2D systems based robust iterative learning control using noncausal finite-time interval data

This paper uses a 2D system setting in the form of repetitive process stability theory to design an iterative learning control law that is robust against model uncertainty. In iterative learning control the same finite duration operation, known as a trial over the trial length, is performed over and over again with resetting to the starting location once each is complete, or a stoppage at the end of the current trial before the next one begins. The basic idea of this form of control is to use information from the previous trial, or a finite number thereof, to compute the control input for the next trial. At any instant on the current trial, data from the complete previous trial is available and hence noncausal information in the trial length indeterminate can be used. This paper also shows how the new 2D system based design algorithms provide a setting for the effective deployment of such information.     

An LMI approach for robust iterative learning control with quadratic performance criterion

This paper presents the design of iterative learning control based on quadratic performance criterion (Q-ILC) for linear systems subject to additive uncertainty. The robust Q-ILC design can be cast as a min–max problem. We propose a novel approach which employs an upper bound of the worst-case performance, then formulates a non-convex quadratic minimization problem to get the update of iterative control inputs. Applying Lagrange duality, the Lagrange dual function of the non-convex quadratic problem is equivalent to a convex optimization over linear matrix inequalities (LMIs). An LMI algorithm with convergence properties is then given for the robust Q-ILC design. Finally, we provide a numerical example to illustrate the effectiveness of the proposed method.     

For model-based control design, closed-loop identification gives better performance

We compare open loop versus closed loop identification when the identified model is used for control design, and when the system itself belongs to the model class, so that only variance errors are relevant. Our measure of controller performance (which is used as our design criterion for identification) is the variance of the error between the output of the ideal closed loop system (with the ideal controller) and that of the actual closed loop system (with the controller computed from the identified model). Under those conditions, we show that, when the controller is a smooth function of the input-output dynamics and the disturbance spectrum, the best controller performance is achieved by performing the identification in closed loop with an operating controller that we characterize. For minimum variance and model reference control design criteria, we show that this ‘optimal operating controller for identification’ is the ideal controller. This then leads to a suboptimal but feasible iterative scheme.     

一种新的实用PI控制闭环辨识方法

对于有PI控制器的闭环系统,提出一种辨识方法,可以在闭环系统运转下得到控制对象的开环传递函数.首先,根据闭环系统的衰减振荡曲线,近似地求出闭环控制系统的二阶加时滞(SOPDT)闭环传递函数.然后,用方框图等效法,在所得的闭环传递函数中将PI控制器分离出去;再通过比较系数就得到对象的开环传递函数.数字仿真和辨识实验表明此法有很好的辨识精度,计算量小且非常易于在线实现,具有比较重要的现实意义.     

一种参数优化的非线性离散系统鲁棒迭代学习控制方法

针对带有扰动的一类离散非线性系统的鲁棒迭代学习控制问题, 设计一种基于参数优化的迭代学习控制算法. 该算法能够保证在有初始状态误差和状态、输出扰动的情况下使闭环系统具有鲁棒BIBO 稳定性, 系统输出能够单调收敛于给定输出轨迹的邻域内; 在没有初始状态误差和扰动的情况下能够以零稳态误差跟踪给定输出轨迹. 最后通过仿真分析验证了所提出算法的有效性.

     

Time domain identification for robust control

In this paper, we are concerned with a problem of robust control-oriented system identification in the time domain. Based on the well-known Schur-Takagi-AAK Theorem, we propose a linear algorithm to obtain the nominal model of the plant to be identified and the minimal bound of the uncertainty of the nominal model error which is measured by H^∞-norm. It is also shown that, in the model set defined by the nominal model and the uncertainty bound, there exists at least one model which matches the prescribed input-output data given in the time domain.     

不确定性机器人系统自适应鲁棒迭代学习控制

利用Lyapunov方法, 提出了一种不确定性机器人系统的自适应鲁棒迭代学习控制策略, 整个系统在迭代域里是全局渐近稳定的. 所考虑的机器人系统同时包含了结构和非结构不确定性. 在设计时, 系统的不确定性被分解成可重复性和非重复性两部分, 并考虑了系统的标称模型. 在所提出的控制策略中, 自适应策略用来估算做法确定性的界, 界的修正与迭代学习控制量一样的迭代域得以实现的. 计算机仿真表明本文提出的控制策略是有效的.     

Switching supervisory control based on controller falsification and closed-loop performance inference

The paper addresses two of the basic issues of switching supervisory control (SSC): controller falsification (CF) and inference of candidate loop behaviour (ICLB). CF is approached as a statistical fault detection problem in that the currently operating controller is falsified as soon as a divergence trend is detected. This is achieved by considering a statistic (or residual) in the form of a ratio of closed-loop variables, and the falsification test is carried out by comparing at each time the ratio statistic with a threshold. It is constructively shown that the thresholds can be fixed, irrespective of the disturbance intensity, in such a way that faults are detected with probability one while probability of false alarms can be made as small as we wish. The ICLB issue is approached by the virtual reference approach. This allows one to obtain an inference of the performance of a candidate loop via a mean-square average of suitably filtered prediction errors. It is shown how a supervisory logic can be built by combining the results on CF with those on ICLB.     

Integrating closed-loop identification and control using control energy sensitivity

This paper extracts a plant model from an identified closed-loop system model, and proposes an iterative procedure to find high performance controllers. The algorithm uses control energy sensitivity to connect closed-loop modelling and control design. This sensitivity describes the gradient of the consumed control energy with respect to the achieved output covariance. Hence it captures the relative importance of each output channel in the closed-loop system behaviour. Therefore the identification incorporating control energy sensitivity can characterize models to generate a controller for achieving better closed-loop performance. The procedure is demonstrated in a structural control problem.     

