Computing actuator bandwidth limits for model reference adaptive control

Although model reference adaptive control theory has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the presence of actuator dynamics can seriously limit the stability and the achievable performance of adaptive controllers. In this paper, a linear matrix inequalities-based hedging approach is developed and evaluated for model reference adaptive control of uncertain dynamical systems in the presence of actuator dynamics. The hedging method modifies the ideal reference model dynamics in order to allow correct adaptation that is not affected by the presence of actuator dynamics. Specifically, we first generalise the hedging approach to cover a variety of cases in which actuator output and the control effectiveness matrix of the uncertain dynamical system are known and unknown. We then show the stability of the closed-loop dynamical system using Lyapunov-based stability analysis tools and propose a linear matrix inequality-based framework for the computation of the minimum allowable actuator bandwidth limits such that the closed-loop dynamical system remains stable. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.     

Wind turbine integrated structural and LPV control design for improved closed-loop performance

An iterative redesign algorithm is proposed to integrate the design of the structural parameters and a linear parameter-varying (LPV) controller for a three-bladed horizontal-axis wind turbine. The LPV controller is designed for an eighth-order lumped model of the wind turbine consisting of blades, drive-train and the tower. The lumped model response is matched with detailed open-loop numerical simulations using the Fatigue, Aerodynamics, Structures and Turbulence (FAST) code. The controller is scheduled in real-time based on the mean wind speed to account for the varying system dynamics. The objective is to track the operating trajectory meanwhile minimise the H _∞ performance index from the wind turbulence to the controlled output vector consisting of pitch angle, blade tip deflection, and the generator speed and torque. Sensitivity analysis of the closed-loop performance index with respect to the structural parameters of the system is examined. The integrated design problem is formulated as an iterative sequential controller/structure redesign to obtain the structural parameters and controller matrices corresponding to a local optimal performance index. Each step of the iterative procedure is formulated as a linear matrix inequality (LMI) optimisation problem that can be solved efficiently using available LMI solvers. The evolution of the structural parameters and performance index through the integrated design is illustrated. The FAST closed-loop simulations for two selected designs with the smallest values of the performance index demonstrate the improved performance of the overall system through the integrated structure/control redesign in both minimising the effect of the wind disturbance on the generator output power, and reducing the structural loads on the wind turbine.     

output feedback control for uncertain stochastic systems with time-varying delays

This paper deals with the problem of H_∞ output feedback control for uncertain stochastic systems with time-varying delays. The parameter uncertainties are assumed to be time-varying norm-bounded. The aim is the design of a full-order dynamic output feedback controller ensuring robust exponential mean-square stability and a prescribed H_∞ performance level for the resulting closed-loop system, irrespective of the uncertainties. A sufficient condition for the existence of such an output feedback controller is obtained and the expression of desired controllers is given.     

Robust H∞ nonlinear control via measurement feedback

This paper deals with the problem of finite-time-horizon robust H_∞ control via measurement feedback, for affine nonlinear systems with nonlinear time-varying parameter uncertainty. The problem addressed is the design of a control law, which processes the measured output and guarantees a prescribed level of closed-loop disturbance attenuation. Conditions for the existence of such a controller are obtained by solving an auxiliary control problem for a related system which is obtained from the original one by converting the parameter uncertainty into exogenous bounded energy signals. This approach allows us to apply the recently developed H_∞ nonlinear control techniques to solve the robust control problem. The problem is investigated in both the continuous- and discrete-time cases. The results are demonstrated by a simple example. © 1997 by John Wiley & Sons, Ltd.     

输入约束系统的滚动时域输出反馈控制方法研究

This paper addresses the H∞ output feedback control problem for discrete-time systems with actuator saturation. Initially, a constrained H∞ output feedback control approach is presented in the framework of linear matrix inequalities (LMI) optimization. Under certain assumptions on the disturbance energy bound, closed-loop H∞ performance is achieved. Furthermore, the moving horizon strategy is applied to an online management of the control performance so that the closed-loop system can satisfy control constraints in the case of unexpected large disturbances. A dissipation constraint is derived to achieve the moving horizon closed-loop system dissipative. Simulation results show that the constrained H∞ controller works effectively under the disturbance assumption and that the moving horizon H∞ controller can trade-off automatically between satisfying control constraints and enhancing performance.     

