Real-Time Iterative Compensation Framework for Precision Mechatronic Motion Control Systems

With regard to precision/ultra-precision motion systems, it is important to achieve excellent tracking performance for various trajectory tracking tasks even under uncertain external disturbances. In this paper, to overcome the limitation of robustness to trajectory variations and external disturbances in offline feedforward compensation strategies such as iterative learning control (ILC), a novel real-time iterative compensation (RIC) control framework is proposed for precision motion systems without changing the inner closed-loop controller. Specifically, the RIC method can be divided into two parts, i.e., accurate model prediction and real-time iterative compensation. An accurate prediction model considering lumped disturbances is firstly established to predict tracking errors at future sampling times. In light of predicted errors, a feedforward compensation term is developed to modify the following reference trajectory by real-time iterative calculation. Both the prediction and compensation processes are finished in a real-time motion control sampling period. The stability and convergence of the entire control system after real-time iterative compensation is analyzed for different conditions. Various simulation results consistently demonstrate that the proposed RIC framework possesses satisfactory dynamic regulation capability, which contributes to high tracking accuracy comparable to ILC or even better and strong robustness.      

内模强化学习型模型预测控制及其在人工胰脏上的应用

在学习型模型预测控制的框架里,迭代学习控制器被用来更新模型预测控制器的设定点.在已经发表的研究成果里,学习型模型预测控制用到的是比例型的学习率,这种学习率的学习能力有限,而且怎样设计学习增益仍然是一个开放性问题.在本文中,基于内模控制理论提出的PID型的迭代学习控制器被用来更新模型预测控制器的设定点.为了方便起见,本文提出的结合算法可称为内模强化学习型模型预测控制.本文提出的算法应用在(1)型糖尿病人的人工胰脏闭环控制上.仿真结果显示,本算法对比于比例学习型模型预测控制可以达到更好的收敛性能,而且对非重复干扰有很好的鲁棒性.     

Set-point-related indirect iterative learning control for multi-input multi-output systems

A form of iterative learning control (ILC) is used to update the set-point for the local controller. It is referred to as set-point-related (SPR) indirect ILC. SPR indirect ILC has shown excellent performance: as a supervision module for the local controller, ILC can improve the tracking performance of the closed-loop system along the batch direction. In this study, an ILC-based P-type controller is proposed for multi-input multi-output (MIMO) linear batch processes, where a P-type controller is used to design the control signal directly and an ILC module is used to update the set-point for the P-type controller. Under the proposed ILC-based P-type controller, the closed-loop system can be transformed to a 2-dimensional (2D) Roesser s system. Based on the 2D system framework, a sufficient condition for asymptotic stability of the closed-loop system is derived in this paper. In terms of the average tracking error (ATE), the closed-loop control performance under the proposed algorithm can be improved from batch to batch, even though there are repetitive disturbances. A numerical example is used to validate the proposed results.     

Iterative learning control of molten steel level in a continuous casting process

In this paper, an iterative learning control (ILC) method is introduced to control molten steel level in a continuous casting process, in the presence of disturbance, noise and initial errors. The general ILC method was originally developed for processes that perform tasks repetitively but it can also be applied to periodic time-domain signals. To propose a more realistic algorithm, an ILC algorithm that consists of a P-type learning rule with a forgetting factor and a switching mechanism is introduced. Then it is proved that the input signal error, the state error and the output error are ultimately bounded in the presence of model uncertainties, periodic bulging disturbances, measurement noises and initial state errors. Computer simulation and experimental results establish the validity of the proposed control method.     

基于Jacobi方法的线性离散时间系统的迭代学习控制

提出线性离散时间系统基于Jacobi方法的迭代学习控制问题.通过构建线性迭代学习控制问题与线性方程组之间的联系,将Jacobi方法引入到迭代学习控制中,并由此构建得到迭代学习控制律.借助于矩阵运算,证明这种学习律能使得系统的输出跟踪误差经有限次迭代后为零.数值例子说明了算法的可适用性.     

