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.     

A model-free design of reduced-order controllers and application to a DC servomotor

This paper presents a new model-free technique to design fixed-structure controllers for linear unknown systems. In the current control design approaches, measured data are used to first identify a model of the plant, then a controller is designed based on the identified model. Due to errors associated with the identification process, degradation in the controller performance is expected. Hence, we use the measured data to directly design the controller without the need for model identification. Our objective here is to design measurement-based controllers for stable and unstable systems, even when the closed-loop architecture is unknown. This proposed method can be very useful for many industrial applications. The proposed control methodology is a reference model design approach which aims at finding suitable parameter values of a fixed-order controller so that the closed-loop frequency response matches a desired frequency response. This reference model design problem is formulated as a nonlinear programming problem using the concept of bounded error, which can then be solved to find suitable values of the controller parameters. In addition to the well-known advantages of data-based control methods, the main features of our proposed approach are: (1) the error is guaranteed to be bounded, (2) it enables us to avoid issues related to the use of minimization methods, (3) it can be applied to stable and unstable plants and does not require any knowledge about the closed-loop architecture, and (4) the controller structure can be selected a priori, which means that low-order controllers can be designed. The proposed technique is experimentally validated through a real position control problem of a DC servomotor, where the results demonstrate the efficacy of the proposed method.     

Design and experimental evaluation of robust controllers for a two-wheeled robot

The paper presents the design and experimental evaluation of two alternative μ-controllers for robust vertical stabilisation of a two-wheeled self-balancing robot. The controllers design is based on models derived by identification from closed-loop experimental data. In the first design, a signal-based uncertainty representation obtained directly from the identification procedure is used, which leads to a controller of order 29. In the second design the signal uncertainty is approximated by an input multiplicative uncertainty, which leads to a controller of order 50, subsequently reduced to 30. The performance of the two μ-controllers is compared with the performance of a conventional linear quadratic controller with 17th-order Kalman filter. A proportional-integral controller of the rotational motion around the vertical axis is implemented as well. The control code is generated using Simulink® controller models and is embedded in a digital signal processor. Results from the simulation of the closed-loop system as well as experimental results obtained during the real-time implementation of the designed controllers are given. The theoretical investigation and experimental results confirm that the closed-loop system achieves robust performance in respect to the uncertainties related to the identified robot model.     

Robust control of robot manipulators based on uncertainty and disturbance estimation

In this work, uncertainty and disturbance estimation (UDE) based robust trajectory tracking controller for rigid link manipulators was proposed. The UDE was employed to estimate the composite uncertainty that comprises the effects of system nonlinearities, external disturbances, and parametric uncertainties. A feedback linearization based controller was designed for trajectory tracking, and the same was augmented by the UDE‐estimated uncertainties to achieve robustness. The resulting controller however required measurement of joint velocities apart from the joint positions. To address the issue, an observer that employed the UDE‐estimated uncertainties for robustness was proposed, giving rise to the UDE‐based controller–observer structure. Closed‐loop stability of the overall system was established. The notable feature of the proposed design was that it neither required accurate plant model nor any information about the uncertainty. Also, the design needed only joint position measurements for its implementation. To demonstrate the effectiveness, simulation results of the proposed approach as applied to the trajectory tracking control of two‐link robotic manipulator and comparison of its performance with some of the well‐known existing controllers were presented. Lastly, hardware implementation of the proposed design for trajectory control of Quanser's single‐link flexible joint module was carried out, and it was shown that the proposed strategy offered a viable approach for designing implementable robust controllers for robots. Copyright © 2011 John Wiley & Sons, Ltd.     

