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)     

Identification for control: Optimal input intended to identify a minimum variance controller

It is well known that the quality of the parameters identified during an identification experiment depends on the applied excitation signal. Prediction error identification using full order parametric models delivers an ellipsoidal region in which the true parameters lie with some prescribed probability level. This ellipsoidal region is determined by the covariance matrix of the parameters. Input design strategies aim at the minimization of some measure of this covariance matrix. We show that it is possible to optimize the input in an identification experiment with respect to a performance cost function of a closed-loop system involving explicitly the dependence of the designed controller on the identified model. In the present contribution we focus on finding the optimal input for the estimation of the parameters of a minimum variance controller, without the intermediate step of first minimizing some measure of the model parameter accuracy. We do this in conjunction with using covariance formulas which are not asymptotic in the model order, which is rather new in the domain of optimal input design. The identification procedure is performed in closed-loop. Besides optimizing the input power spectrum for the identification experiment, we also address the question of optimality of the controller. It is a wide belief that the minimum variance controller should be the optimal choice, since we perform an experiment for designing a minimum variance controller. However, we show that this may not always be the case, but rather depends on the model structure.     

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.     

Fixed‐order robust H∞ control and control‐oriented uncertainty set shaping for systems with ellipsoidal parametric uncertainty

In this paper, sufficient conditions for robust output feedback controller design for systems with ellipsoidal parametric uncertainty are given in terms of solutions to a set of linear matrix inequalities. A polynomial method is employed to design a fixed‐order controller that assigns closed‐loop poles within a given region of the complex plane and that satisfies an H_∞ performance specification. The main feature of the proposed method is that it can be extended easily for control‐oriented uncertainty set shaping using a standard input design approach. Consequently, the results can be extended to joint robust control/input design procedure whose controller structure and performance specifications are translated into the requirements on the input signal spectrum used in system identification. This way, model uncertainty set can be tuned for the robust control design procedure. The simulation results show the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

基于小波分解的MIMO系统辨识最优实验设计

提出了一种基于小波分解的MIMO系统辨识最优输入信号的设计方法,将小波的多 分辨率分析应用于MIMO系统的最小二乘辨识中,并且与闭环系统的控制性能指标关联起来, 从而得出一种最优实验的设计方法.由于小波变换的多分辨特性和良好的去相关作用(对有色 噪声的白化作用),这种方法能获得比普通的系统辨识方法更好的结果.仿真实验证明了这种方 法的有效性.     

Relations between uncertainty structures in identification for robust control

Various techniques of system identification exist that provide a nominal model and an uncertainty bound. An important question is what the implications are for the particular choice of the structure in which the uncertainty is described when dealing with robust stability/performance analysis of a given controller and when dealing with robust synthesis. It is shown that an amplitude-bounded (circular) uncertainty set can equivalently be described in terms of an additive, Youla parameter and ν-gap uncertainty. As a result, the choice of structure does not matter provided that the identification methods deliver optimal uncertainty sets rather than an uncertainty bound around a prefixed nominal model. Frequency-dependent closed-loop performance functions based on the uncertainty sets are again bounded by circles in the frequency domain, allowing for analytical expressions for worst-case performance and for the evaluation of the consequences of uncertainty for robust design. The results can be used to tune optimal experimental conditions in view of robust control design and in the further development of experiment-based robust control design methods.     

A decade of progress in iterative process control design: from theory to practice

One of the most active areas of research in the nineties has been the study of the interplay between system identification and robust control design. It has led to the development of “control-oriented identification design”, the paradigm being that, since the model is only a tool for the design of a controller, its accuracy (or its error distribution) must be tuned towards the control design objective. This observation has led to the concept of “iterative identification and control design” and, subsequently, to model-free iterative controller design, in which the controller parameters are iteratively tuned on the basis of successive experiments performed on the real plant, leading to better and better closed-loop behaviour. These iterative methods have found immediate applications in industry; they have also been applied to the optimal tuning of PID controllers. This paper presents the progress that has been accomplished in iterative process control design over the last decade. It is illustrated with some applications in the chemical industry.     