Adaptive iterative learning control for robot manipulators

In this paper, we propose some adaptive iterative learning control (ILC) schemes for trajectory tracking of rigid robot manipulators, with unknown parameters, performing repetitive tasks. The proposed control schemes are based upon the use of a proportional-derivative (PD) feedback structure, for which an iterative term is added to cope with the unknown parameters and disturbances. The control design is very simple in the sense that the only requirement on the PD and learning gains is the positive definiteness condition and the bounds of the robot parameters are not needed. In contrast to classical ILC schemes where the number of iterative variables is generally equal to the number of control inputs, the second controller proposed in this paper uses just two iterative variables, which is an interesting fact from a practical point of view since it contributes considerably to memory space saving in real-time implementations. We also show that it is possible to use a single iterative variable in the control scheme if some bounds of the system parameters are known. Furthermore, the resetting condition is relaxed to a certain extent for a certain class of reference trajectories. Finally, simulation results are provided to illustrate the effectiveness of the proposed controllers.     

Adaptive ILC algorithms of nonlinear continuous systems with non-parametric uncertainties for non-repetitive trajectory tracking

In this article, two adaptive iterative learning control (ILC) algorithms are presented for nonlinear continuous systems with non-parametric uncertainties. Unlike general ILC techniques, the proposed adaptive ILC algorithms allow that both the initial error at each iteration and the reference trajectory are iteration-varying in the ILC process, and can achieve non-repetitive trajectory tracking beyond a small initial time interval. Compared to the neural network or fuzzy system-based adaptive ILC schemes and the classical ILC methods, in which the number of iterative variables is generally larger than or equal to the number of control inputs, the first adaptive ILC algorithm proposed in this paper uses just two iterative variables, while the second even uses a single iterative variable provided that some bound information on system dynamics is known. As a result, the memory space in real-time ILC implementations is greatly reduced.     

Disturbance aspects of iterative learning control

Disturbance aspects of iterative learning control (ILC) are considered. By using a linear framework it is possible to investigate the influence of the disturbances in the frequency domain. The effects of the design filters in the ILC algorithm on the disturbance properties can then be analyzed. The analysis is supported by simulations and experiments.     

Analysis of boundary effects in iterative learning control

Boundary effects in iterative learning control (ILC) algorithms are considered in this article. ILC algorithms involve filtering of input and error signals over finite-time intervals, often using non-causal filters, and it is important that the boundary effects of the filtering operations are handled in an appropriate way. The topic is studied using both a proposed theoretical framework and simulations, and it is shown that the method for handling the boundary effects has impact on the stability and convergence properties of the ILC algorithm.     

Batch-to-batch control of fed-batch processes using control-affine feedforward neural network

A control strategy for fed-batch processes is proposed based on control affine feed-forward neural network (CAFNN). Many fed-batch processes can be considered as a class of control affine nonlinear systems. CAFNN is constructed by a special structure to fit the control affine system. It is similar to a multi-layer feed-forward neural network, but it has its own particular feature to model the fed-batch process. CAFNN can be trained by a modified Levenberg–Marquardt (LM) algorithm. However, due to model-plant mismatches and unknown disturbances, the optimal control policy calculated based on the CAFNN model may not be optimal when applied to the fed-batch process. In terms of the repetitive nature of fed-batch processes, iterative learning control (ILC) can be used to improve the process performance from batch to batch. Due to the special structure of CAFNN, the gradient information of CAFNN can be computed analytically and applied to the batch-to-batch ILC. Under the ILC strategy from batch to batch, endpoint product qualities of fed-batch processes can be improved gradually. The proposed control scheme is illustrated on a simulated fed-batch ethanol fermentation process.     

Kinematic path‐tracking of mobile robot using iterative learning control

This paper develops a kinematic path‐tracking algorithm for a nonholonomic mobile robot using an iterative learning control (ILC) technique. The proposed algorithm produces a robot velocity command, which is to be executed by the proper dynamic controller of the robot. The difference between the velocity command and the actual velocity acts as state disturbances in the kinematic model of the mobile robot. Given the kinematic model with state disturbances, we present an ILC‐based path‐tracking algorithm. An iterative learning rule with both predictive and current learning terms is used to overcome uncertainties and the disturbances in the system. It shows that the system states, outputs, and control inputs are guaranteed to converge to the desired trajectories with or without state disturbances, output disturbances, or initial state errors. Simulations and experiments using an actual mobile robot verify the feasibility and validity of the proposed learning algorithm. © 2005 Wiley Periodicals, Inc.     