参数摄动机械臂鲁棒控制器的演化设

对于存在参数区间摄动的机械臂，提出了一种利用遗传算法进行鲁棒控制器演化设计的方法．将具有给定结构的控制器的参数编码后作为控制器种群，将机械臂的摄动参数编码后作为受控对象种群；对两个种群进行双向演化操作，得到对区间摄动系统具有足够鲁棒性的控制器和最差控制性能所对应的受控对象模型．对存在参数摄动的二自由度机械臂进行鲁棒控制器设计的结果表明，所提出的方法是有效的．     

Bridging the gap between designed and implemented controllers via adaptive robust discrete sliding mode control

Bridging the gap between designed and implemented model-based controllers is a major challenge in the design cycle of industrial controllers. This gap is created due to (i) digital implementation of controller software that introduces sampling and quantization uncertainties, and (ii) uncertainties in the modeled plant's dynamics. In this paper, a new adaptive and robust model-based control approach is developed based on a nonlinear discrete sliding mode controller (DSMC) formulation to mitigate implementation imprecisions and model uncertainties, that consequently minimizes the gap between designed and implemented controllers. The new control approach incorporates the predicted values of the implementation uncertainties into the controller structure. Moreover, a generic adaptation mechanism will be derived to remove the errors in the nonlinear modeled dynamics. The proposed control approach is illustrated on a nonlinear automotive engine control problem. The designed DSMC is tested in real-time in a processor-in-the-loop (PIL) setup using an actual electronic control unit (ECU). The verification test results show that the proposed controller design, under ADC and model uncertainties, can improve the tracking performance up to 60% compared to a conventional controller design.     

An Iterative Method of the Structural-Parametric Design of Robust Systems with State Controllers

An iterative method for designing a robust control system with state controllers is proposed that includes a transformation of the plant structure to improve its controllability by correcting the singular values of the controllability Gramian and the subsequent synthesis of the basic controller for the corrected plant using modal control. This approach allows us to design systems satisfying the robust stability condition for the given intervals of variation of the plant parameters.     

Indirect adaptive techniques for fixed controller performance enhancement

This paper develops the adaptive disturbance estimate feedback schemes of a companion paper for enhancing the performance of controllers designed by off-line techniques. The developments are based on the parametrization theory for the class of all stabilizing controllers for a nominal plant, and the dual class of plants stabilized by a nominal controller. Such parametrization allows us conveniently to parametrize plant uncertainties for on-line identification and control purposes, minimizing the effects of unmodelled dynamics. Based on these parametrizations, along with prefiltering which minimizes the effect of unmodelled dynamics, standard adaptive stabilization, adaptive pole assignment, or adaptive linear quadratic schemes are shown to achieve controller enhancement. The idea is to exploit a priori information about a plant and design objectives in an off-line design, and yet exploit the power of adaptive techniques to learn and tune on-line. Attention is focused on techniques for fixed but uncertain plants.     

A Measurement‐Based Approach for Designing Fixed‐Order Controllers for Unknown Closed‐Loop Architecture

This paper presents a new technique to design fixed‐structure controllers for linear unknown systems using a set of measurements. In model‐based approaches, the measured data are used to identify a model of the plant for which a suitable controller can be designed. Due to the fact that real processes cannot be described perfectly by mathematical models, designing controllers using such models to guarantee some desired closed‐loop performance is a challenging task. Hence, a possible alternative to model‐based methods is to directly utilize the measured data in the design process. We propose an approach to designing structured controllers using a set of closed‐loop frequency‐domain data. The principle of such an approach is based on computing the parameters of a fixed‐order controller for which the closed‐loop frequency response fits a desired frequency response that describes some desired performance indices. This problem is formulated as an error minimization problem, which can be solved to find suitable values of the controller parameters. The main feature of the proposed control methodology is that it can be applied to stable and unstable plants. Additionally, the design process depends on a pre‐selected controller structure, which allows for the selection of low‐order controllers. An application of the proposed method to a DC servomotor system is presented to experimentally validate and demonstrate its efficacy.     

QFT-based design of force and contact transition controllers for a flexible link manipulator

This paper deals with the modeling, system identification and robust control of flexible link manipulators that are required to perform contact task operations. For a single flexible link (SFL) manipulator in contact, two infinite dimensional models are developed and dynamic differences with respect to the force sensing devices are examined. Generalized orthonormal basis functions (GOBFs) are adopted for system identification and new algorithms are developed that improve the identification of resonant systems. The identification results, combined with estimated measures of model uncertainties, are directly used in the design of robust controllers. For the contact transition control, a switching condition is proposed based on robust position and force controllers. The stability of the switching controller is examined using a piecewise quadratic Lyapunov approach. Both simulation and experimental results are presented showing the effectiveness of the proposed technique.     