Robust MPC for systems with output feedback and input saturation

In this work, it is proposed an MPC control algorithm with proved robust stability for systems with model uncertainty and output feedback. It is assumed that the operating strategy is such that system inputs may become saturated at transient or steady state. The developed strategy aims at the case in which the controller performs in the output-tracking scheme following an optimal set point that is provided by an upper optimization layer of the plant control structure. In this case, the optimal operating point usually lies at the boundary of the region where the input is defined. Assuming that the system remains stabilizable in the presence of input saturation, the design of the robust controller is performed off-line and an on-line implementation strategy is proposed. At each sampling step, a sub optimal control law is obtained by combining control configurations that correspond to particular subsets of available manipulated inputs. Stability of the closed-loop system is forced by considering in the off-line step of the controller design, a state contracting restriction for the closed-loop system. To produce an offset free controller and to attend the case of unknown steady state, the method is developed for a state-space model in the incremental form. The method is illustrated with simulation examples extracted from the process industry.     

Least costly closed-loop performance diagnosis and plant re-identification

The inherent time-varying nature of dynamics in chemical processes often limits the lifetime performance of model-based control systems, as the plant and disturbance dynamics change over time. A critical step in the maintenance of model-based controllers is distinguishing control-relevant plant changes from variations in disturbance characteristics. In this paper, prediction error identification is used to evaluate a hypothesis test that detects if the performance drop arises from control-relevant plant changes. The decision rule is assessed by verifying whether an identified model of the true plant lies outside the set of all plant models that lead to adequate closed-loop performance. A unified experiment design framework is presented in the least costly context (i.e., least intrusion of nominal plant operation) to address the problem of input signal design for performance diagnosis and plant re-identification when the performance drop is due to plant changes. The application of the presented performance diagnosis approach to a (nonlinear) chemical reactor demonstrates the effectiveness of the approach in detecting the cause of an observed closed-loop performance drop based on the designed least costly diagnosis experiment.     

Controller performance assessment by frequency domain techniques

A system identification based method for assessing the performance of closed-loop systems is proposed, utilizing measures which coincide naturally with classical and modern frequency domain design specifications. Standard robust control system design methodologies seek to maximize closed-loop performance, subject to strict robustness requirements and include specifications for bandwidth and peak magnitude of the sensitivity and complementary sensitivity functions. Estimates of these transfer functions can be obtained by exciting the reference input with a zero mean, pseudo random binary sequence, observing the process output and error response, and developing a closed-loop model. Performance assessment is based on the comparison between the observed frequency response characteristics and the design specifications. Selection of appropriate model structures, experiment design, and model validation which will ensure reasonable estimates of the closed-loop transfer functions are considered in this paper. A case study involving the performance assessment of a packed bed tubular reactor control system is presented.     

Nonlinear controller tuning based on a sequence of identifications of linearized time-varying models

A novel algorithm for tuning controllers for nonlinear plants is presented. The algorithm iteratively minimizes a criterion of the control performance. In each iteration one experiment is performed with a reference signal slightly different from the previous reference signal. The input–output signals of the plant are used to identify a linear time-varying model of the plant which is then used to calculate an update of the controller parameters. The algorithm requires an initial feedback controller that stabilizes the closed loop for the desired reference signal and in its vicinity, and that the closed-loop outputs are similar for the previous and current reference signals. The tuning algorithm is successfully tested on a laboratory set-up of the Furuta pendulum.     

Control relevant identification for robust optimal control

This paper presents an approach to designing the input signal for an identification experiment, in which the process model estimate is to be used to formulate and solve for a robust (in a worst case sense) optimal controller. The input signal is designed to contain the information that is relevant for the end use of the model, that is for control purposes. The proposed approach uses sensitivity analysis to determine the input signal frequencies that are important with respect to a certain measure of achievable controller performance in conjunction with a frequency sampling filter model of the process. Based on the sensitivity analysis, an iterative experimental design methodology is suggested.     

Intelligent robust control design of a precise positioning system

This paper addresses an intelligent uncertainty function to improve the robust stability and performance of H _∞ controlled system in terms of reduced conservatism. The system is identified, output performance and control signal requirements are controlled by proper selection of performance and control weighting functions. Adaptive Neuro Fuzzy Inference System (ANFIS) learns the uncertainty bounds of model uncertainty that results from unmodeled dynamics and parameter variations, then the developed uncertainty weighting function will be included in the synthesis of the H _∞ controller. ν-gap measure is utilized to validate the intelligent identified uncertainty bounds and measure the stability of the designed H _∞ controlled system as well. Experimental results on a servo motion system reveal the advantages of combining intelligent uncertainty identification and robust control. Improved performance is achieved. The proposed approach also allows for iterative experiment design.     

