A generalised optimal linear quadratic tracker with universal applications – part 1: continuous-time systems

This paper presents a generalised optimal linear quadratic analog tracker (LQAT) with universal applications for the continuous-time (CT) systems. This includes: (1) a generalised optimal LQAT design for the system with the pre-specified trajectories of the output and the control input and additionally with both the input-to-output direct-feedthrough term and known/estimated system disturbances or extra input/output signals; (2) a new optimal filter-shaped proportional plus integral state-feedback LQAT design for non-square non-minimum phase CT systems to achieve a minimum phase-like tracking performance; (3) a new approach for computing the control zeros of the given non-square CT system; and (4) a one-learning-epoch input-constrained iterative learning LQAT design for the repetitive CT system.     

A new control method for MIMO first order time delay non-square systems

This paper proposes a new method using internal model control (IMC) to design Smith delay compensation decoupling controller for multivariable non-square systems with transfer function elements consisting of first order + time delay. This proposed method is applied to a shell control problem in multiple-input-multiple-output (MIMO) first order plus dead time non-square systems in which the number of input variables exceeds the number of output variables, with input and output variables being 3 and 2 respectively. This method does not only dynamically compensate for shortcoming caused by static decoupling but also overcomes the impact of model error on system performance caused by model approximation and uncertainty. In other words, the design method proposed in this paper is capable of significantly improving dynamic quality and robustness of the control system as can be seen from the simulation results. Moreover, this new method is simple and easy to implement. Integral of squared error (ISE) performance criterion is employed to quantitatively evaluate the design method.     

PLS based dEWMA run-to-run controller for MIMO non-squared semiconductor processes

This paper focuses on the modification of the PLS (partial least squares) modeling. The new method allows incorporation of a dEWMA (double exponentially weighted moving average) control algorithm into the standard run-to-run controller design for semiconductor processes. The resulting structure of the PLS model can extract the strongest relationship between the input and the output variables. It is particularly useful for inherent noise suppression. In addition, the resulting non-square MIMO control system can be decomposed into a multi-loop control system by employing pre-compensators and post-compensators of the PLS model, which is constructed from the input and output loading matrices. Subsequently, the conventional dEWMA controller can be separately and directly applied to each SISO control loop. The performance of the proposed method is illustrated through a chemical–mechanical polishing process in the manufacturing of the semiconductor.     

多变量预测控制系统稳态解的相容性与唯一性分析

多变量控制系统在结构形态上可以划分为方系统和非方系统, 非方系统可进一步划分为胖系统和瘦系统. 对瘦系统和胖系统, 预测控制系统分别可能出现输出静差和输入稳态值不确定问题. 本文从控制输入与被控输出稳态关系入手, 将上述问题归结为非齐次线性方程组的相容性与唯一性问题. 通过非齐次方程组解的判定定理分析了多变量预测控制系统稳态解出现相容性和唯一性问题的原因, 并由此给出了双层结构控制策略及解决方案. 上层稳态优化方法从理论上解决了瘦系统的相容性问题, 并从胖系统的无穷多个相容解中找到最优解. 下层集成控制输入目标的预测控制从根本上保证了胖系统控制输入稳态解的唯一性, 并实现了方系统与非方系统预测控制在算法描述上的统一. 仿真结果验证了本文提出的双层结构预测控制算法的有效性, 即多变量预测控制系统稳态解既是相容的又是唯一的.     

Robust observer-based optimal linear quadratic tracker for five-degree-of-freedom sampled-data active magnetic bearing system

This paper presents three observer/Kalman filter identification (OKID) approaches and develops a robust observer-based optimal linear quadratic digital tracker (LQDT) for the five-degree-of-freedom (five-DOF) sampled-data active magnetic bearing (AMB) system with various disturbances. The more detailed objectives are: (i) to construct both an equivalent linear time-invariant discrete-time model and its state estimator via the proposed OKID approaches for the AMB system, which might be an unknown nonlinear time-varying unstable system with both a specified rotation speed and a sampling rate; (ii) to provide an adaptive disturbance estimation scheme, which establishes an equivalent input disturbance (EID) estimator for the AMB system with unexpected disturbances; and (iii) to develop a robust observer-based optimal LQDT for the sampled-data AMB system with both a pre-specified time-varying speed and unexpected disturbances. The developed LQDT is able to recover the displacement of the rotor to the pre-specified trajectory position whenever it deviates from such trajectory.     

Optimal Control for a Class of Complex Singular System Based on Adaptive Dynamic Programming

This paper presents a new design approach to achieve decentralized optimal control of high-dimension complex singular systems with dynamic uncertainties. Based on robust adaptive dynamic programming (robust ADP) method, controllers for solving the singular systems optimal control problem are designed. The proposed algorithm can work well when the system model is not exactly known but the input and output data can be measured. The policy iteration of each controller only uses their own states and input information for learning, and do not need to know the whole system dynamics. Simulation results on the New England 10-machine 39-bus test system show the effectiveness of the designed controller.      