Robust control of systems with fuzzy representation of uncertainties

In this paper, an approach is proposed to design robust controllers for uncertain systems with the linguistic uncertainties represented by fuzzy sets. With a provided technique, the fuzzy sets are best approximated by intervals (crisp sets). Then the Kharitonovs theorem is applied to construct a robust PID controller for the uncertain plant with time-invariant uncertainties represented by interval models. Also, for the uncertain system with linguistic values of the time-varying uncertainties best approximated by intervals (which are bounded), a robust sliding mode controller is developed to stabilize the uncertain system if the sliding coefficient conditions are satisfied. Moreover, the best approximation intervals are shown to be more related to the possibility distribution of the elements in the universes of discourse of fuzzy sets than the type of membership functions used for fuzzy sets. Examples and simulation results are included to indicate the design approach and the effectiveness of the proposed robust controller.This work is partly supported by the the R.O.C. National Science Council through Grant NSC 90-2213-E-197-002.     

基于连续故障模型的Delta算子系统可靠鲁棒H_∞控制

研究具有执行器故障的Delta算子线性不确定系统的可靠鲁棒H_∞问题.设计控制器,确保在执行器发生故障时闭环系统仍能保持鲁棒稳定,且满足给定的H_∞指标.针对执行器连续故障模型,运用线性矩阵不等式方法,得到Delta算子系统α-次优可靠鲁棒H_∞状态反馈控制器的存在条件和设计方法,并进一步给出了Delta算子系统最优可靠鲁棒H_∞控制器的设计方法.数值算例表明,该设计方法是有效而可行的.

Abstract：

The reliable robust H_∞ control problem is studied for the Delta operator systems with actuator failure.The purpose is to design a controller which can tolerate actuator failures,such that the Delta operator closed-loop system is asymptotic stable for all admissible uncertainties,and the H_∞-performance index of the closed-loop system is less than a given upper bound.A more practical model of actuator failure,continuous failure model,is considered.A sufficient condition for the existence of the state feedback α-suboptimal reliable robust H_∞ controllers is derived by using the linear matrix inequality approach.Then the design procedures of such controllers and optimal reliable robust H_∞ controllers are proposed respectively.A numerical example demonstrates the effectiveness and feasibility of the design methods.     

Robust performance optimization based on stochastic model errors: the stable case

Robust control aims to account for model uncertainty in design. Traditional methods for robust control typically assume knowledge of hard bounds on the system frequency response. However, this does not match well with system identification procedures which typically yield statistical confidence bounds on the estimated model. This paper explores a new procedure for obtaining a better match between robust control and system identification by using stochastic confidence bounds for robust control design. Given a nominal design, we set up an optimization problem which is aimed at reducing the statistical variability, measured in a mean square sense, from the nominal sensitivity. The proposed procedure is straightforward and leads to an easily computable solution for the final robust controller in the case of a stable plant and modest plant uncertainty. An illustrative example is provided which shows the advantages of the method. Copyright © 2002 John Wiley & Sons, Ltd.     

Robust reliable guaranteed cost control of positive interval systems with multiple time delays and actuator failure

This paper addresses the robust reliable guaranteed cost control problem of positive interval systems with multiple time delays and actuator failure for a given quadratic cost function. Through constructing a Lyapunov–Krasovskii functional, a sufficient condition for the existence of robust reliable guaranteed cost controllers is established such that the closed-loop system is positive and asymptotically stable, and the cost function is guaranteed to be no more than a certain upper bound. Based on the linear matrix inequality method, a criterion for the design of robust reliable guaranteed cost controllers is derived which can tolerate all admissible uncertainties as well as actuator failure. Moreover, a convex optimisation problem with linear matrix inequality constraints is formulated to design the optimal robust reliable guaranteed cost controller which minimises the upper bound of the closed-loop system cost. A numerical example is given to show the effectiveness of the proposed methods.     

