involving structured real-valued plant parameter uncertainties is considered. A quadratic Lyapunov bound suggested by recent work of I.R. Petersen and C.V. Hollot (1986) is utilized in conjunction with the guaranteed cost approach of S.S.L. Chang and T.K.C. Peng (1972) to guarantee robust stability with robust performance bound. Necessary conditions that generalize the optimal projection equations for fixed-order dynamic compensation are used to characterize the controller that minimizes the performance bound. The design equations thus effectively serve as sufficient conditions for synthesizing dynamic output-feedback controllers that provide robust stability and performance     

Stability and weighted sensitivity analysis of robust controller for heat exchanger

This study presents a parametric system identification approach to estimate the dynamics of a chemical plant from experimental data and develops a robust PID controller for the plant. Parametric system identification of the heat exchanger system has been carried out using experimental data and prediction error method. The estimated model of the heat exchanger system is a time-delay model and a robust PID controller for the time-delayed model has been designed considering weighted sensitivity criteria. The mathematical background of parametric system identification, stability analysis, and ${{\rm H}_\infty }$ weighted sensitivity analysis have been provided in this paper. A graphical plot has been provided to determine the stability region in the $( {{K_{\rm p}},{K_{\rm i}}} )$, $( {{K_{\rm p}},{K_{\rm d}}} )$ and $( {{K_{\rm i}},{K_{\rm d}}} )$ plane. The stability region is a locus dependent on parameters of the controller and frequency, in the parameter plane.     

Stabilization of perturbed system via IMC: An application to load frequency control

This paper proposes a robust controller for a parametric uncertain system of order three. The scheme conceptualizes the approach of selecting the worst-case plant and then the controller is designed using the internal model control principle which constitutes the reduced model of worst-case plant. The beauty of the proposed approach is that even though the plant is uncertain, the complete robust stability analysis and controller design is carried out by a single linear model. As an illustrative example, a load frequency control (LFC) problem is considered for single- and multi-area power systems in presence of unexpected disturbances, parametric uncertainties and physical constraints. The proposed controller is also applied to the network topology similar to standard IEEE 39 bus system (New England 10 machine test system) to validate the more realistic LFC application. Simulation studies show that the proposed controller brings robust and fast disturbance rejection attributes.     

机器人柔性手臂混合ITAE最佳鲁棒控制研究

机器人柔性手臂动力学模型的复杂性及客观系统中的不确定因素,使传统的控制系统很难达到预定的控制要求,寻求鲁棒性强的控制策略势在必行。针对模型参数及扰动的不确定性,进行混合ITAE最佳控制、H∞PID鲁棒控制策略研究,同时利用遗传算法(GA)的隐含并行性和全局搜索特点整定控制器的控制参数以达到混合ITAE、H∞优化性能,并用MATLAB软件进行数值仿真,结果表明这种控制设计方法适用于柔性机器人手臂的控制。     

Robust strict positive realness: new results for intervalplant-controller families

A frequency domain approach is used to derive several robust strict positive realness results for interval plants and interval plant plus controller families of transfer functions. Based on simple frequency domain properties of transfer functions, the approach provides a framework for obtaining new results and constructing easy proofs of several important existing results on robust strict positive realness. The main new result states that the minimum of the real part of the transfer functions belonging to an interval plant controller family is achieved on one of the 32 Kharitonov segments of the interval plant. The argument used in the proof is of wider interest and suggests easy ways of proving that robustness of other different frequency properties of interval plant plus controller families of transfer functions, such as robust stability of H_∞-norm computation, can be deduced from a fixed number of segments of transfer functions of the family     

基于LMI的非线性摄动系统鲁棒绝对稳定性判据

讨论了前馈通道同时存在对象和控制器的范数摄动,而反馈通道存在扇区非线性的摄动系统的稳定性问题.基于H∞理论和LMI方法,得到了一组由线性矩阵不等式表达的充分性条件,建立了判断非线性摄动系统鲁棒绝对稳定性的新判据.     

Reducing conservatism in the design of a robust gain-scheduled controller for non-linear chemical processes

A robust control approach has been used to design gain-scheduled controllers, which guarantee closed-loop stability and performance. The inherent conservatism of robust control results in smaller ranges of parameters that satisfy the design criteria and consequently in degraded performance. The main focus of this paper is to reduce the conservatism to enhance the efficiency of the robust design method. Two approaches, the use of parameter-dependent Lyapunov condition and calculation of saturation factor bounds, are proposed to reduce the conservatism of the controller design.     