Robust intelligent backstepping tracking control for wheeled inverted pendulum

In this study, a robust intelligent backstepping tracking control (RIBTC) system combined with adaptive output recurrent cerebellar model articulation controller (AORCMAC) and H ^∞ control technique is proposed for wheeled inverted pendulums (WIPs) with unknown system dynamics and external disturbance. The AORCMAC is a nonlinear adaptive system with simple computation, good generalization capability and fast learning property. Therefore, the WIP can stand upright when it moves to a designed position stably. In the proposed control system, an AORCMAC is used to copy an ideal backstepping control, and a robust H ^∞ controller is designed to attenuate the effect of the residual approximation errors and external disturbances with desired attenuation level. Moreover, the all adaptation laws of the RIBTC system are derived based on the Lyapunov stability analysis, the Taylor linearization technique and H ^∞ control theory, so that the stability of the closed-loop system and H ^∞ tracking performance can be guaranteed. The proposed control scheme is practical and efficacious for WIPs by simulation results.     

LPV gain-scheduled control of SCR aftertreatment systems

Hydrocarbons, carbon monoxide and some of other polluting emissions produced by diesel engines are usually lower than those produced by gasoline engines. While great strides have been made in the exhaust aftertreatment of vehicular pollutants, the elimination of nitrogen oxide (NO _x ) from diesel vehicles is still a challenge. The primary reason is that diesel combustion is a fuel-lean process, and hence there is significant unreacted oxygen in the exhaust. Selective catalytic reduction (SCR) is a well-developed technology for power plants and has been recently employed for reducing NO _x emissions from automotive sources and in particular, heavy-duty diesel engines. In this article, we develop a linear parameter-varying (LPV) feedforward/feedback control design method for the SCR aftertreatment system to decrease NO _x emissions while keeping ammonia slippage to a desired low level downstream the catalyst. The performance of the closed-loop system obtained from the interconnection of the SCR system and the output feedback LPV control strategy is then compared with other control design methods including sliding mode, and observer-based static state-feedback parameter-varying control. To reduce the computational complexity involved in the control design process, the number of LPV parameters in the developed quasi-LPV (qLPV) model is reduced by applying the principal component analysis technique. An LPV feedback/feedforward controller is then designed for the qLPV model with reduced number of scheduling parameters. The designed full-order controller is further simplified to a first-order transfer function with a parameter-varying gain and pole. Finally, simulation results using both a low-order model and a high-fidelity and high-order model of SCR reactions in GT-POWER interfaced with MATLAB/SIMULINK illustrate the high NO _x conversion efficiency of the closed-loop SCR system using the proposed parameter-varying control law.     

Multi-objective performance optimisation for model predictive control by goal attainment

This article proposes an approach for performance tuning of model predictive control (MPC) using goal-attainment optimisation of the cost function weighting matrices. The approach is developed for three formulations of the control problem: (i) minimal and (ii) non-minimal design based on the same cost function and (iii) a non-minimal MPC approach with an explicit integral-of-error state variable and modified cost function. This approach is based on earlier research into multi-objective optimisation for proportional-integral-plus control systems. Simulation experiments for a 3-input, 3-output Shell heavy oil fractionator model illustrate the feasibility of MPC goal attainment for multivariable decoupling and attainment of a specific output response. For this example, the integral-of-error state variable offers improved design flexibility and hence, when it is combined with the proposed tuning method, yields an improved closed-loop response in comparison to minimal MPC.     