一类2-D不确定离散系统的弹性保成本控制

当被控系统的数学模型存在不确定性时,需要设计鲁棒控制器才能使得受控系统稳定,然而,如果控制器本身也存在不确定性时,系统就会变得复杂难以控制,使用传统的鲁棒控制方法很难达到期望的控制目标,甚至不能保证受控系统的稳定性.本研究就是针对当系统模型和控制器同时存在不确定性时,给出了设计稳定控制器的简便方法.通过将控制器的不确定性分别表示为加法式和乘法式摄动,研究了以上两种系统的弹性保成本控制问题,并给出了相应控制器的设计方法.在主要结果推导过程中,巧妙运用了各种矩阵不等式放缩和等价参数变换等数学方法,最终将主要结果表示为线性矩阵不等式(LMI),利用Matlab的LMI工具箱,可以很方便地设计所需要的控制器.最后,对同一个受控系统,分别施加利用本文结果和已有结果设计的控制器,发现前者可以很好地控制系统,而后者却不能使受控系统稳定,从而验证了所得结果的有效性.     

基于调节函数的一类三角结构非线性系统的自适应滑模控制

针对一类三角结构的非线性系统,基于状态参考自适应控制算法和滑模控制技术,研究了其在非匹配未知参数和不确定性干扰下的跟踪控制问题,提出了自适应滑模控制策略,实现了不确定非线性系统的鲁棒输出跟踪.与一般自适应控制相比,允许系统存在非参数化的不确定性和未知扰动,增强了控制系统鲁棒性.仿真算例证明了理论研究成果的正确性和可行性.     

Input to state stability of min-max MPC controllers for nonlinear systems with bounded uncertainties

Min-max model predictive control (MPC) is one of the control techniques capable of robustly stabilize uncertain nonlinear systems subject to constraints. In this paper we extend existing results on robust stability of min-max MPC to the case of systems with uncertainties which depend on the state and the input and not necessarily decaying, i.e. state and input dependent bounded uncertainties. This allows us to consider both plant uncertainties and external disturbances in a less conservative way.It is shown that the input-to-state practical stability (ISpS) notion is suitable to analyze the stability of worst-case based controllers. Thus, we provide Lyapunov-like sufficient conditions for ISpS. Based on this, it is proved that if the terminal cost is an ISpS-Lyapunov function then the optimal cost is also an ISpS-Lyapunov function for the system controlled by the min-max MPC and hence, the controlled system is ISpS. Moreover, we show that if the system controlled by the terminal control law locally admits certain stability margin, then the system controlled by the min-max MPC retains the stability margin in the feasibility region.     

Robust grid‐oriented control of high voltage DC links embedded in an AC transmission system

Several studies have shown that the way to design controllers for the high‐voltage direct current (HVDC) links impacts the transient behavior of the electric system in which the latter are inserted. This can be exploited to improve the performances of the stability of the power system. In this paper, a robust multivariable control design for the converters of an HVDC link is proposed. It is based on the coordination of the control actions of the HVDC converters and the use of a control model. The latter takes into consideration, in addition to the dynamics that mostly impact the stability of the neighbor zone of the HVDC link, several cases of faulted situations modeled as uncertainties. An H_∞ controller allowed us to achieve robustness against such uncertainties. The new controller is tested in comparison with the standard vector control and an optimal linear quadratic controller using the EUROSTAG simulation software (Tractebel Engineering, Brussels, Belgium and Réseau de Transport d'Electricité (RTE) ‐ France) on both academic and realistic large‐scale power systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust distributed model predictive control of linear systems with structured time-varying uncertainties

In this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min–max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.     

Data-based supervisory control of uncertain systems with application to automatic drug delivery for anesthesia

Control of nonlinear noisy systems affected by large uncertainties is approached via the introduction of a supervisor which, whenever needed, switches on, in feedback to the plant, a controller selected from a finite set of precomputed controllers. A Lyapunov-based falsification criterion allows one to ensure robust stability in the presence of uncertain constant parameters and exogenous bounded disturbances without a priori information on the system. Applicability of the method is illustrated through simulations on an automatic drug delivery system for anesthesia.