Improvement in DTC-SVM of AC drives using a new robust adaptive control algorithm

In this paper a new robust adaptive speed controller algorithm for AC motor drives is presented. The main feature of this algorithm is that minimum synthesis is required to implement the strategy. MCS algorithm is a significant development of MRAC. The stability of the proposed system is achieved through Popov’s Hyperstability criteria. The new algorithm appeared to be robust in the face of totally unknown plant dynamics, external disturbances and parameter variations with the plant. Finally, a new approach has been successfully implemented on DTC-SVM. Extensive simulation results are presented to validate the proposed technique. The system is tested at different speeds and a very satisfactory performance has been achieved.     

Design of robust digital controllers and sampling-time selection for SISO systems

The stability of a digital control system and its performance in terms of the continuous plant output are studied. A two-step controller design is proposed. In the first step, the assumption of no modelling error is made and a controller that combines properties of the algorithm that minimizes the sum of squared errors and a deadbeat-type algorithm is designed so that no intersample rippling appears. In the second step, a filter is designed so that appropriate conditions which guarantee robust stability and performance in the presence of model-plant mismatch are satisfied. The effect of the sampling time on the achievable performance and the robustness properties of the system is examined and the results are incorporated in a complete procedure for sampling-time selection and robust controller design. Finally, the procedure and some theoretical implications are illustrated with examples.     

改进型内模控制系统的稳定性与鲁棒跟踪条件

为了改善系统的响应性能或解决常规内模控制不能用于不稳定对象的问题,通常在常规内模控制结构中增设一个反馈环节,但这种改进型内模控制系统的性能分析尚缺乏系统的、令人满意的结果．为此,利用基于传递函数互质分解的频域理论,系统地分析了这种改进型内模控制系统的稳定性和稳态性能,得到了保证系统内稳定和鲁棒跟踪的一般性结论,并且无论控制对象稳定与否、系统连续或离散,该结论都适用．     

A closed-loop data based test for robust performance improvement in iterative identification and control redesigns

In robust iterative identification and control redesign techniques, a stabilizing controller connected in a closed loop is normally replaced by an alternative attractive stabilizing controller to improve robustness and performance of the closed-loop system. In this paper, novel test methods are proposed to check whether a new stabilizing controller improves performance or not when the existing controller is replaced by this new controller in the closed loop. The proposed tests are based on closed-loop data and no plant model, and can be used for both the SISO and MIMO linear time-invariant systems. For the proposed tests, the plant dynamics is assumed to be unknown whereas the existing and new controller transfer function matrices are known to the designer. These assumptions are common in iterative identification and control redesign techniques. The performance improvement test methods proposed in this paper build on the experimental set-up proposed in Dehghani, Lecchini, Lanzon, and Anderson (2009) which was used to only check whether controllers ensure internal stability of a feedback interconnection or not. In this paper, new test methods are proposed to ascertain robust performance improvement that cannot be obtained from test results of Dehghani et al. (2009). A numerical example is illustrated to show effectiveness of the proposed test methods.     

Operator‐based robust control for nonlinear plants with uncertain non‐symmetric backlash

This paper presents an operator‐based robust nonlinear control method for nonlinear plants with uncertain non‐symmetric backlash. The control design is achieved by introducing operator‐based robust right coprime factorization. In more detail, using an operator‐theoretic approach, the uncertain non‐symmetric backlash is described as a generalized Lipschitz operator and a bounded parasitic term. Since the generalized Lipschitz operator is unknown, a new robust condition using robust right coprime factorization is proposed to guarantee robust stability of the controlled plant with the uncertain backlash. As a result, based on the proposed robust condition, a stabilized plant is obtained. For eliminating the effect from the parasitic term to ensure the output tracking performance, a nonlinear tracking controller is designed. Simulation results are presented to validate the effectiveness of the proposed control design method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust PID controller tuning based on the constrained particle swarm optimization

This paper proposes a novel tuning strategy for robust proportional-integral-derivative (PID) controllers based on the augmented Lagrangian particle swarm optimization (ALPSO). First, the problem of PID controller tuning satisfying multiple H_∞ performance criteria is considered, which is known to suffer from computational intractability and conservatism when any existing method is adopted. In order to give some remedy to such a design problem without using any complicated manipulations, the ALPSO based robust gain tuning scheme for PID controllers is introduced. It does not need any conservative assumption unlike the conventional methods, and often enables us to find the desired PID gains just by solving the constrained optimization problem in a straightforward way. However, it is difficult to guarantee its effectiveness in a theoretical way, because PSO is essentially a stochastic approach. Therefore, it is evaluated by several simulation examples, which demonstrate that the proposed approach works well to obtain PID controller parameters satisfying the multiple H_∞ performance criteria.     