Integrated identification and robust control

A framework for integrated identification and control is presented. As part of this framework, frequency domain uncertainty bounds are derived for robust stability tests, a robust stability test for elliptical bounds is developed for SISO systems, a methodology for estimating controller performance is derived, and an optimal experiment design methodology for control-relevant identification is outlined. An example is presented to illustrate how the tools of the framework fit together.     

A projection method for closed-loop identification

A new method for closed-loop identification that allows fitting the model to the data with arbitrary frequency weighting is described and analyzed. Just as the direct method, this new method is applicable to systems with arbitrary feedback mechanisms. This is in contrast to other methods, such as the indirect method and the two-stage method, that assume linear feedback. The finite sample behavior of the proposed method is illustrated in a simulation study.     

Direct and two-step methods for closed-loop identification: a comparison of asymptotic and finite data set performance

The asymptotic and finite data behavior of some closed-loop identification methods are investigated. It is shown that, when the output power is limited, closed-loop identification can generally identify models with smaller variance than open-loop identification. Several variations on some two-step identification methods are compared with the direct identification method. High order FIR models are used as process models to avoid bias issues arising from inadequate model structures for the processes. Comparisons are, therefore, made based on the variance of the identified process models both for asymptotic situations and for finite data sets. Process model bias resulting from improper selection of the noise and sensitivity function models is also investigated. In this context, the results support the use of direct identification methods on closed-loop data.     

How auxiliary variables and plant data collection affect closed-loop performance of inferential control

The design of property estimators for inferential control is addressed in this paper, and the effects of the auxiliary variables (estimator’s inputs) and of the approach to collect plant data, used to compute the model coefficients, are investigated. The concept of steady-state closed-loop consistency, which is the ability of an estimator to guarantee low offset in the unmeasured controlled variables, is adopted and theoretical results about this property are derived. It is shown how the selection of auxiliary variables represents the most crucial design step that determines the final closed-loop performance of an inferential control system. When this selection is done on a steady-state closed-loop consistency basis, the closed-loop performance is satisfactory, and it is secondary how the dataset is built. On the other hand, when “inconsistent” inputs are used, the performance is, in general, poor and may be significantly affected (in positive or in negative) by the dataset characteristics.     

Robust iterative learning control design is straightforward for uncertain LTI systems satisfying the robust performance condition

This note demonstrates that the design of a robust iterative learning control is straightforward for uncertain linear time-invariant systems satisfying the robust performance condition. It is shown that once a controller is designed to satisfy the well-known robust performance condition, a convergent updating rule involving the performance weighting function can be directly obtained. It is also shown that for a particular choice of this weighting function, one can achieve a perfect tracking. In the case where this choice is not allowable, a sufficient condition ensuring that the least upper bound of the /spl Lscr//sub 2/-norm of the final tracking error is less than the least upper bound of the /spl Lscr//sub 2/-norm of the initial tracking error is provided. This sufficient condition also guarantees that the infinity-norm of the final tracking error is less than the infinity-norm of the initial tracking error.     

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.

     

A global robust iterative learning position control for current-fed permanent magnet step motors

The tracking control problem via state feedback for uncertain current-fed permanent magnet step motors with non-sinusoidal flux distribution and uncertain position-dependent load torque is addressed: a periodic reference signal (of known period) for the rotor position is required to be tracked. A robust iterative learning control algorithm is designed which, for any motor initial condition and without requiring any resetting procedure, guarantees, despite system uncertainties: exponential convergence of the rotor position tracking error to a residual ball (centered at the origin) whose radius can be made arbitrarily small by properly setting the learning gain; asymptotic convergence of the rotor position tracking error to zero. A sufficient condition for the asymptotic estimation of the uncertain reference input achieving, for compatible initial conditions, perfect tracking is derived. Robustness with respect to a finite memory implementation of the control algorithm based on the piecewise linear approximation theory is shown to be guaranteed; satisfactory performances of a discrete-time implementation of the control algorithm are obtained in realistic simulations for the full-order voltage-fed motor.     

An integrated robust iterative learning control strategy for batch processes based on 2D system

This paper studies the problem of integrated control in the 2-dimensional (2D) system with parameter uncertainties for batch processes. An integrated iterative learning control (ILC) strategy based on quadratic performance for batch processes is proposed. It realizes comprehensive control by combining robust ILC in batch-axis with model predictive control (MPC) in time-axis. The design of quadratic-criterion-based ILC for the system can be converted into a min-max problem. Then a model predictive controller with time-varying prediction horizon is designed based on a quadratic cost function. For an uncertain model, a novel integrated robust ILC scheme based on a nominal model is further proposed. As a result, the control law of the 2D system can be regulated during one batch, which leads to good tracking performance and strong robustness against the disturbance and the uncertainties. Moreover, the analyses of the convergence and tracking performance are given. The proposed methods are applied to batch reactor, and results demonstrate that the system has good robustness and convergence. This paper provides a new way for batch processes control.     

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.     

基于模糊辨识的非线性连续系统的迭代学习控制

基于非线性连续动态的模型辨识算法，给出了非线性连续系统的一种非常有效的迭代学习控制方案。该控制方案不要求非线性连续系统中具体的非线性关系，并且容许系统初始误差的存在。