广义输出误差前馈自校正鲁棒控制器

本文提出了一种新型的隐式自校正鲁棒控制器,即在最优零极点配置自校正控制器的基础上,引入了一个广义输出误差前馈控制信号,文中给出了广义输出误差前馈控制器的设计准则及仿真研究结果。     

Optimal behaviour prediction using a primitive-based data-driven model-free iterative learning control approach

This paper suggests an optimal behaviour prediction mechanism for Multi Input-Multi Output control systems in a hierarchical control system structure, using previously learned solutions to simple tasks called primitives. The optimality of the behaviour is formulated as a reference trajectory tracking problem. The primitives are stored in a library of pairs of reference input/controlled output signals. The reference input primitives are optimized at the higher hierarchical level in a model-free iterative learning control (MFILC) framework without using knowledge of the controlled process. Learning of the reference input primitives is performed in a reduced subspace using radial basis functions for approximations. The convergence of the MFILC learning scheme is achieved via a Virtual Reference Feedback Tuning design of the feedback controllers in the lower level feedback control loops. The new complex trajectories to be tracked are decomposed into the output primitives regarded as basis functions. Next, the optimal reference input fed to the control system in order to track the desired new trajectory is then recomposed from the reference input primitives. The efficiency of this approach is demonstrated on a case study concerning the control of a two-axis positioning mechanism, and the experimental validation is offered.     

A new PI optimal linear quadratic state-estimate tracker for continuous-time non-square non-minimum phase systems

Based on the proportional-integral-derivative (PID) filter-shaping approach, this paper presents a new proportional-plus-integral (PI) optimal linear quadratic state estimator (LQSE) for the continuous-time non-square and non-minimum phase (NMP) multivariable systems. Together with the recently developed optimal linear quadratic tracker (LQT), the proposed LQSE-based tracker is able to optimally achieve good minimum phase-like tracking performances for a non-square NMP multivariable system with unmeasurable states and arbitrary command inputs.     

Asymptotic rejection of unmatched general periodic disturbances in a class of non-minimum-phase non-linear systems

This article deals with asymptotic rejection of unmatched general periodic disturbances in nonminimum phase non-linear output feedback systems. The steady state responses are defined for unstable systems subject to general periodic disturbances, and the generalised gain and phase are defined for stable systems subject to general periodic disturbances. Based on the new definitions, new results are obtained for the equivalent input disturbance and disturbance estimation. An L _p -convergent estimate of the equivalent input disturbance is incorporated in the control design to ensure the asymptotic rejection of unmatched general periodic disturbances while maintaining the stability of the non-linear system.     

Data-driven output-feedback fault-tolerant control for unknown dynamic systems with faults changing system dynamics

This paper studies the data-driven output-feedback fault-tolerant control (FTC) problem for unknown dynamic systems with faults changing system dynamics. In a framework of active FTC, two basic issues are addressed: the fault detection employing only the measured input–output information; the controller reconfiguration to achieve optimal output-feedback control in the presence of multiple faults. To detect faults and write the system state via the input–output data, an approach to data-driven design of a residual generator with a full-rank transformation matrix is presented. An output-feedback approximate dynamic programming method is developed to solve the optimal control problem under the condition that the unknown linear time-invariant discrete-time plant has multiple outputs. According to the above results and the proposed input–output data-based value function approximation structure of time-varying plants, a model-free output-feedback FTC scheme considering optimal performance is given. Finally, two numerical examples and a practical example of a DC motor control system are used to demonstrate the effectiveness of the proposed methods.     

Distributed Periodic Event-Triggered Optimal Control of DC Microgrids Based on Virtual Incremental Cost

This article presents a distributed periodic eventtriggered(PET)optimal control scheme to achieve generation cost minimization and average bus voltage regulation in DC microgrids.In order to accommodate the generation constraints of the distributed generators(DGs),a virtual incremental cost is firstly designed,based on which an optimality condition is derived to facilitate the control design.To meet the discrete-time(DT)nature of modern control systems,the optimal controller is directly developed in the DT domain.Afterward,to reduce the communication requirement among the controllers,a distributed event-triggered mechanism is introduced for the DT optimal controller.The event-triggered condition is detected periodically and therefore naturally avoids the Zeno phenomenon.The closed-loop system stability is proved by the Lyapunov synthesis for switched systems.The generation cost minimization and average bus voltage regulation are obtained at the equilibrium point.Finally,switch-level microgrid simulations validate the performance of the proposed optimal controller.     

基于奇异值分解的内模控制方法及在非方系统中的应用

针对复杂工业生产过程中常常出现的输入与输出变量数目不相等的非方系统, 首次提出一种基于奇异值分解(Singular value decomposition, SVD)的内模控制(Internal model control, IMC)新方法. 该方法通过添加补偿项实现对非方系统的解耦并消除不可实现因素, 并应用SVD矩阵理论设计一种非对角型滤波器, 使控制系统不仅具备良好的高维解耦能力和响应速度快的优点, 而且因设置新型滤波结构而具备极强的鲁棒性. 仿真结果表明了这种方法的有效性和可靠性.     