Controller design for nonlinear systems using the Contoured Robust Controller Bode plot

In this paper, we develop the Contoured Robust Controller Bode (CRCBode) plot and demonstrate its use in the design of robust controllers for nonlinear single‐input single‐output (SISO) systems. The CRCBode plot shows contours (level sets) of a robust performance quantity on the Bode magnitude and phase plots of the controller. An iterative frequency domain loop‐shaping design approach is employed to eliminate all intersections of the controller frequency response with certain ‘forbidden regions,’ indicating that a standard SISO robust stability and performance criterion is satisfied. Nonlinearities are accounted for by avoiding the maximum forbidden regions over a structured uncertainty set consisting of linearizations of the system dynamics about several operating points. We demonstrate this technique by designing and experimentally verifying a flow‐rate controller for a butterfly‐valve based liquid cooling system, which is robust to valve nonlinearities and flow disturbances. Finally, we compare this compensator with one generated using an automated H _∞ synthesis algorithm and discuss the advantages of the CRCBode approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust control design using eigenstructure assignment and multi-objective optimization

This paper develops a new approach to multiple objective optimization design for robust multivariable control systems, based on eigenstructure assignment and genetic algorithms. It considers various performance indices (or cost functions) in the objectives, which are individual eigenvalue sensitivity functions, and the sensitivity and the complementary sensitivity functions in the frequency domain, instead of a single performance index for a control system. Based on these performance indices, the robustness criteria are expressed by a set of inequalities. The paper will make full use of the freedom provided by eigenstructure assignment to find a controller to satisfy the robustness criteria. A numerical algorithm for multi-objective optimization using genetic algorithm approaches is developed and applied to the simulation of a distillation column control system design     

性能指标含交叉项的不确定线性系统鲁棒保稳定控制

针对不确定线性系统,提出了一种性能指标中含交叉项的鲁棒保稳定控制系统分析和设计方法。建立了改进的鲁棒回差方程,给出了闭环系统鲁棒保稳定的充分条件,增益和相位裕度描述形式,以及鲁棒保稳定控制器设计方法。并以造纸打过程为实例给出了重棒保稳定控制系统的设计和仿真。     

Fixed-architecture controller synthesis for systems with input–output time-varying nonlinearities

In this paper we develop a fixed-architecture controller analysis and synthesis framework that addresses the problem of multivariable linear time-invariant systems subject to plant input and plant output time-varying nonlinearities while accounting for robust stability and robust performance over the allowable class of nonlinearities. The proposed framework is based on the classical Luré problem and the related Aizerman conjecture concerning the stability of a feedback loop involving a sector-bounded nonlinearity. Specifically, we extend the classical notions of absolute stability theory to guarantee closed-loop stability of multivariable systems in the presence of input nonlinearities. In order to capture closed-loop system performance we also consider the minimization of a quadratic performance criterion over the allowable class of input nonlinearities. Our approach is directly applicable to systems with saturating actuators and provides full and reduced-order dynamic compensators with a guaranteed domain of attraction. The principal result is a set of constructive sufficient conditions for absolute stabilization characterized via a coupled system of algebraic Riccati and Lyapunov equations. The effectiveness of design approach is illustrated by several numerical examples. © 1997 John Wiley & Sons, Ltd.     

Design of robust gain-scheduled PI controllers for nonlinear processes

Gain-scheduling has proven to be a successful design methodology in many engineering applications. However, in the absence of a sound theoretical analysis, these designs come with no guarantees of robust stability, performance or even nominal stability of the overall gain-scheduled deign.This paper presents such an analysis for one type of nonlinear gain-scheduled control system based on the process input for nonlinear chemical processes. A methodology is also proposed for the design and optimization of the robust gain-scheduled PI controller. Conditions which guarantee robust stability and performance are formulated as a finite set of linear matrix inequalities (LMIs) and hence, the resulting problem is numerically tractable. Issues of modeling error and input-saturation are explicitly incorporated into the analysis. A simulation study of a nonlinear continuous stirred tank reactor (CSTR) process indicates that this approach can produce efficient sub-optimal robust gain-scheduled controllers.