基于状态观测器的约束鲁棒模型预测控制

模型不确定情况下的鲁棒问题是模型预测控制的一个根本问题。本文采用线性矩阵不等式(LMI)，研究多模型不确定性描述情况下的鲁棒模型预测控制问题。在输入输出约束条件下，最小化最坏情况下的无穷时域目标函数，获得保证系统稳定的基于状态观测器的状态反馈增益并且给出观测器增益的设计方法。实例说明算法可行且保证闭环系统渐近稳定。     

Hierarchical design of an electro-hydraulic actuator based on robust LPV methods

The paper proposes a hierarchical control design of an electro-hydraulic actuator, which is used to improve the roll stability of vehicles. The purpose of the control system is to generate a reference torque, which is required by the vehicle dynamic control. The control-oriented model of the actuator is formulated in two subsystems. The high-level hydromotor is described in a linear form, while the low-level spool valve is a polynomial system. These subsystems require different control strategies. At the high level, a linear parameter-varying control is used to guarantee performance specifications. At the low level, a control Lyapunov-function-based algorithm, which creates discrete control input values of the valve, is proposed. The interaction between the two subsystems is guaranteed by the spool displacement, which is control input at the high level and must be tracked at the low-level control. The spool displacement has physical constraints, which must also be incorporated into the control design. The robust design of the high-level control incorporates the imprecision of the low-level control as an uncertainty of the system.     

Perspectives on control-relevant identification through the use of interactive tools

System identification is an essential part of control design. Control engineers must devote substantial effort to identification issues in order to obtain suitable models for closed-loop control. Control-relevant identification seeks to both simplify the modelling task and improve the usefulness of the model by taking into account controller requirements during system identification. The advantages of this methodology can be better understood and appreciated through the interactive software tool described in this paper. The Interactive Tool for Control Relevant Identification (ITCRI) comprehensively captures the control-relevant identification process for the monovariable problem, from input design to closed-loop control, depicting these stages simultaneously and interactively in one screen. By simultaneously displaying both open- and closed-loop responses of the estimated models, ITCRI enables the user to readily assess how design variable choices during identification and control performance requirements impact model error and ultimately, closed-loop performance. Moreover, the work presents several examples which the aim to illustrate the tool and the considerations that arise when control requirements are taken into account during the identification stage.     

数据驱动闭环子空间预测控制方法研究与应用

提出一种完全数据驱动的闭环子空间辨识及预测控制器设计方法. 该方法完全由闭环系统的输入输出数据辨识子空间矩阵, 通过子空间矩阵的拆分, 排除了与扰动相关的模型输入, 进而获取子空间矩阵参数的无偏估计; 将辨识得到的闭环系统子空间矩阵描述直接作为预测模型, 设计预测控制器; 将其应用于某钢铁集团焦炉炭化室压力控制系统, 取得了良好的控制效果.

     

Wiener sliding-mode control for artificial pancreas: a new nonlinear approach to glucose regulation

Type 1 diabetic patients need insulin therapy to keep their blood glucose close to normal. In this paper an attempt is made to show how nonlinear control-oriented model may be used to improve the performance of closed-loop control of blood glucose in diabetic patients. The nonlinear Wiener model is used as a novel modeling approach to be applied to the glucose control problem. The identified Wiener model is used in the design of a robust nonlinear sliding mode control strategy. Two configurations of the nonlinear controller are tested and compared to a controller designed with a linear model. The controllers are designed in a Smith predictor structure to reduce the effect of system time delay. To improve the meal compensation features, the controllers are provided with a simple feedforward controller to inject an insulin bolus at meal time. Different simulation scenarios have been used to evaluate the proposed controllers. The obtained results show that the new approach outperforms the linear control scheme, and regulates the glucose level within safe limits in the presence of measurement and modeling errors, meal uncertainty and patient variations.     

Time complexity and model complexity of fast identification ofcontinuous-time LTI systems

The problem of fast identification of continuous-time systems is formulated in the metric complexity theory setting. It is shown that the two key steps to achieving fast identification, i.e., optimal input design and optimal model selection, can be carried out independently when the true system belongs to a general a priori set. These two optimization problems can be reduced to standard Gel'fand and Kolmogorov n-width problems in metric complexity theory. It is shown that although arbitrarily accurate identification can be achieved on a small time interval by reducing the noise-signal ratio and designing the input carefully, identification speed is limited by the metric complexity of the a priori uncertainty set when the noise/signal ratio is fixed