Robust controller design for simultaneous control of throttle pressure and megawatt output in a power plant unit

This paper presents an application of H_∞ and μ-synthesis controller design methods to a coal-fired power generation unit and compares the closed-loop performance and robustness of H_∞ and μ-synthesis control laws with those of an H₂ control law. The model which relates firing rate and turbine valve position inputs to throttle pressure and megawatt outputs presented by Ollat and Smoak in an earlier work is modified to match the test data from a Tennessee Valley Authority (TVA) power generation unit. All three controller synthesis procedures are applied to a two-input two-output plant model which has time delay, differential part, colored noise output disturbance, and sensor noise disturbance. Application of the procedures to the model shows that when the shape of the closed loop control signals of all three designs is closely matched, in the low-frequency range the μ-synthesis and H_∞ control laws have robustness much better than that of H₂ control law, while providing adequate robustness in the high-frequency range. H_∞ control law gives the best performance, and H₂ – the worst of the three designs, exhibiting the largest overshoot. The balancing procedure permits significant reduction of the order of the controllers without degradation in performance and robustness. The comparative evaluation of three designs shows that in power plant control problem H_∞ and μ-synthesis designs provide much more consistent and convenient performance/robustness trade-off than H₂ design. Copyright © 1999 John Wiley & Sons, Ltd.     

Optimal control problem in bond graph formalism

This paper presents a new way to derive an optimal control system for a specific optimisation problem, based on bond graph formalism. The procedure proposed concerns the optimal control of linear time invariant MIMO systems and can deal with both cases of the integral performance index, these correspond to dissipative energy minimization and output error minimization. An augmented bond graph model is obtained starting from the bond graph model of the system associated with the optimal control problem. This augmented bond graph, consisting of the original model representation coupled to an optimizing bond graph, supplies, by its bicausal exploitation, the set of differential-algebraic equations that analytically give the solution to the optimal control problem without the need to develop the analytical steps of Pontryagin’s method. The proof uses the Pontryagin Maximum Principle applied to the port-Hamiltonian formulation of the system.     

Iterative identification and control design with optimal excitation signals based on <Emphasis Type="Italic">υ</Emphasis>-gap

An iterative identification and control design method based on υ-gap is given to ensure the stability of closed-loop system and control performance improvement. The whole iterative procedure includes three parts: the optimal excitation signals design, the uncertainty model set identification and the stable controller design. Firstly the worst case υ-gap is used as the criterion of the optimal excitation signals design, and the design is performed via the power spectrum optimization. And then, an uncertainty model set is attained by system identification on the basis of the measure signals. The controller is designed to ensure the stability of closed-loop system and the closed-loop performance improvement. Simulation result shows that the proposed method has good convergence and closed-loop control performance. Supported by the National Natural Science Foundation of China (Grant Nos. 60574055, 60874073), the Specialized Research Fund for Doctoral Program of Higher Education of China (Grant No. 20050056037), and the Tianjin Science and Technology Keystone Project (Grant No. 08ZCKFJC27900)     

Output tracking control of a parallel-flow heat exchange process

In this paper, we consider an output tracking problem of a parallel-flow heat exchange process with distributed and boundary inputs. As the distributed inputs to the system, the output feedback control is first applied. Under zero boundary inputs, it is shown that the C₀-semigroup describing the closed-loop system satisfies the spectrum determined growth condition. Next, we apply a backstepping method to the design of the boundary inputs for output tracking. Our main result shows that the output of the system reaches a reference signal in finite time under both the output feedback control and the boundary control law derived by the backstepping method.     

Dynamic output feedback H ∞ control for networked control systems with quantisation and random communication delays

This article is concerned with the dynamic output feedback H _∞ control problem for networked control systems with quantisation and random communication delays, where the random communication delays from the sensor to the controller and from the controller to the actuator are considered simultaneously. A novel quantised random delay model is proposed, and by using this model, the relationship of the quantisations, delays and the system performance is studied. The quantiser considered here is dynamic and composed of an adjustable zoom parameter and a static quantiser. With the condition on the quantisation range and the error bound satisfied, a quantised H _∞ control strategy is derived such that the closed-loop system is exponentially mean-square stable and with a prescribed H _∞ performance bound. An example is presented to illustrate the effectiveness of the proposed method.     