Unknown input observer design and analysis for networked control systems

The insertion of communication networks in the feedback loops of control systems is a defining feature of modern control systems. These systems are often subject to unknown inputs in a form of disturbances, perturbations, or attacks. The objective of this paper is to design and analyse an observer for networked dynamical systems with unknown inputs. The network effect can be viewed as either a perturbation or time-delay to the exchanged signals. In this paper, we (1) review an unknown input observer (UIO) design for a non-networked system, (2) derive the networked unknown input observer (N_etUIO) dynamics, (3) design a N_etUIO such that the effect of higher delay order terms are nullified and (4) establish stability-guaranteeing bounds on the networked-induced time-delay and perturbation. The formulation and results derived in this paper can be generalised to scenarios and applications where the signals are perturbed due to a different source of perturbation or delay.     

Direct computation of infimum in discrete-time H∞-optimization using measurement feedback

A direct and non-iterative method for the computation of the infimum for a class of discrete-time H_∞ optimal control problem is considered in this paper. The problem formulation is fairly general and does not place any restrictions on any direct feedthrough terms of the given systems. The method is applicable to systems where (i) the transfer function from the disturbance input to the measurement output is free of unit circle invariant zeros and left invertible, and (ii) the transfer function from the control input to the controlled output of the given system is free of the unit circle invariant zeros and right invertible.     

Asymptotic Stabilisation of Multiple Input Nonlinear Systems via Sliding Modes

A dynamic feedback controller design method is proposed for multiple input systems. The method uses a novel choice of sliding surface to effect asymptotic linearisation of nonlinear differential input output systems and a class of state space systems. The stability of the overall system, that is a canonical state space form with a dynamic feedback, is analysed with a generalised Lyapunov approach plus an asymptotic analysis in a neighbourhood of the origin. The nonlinear system does not have to be expressed in regular form as is the case in many other sliding mode control approaches. A type of zero dynamics, which are the dynamics of the control, are involved. The resulting dynamic feedback is shown to provide chatter free control if the system is minimum phase with respect to the zero dynamics. The theoretical results are applied to Gas Jet systems with two controls.     

基于容错学习的智能车辆路径跟踪控制

针对复杂驾驶环境中智能车辆的路径跟踪问题,提出了一种新型自适应容错学习控制策略.为了便于路径跟踪控制器的设计,首先,创新地将车辆动力学转化为一种参数化形式.在此基础上,考虑到车辆动力系统的欠驱动特性,我们控制器设计中引入一种新型处理非方输入矩阵的方法.该方法不仅拓展了自适应学习算法的应用范围,同时也为处理一般非方动力系...     

Self-tuning adaptive control of cement raw material blending

A new, modified self-tuning (ST) minimum variance (MV) regulator algorithm developed for multiple input multiple output (MIMO) systems is presented with required average for finite time (RAFT). This control strategy has been developed for the self-tuning optimal control of cement raw material blending. After a brief survey of the technological background the algorithm of MIMO-ST-MV-RAFT control strategy is derived. A self-tuning blending control system is described with real-time experimental results illustrating the efficiency of the new multivariable regulator.     

Semi-global sampled-data output feedback disturbance rejection control for a class of uncertain nonlinear systems

This paper investigates the semi-global output feedback disturbance rejection control problem for a class of uncertain nonlinear systems with additive disturbances using linear sampled-data control. Aiming to reject the adverse effects caused by the uncertainties and unknown nonlinear perturbations which may not satisfy the strict feedback or feedforward structure, a new generalised discrete-time extended state observer is proposed to estimate the disturbance at sampling points. An output feedback disturbance rejection control law is then constructed in a sampled-data form which facilitates digital implementations. By selecting adequate control gains and a sufficiently small sampling period to restrain the state growth under a zero-order-hold input, the semi-global asymptotic stability of the hybrid closed-loop system and the disturbance rejection ability are proved. Both numerical example and an application of a single-link robot arm system demonstrate the feasibility and efficacy of the proposed method.     

Robust control applications

This paper (first presented as a plenary lecture at the Fifth IFAC Symposium on Robust Control Design, Toulouse, July 2006) demonstrates the practical importance of robust control theory by describing its application to two non-trivial practical control problems. Part 1 considers helicopter control and Part 2 addresses saturation problems in high-performance head-positioning servo systems in high-density hard-disk drives.In Part 1, we present the design and flight test of a new batch of H_∞ controllers for the Bell 205 helicopter. At the heart of each controller is an H_∞ loop-shaping controller, augmented with a hand-tuned reference filter to improve tracking performance and to reduce a perceived phase lag which pilots had complained of previously. Flight testing revealed that, with such an architecture, it was relatively easy to get Level 1 handling qualities ratings in low aggression manoeuvres. Further fine tuning resulted in Level 1 qualities for high aggression manoeuvres and one controller performed to Level 1 standard in all manoeuvres tested.In Part 2, we consider how robust control techniques can be used to design anti-windup compensators to counter performance and stability problems associated with saturating actuators in state-of-the-art hard-disk drive servo systems. A promising two-stage approach is given and illustrated with experimental results.