从机器人输出反馈自适应神经控制中学习

针对系统参数完全未知且仅输出可测的机器人,使用径向基函数(RBF)神经网络和高增益观测器设计了一种自适应神经控制算法.该算法不仅实现了闭环系统所有信号的最终一致有界,而且沿周期跟踪轨迹实现了对未知闭环系统动态的确定学习.学过的知识可用来改进系统的控制性能,也可应用于后续相同或相似的控制任务以节约时间和能量.仿真研究表明了所设计的控制算法的正确性和有效性.     

Bounded real lemma and robust control of 2-D singular Roesser models

This paper discusses the problem of robust H_∞ control for linear discrete time two-dimensional (2-D) singular Roesser models (2-D SRM) with time-invariant norm-bounded parameter uncertainties. The purpose is the design of static output feedback controllers such that the resulting closed-loop system is acceptable, jump modes free, stable and satisfies a prescribed H_∞ performance level for all admissible uncertainties. A version of bounded realness of 2-D SRM is established in terms of linear matrix inequalities. Based on this, a sufficient condition for the solvability of the robust H_∞ control problem is solved, and a desired output feedback controller can be constructed by solving a set of matrix inequalities. A numerical example is provided to demonstrate the applicability of the proposed approach.     

High-performance decentralized control design for general interconnected systems with applications in cooperative control

This paper deals with the decentralized control of an interconnected system, where each subsystem has models of all other subsystems (subject to uncertainty). A decentralized controller is constructed based on a reference centralized controller. It is shown that when a priori knowledge of each subsystem about the other subsystems’ models is exact, then the decentralized closed-loop system can perform exactly the same as its centralized counterpart. An easy-to-check necessary and sufficient condition for the internal stability of the decentralized closed-loop system is obtained. Moreover, the stability of the closed-loop system in the presence of the perturbation in the parameters of the system is investigated, and it is shown that the decentralized control system is probably more robust than its centralized counterpart. A proper cost function is then defined to evaluate the closeness of the decentralized closed-loop system to the corresponding centralized control system. This enables the designer to obtain the maximum allowable standard deviation for the modelling errors of the subsystems to achieve a satisfactorily small relative performance deviation with a sufficiently high probability. Finally, the proposed method is exploited to design a near-optimal decentralized control law with respect to a quadratic cost function, whose performance can, under certain conditions, be equal to the minimum achievable performance index corresponding to the centralized LQR control law. The effectiveness of the proposed method is demonstrated in three numerical examples.     

Minimal energy covariance control

In general, the covariance controller which assigns a specified state covariance X to the system is not unique, and the whole set of such controllers can be parametrized by a skew-symmetric matrix S of appropriate dimension. This paper describes how to minimize the control energy by using this freedom and reveals some properties of closed-loop system poles with respect to S.     

H∞ control for a class of structured time-delay systems

In this paper, we design an H_∞ controller for a class of lower-triangular time-delay systems. Backstepping is applied to construct an explicit feedback controller, and the closed-loop system maintains internal stability and an L₂-gain from the disturbance input to the output. The design is delay-dependent. Simulations on an example system demonstrate the good performance of the proposed design.     

Linear programming and model predictive control

The practicality of model predictive control (MPC) is partially limited by the ability to solve optimization problems in real time. This requirement limits the viability of MPC as a control strategy for large scale processes. One strategy for improving the computational performance is to formulate MPC using a linear program. While the linear programming formulation seems appealing from a numerical standpoint, the controller does not necessarily yield good closed-loop performance. In this work, we explore MPC with an l₁ performance criterion. We demonstrate how the non-smoothness of the objective function may yield either dead-beat or idle control performance.     

Reliable observer-based H∞ control of uncertain state-delayed systems

This paper is concerned with the reliable H_∞ control design problem for linear state-delayed system using observed-based output feedback. It proposes a reliable control design scheme for the case of possibly a simultaneous presence of actuator failures and sensor failures. Modified algebraic Riccati inequalities are developed to solve the problem addressed. Based on this approach, observer-based feedback control laws are designed that guarantee closed-loop asymptotic stability and reduction of the effect of an augmented disturbance input on the controlled output of a prescribed level, not only when the system is operating properly, but also under actuator and sensor failures. A numerical example is presented to demonstrate the applicability and effectiveness of the proposed approach.