Iterative learning control for constrained linear systems

This article considers iterative learning control (ILC) for linear systems with convex control input constraints. First, the constrained ILC problem is formulated in a novel successive projection framework. Then, based on this projection method, two algorithms are proposed to solve this constrained ILC problem. The results show that, when perfect tracking is possible, both algorithms can achieve perfect tracking. The two algorithms differ, however, in that one algorithm needs much less computation than the other. When perfect tracking is not possible, both algorithms can exhibit a form of practical convergence to a ‘best approximation’. The effect of weighting matrices on the performance of the algorithms is also discussed and finally, numerical simulations are given to demonstrate the effectiveness of the proposed methods.     

Iterative Path Tracking of an Omni-Directional Mobile Robot

We propose a path-tracking algorithm that is developed using an iterative learning control (ILC) technique and use the algorithm to control an omni-directional mobile robot. The proposed algorithm can be categorized as an open–closed PD-type ILC; it generates robot velocity commands by a PD-type ILC update rule using both previous and current information. When applied to the omni-directional mobile robot, it can decrease position errors and track the desired trajectory. Under the general problem setting that includes a mobile robot, we show that the proposed algorithm guarantees that the system states, outputs and control inputs converge to within small error bounds around the desired ones even under state disturbances, measurement noises and initial state errors. By using simulation and experimental tests, we demonstrate that the proposed algorithm converges fast to the desired path, and results in small root-mean-square (r.m.s.) position error under various surface conditions. The proposed algorithm shows better path-tracking performance than the conventional PID algorithm and achieves faster convergence and lower r.m.s. error than the existing two ILC algorithms.     

Iterative Learning Control for Linear Discrete‐Time Systems with Unknown High‐Order Internal Models: A Time‐Frequency Analysis Approach

This work focuses on the iterative learning control (ILC) for linear discrete‐time systems with unknown initial state and disturbances. First, multiple high‐order internal models (HOIMs) are introduced for the reference, initial state, and disturbances. Both the initial state and disturbance consist of two components, one strictly satisfies HOIM and the other is random bounded. Then, an ILC scheme is constructed according to an augmented HOIM that is the aggregation of all HOIMs. For all known HOIMs, an ILC design criterion is introduced to achieve satisfactory tracking performance based on the 2‐D theory. Next, the case with unknown HOIMs is discussed, where a time‐frequency‐analysis (TFA)‐based ILC algorithm is proposed. In this situation, it is shown that the tracking error inherits the unknown augmented HOIM that is an aggregation of all unknown HOIMs. Then, a TFA‐based method, e.g., the short‐time Fourier transformation (STFT), is employed to identify the unknown augmented HOIM, where the STFT could ignore the effect of the random bounded initial state and disturbances. A new ILC law is designed for the identified unknown augmented HOIM, which has the ability to reject the unknown the initial state and disturbances that strictly satisfy HOIMs. Finally, a gantry robot system with iteration‐invariant or slowly‐varying frequencies is given to illustrate the efficiency of the proposed TFA‐based ILC algorithm.     

A statistical analysis of certain iterative learning control algorithms

Iterative learning control (ILC) is a technique used to improve the tracking performance of systems carrying out repetitive tasks, which are affected by deterministic disturbances. The achievable performance is greatly degraded, however, when non-repeating, stochastic disturbances are present. This paper aims to compare a number of different ILC algorithms, proposed to be more robust to the presence of these disturbances, first by a statistical analysis and then by simulation results and their application to a linear motor. New expressions for the expected value and variance of the controlled error are developed for each algorithm. The different algorithms are then tested in simulation and finally applied to the linear motor system to test their performance in practice. A filtered ILC algorithm is proposed when the noise and desired output spectra are separated. Otherwise an algorithm with a decreasing gain gives good robustness to noise and achievable precision but at a slower convergence rate.     

On the disturbance properties of high order iterative learning control algorithms

The disturbance properties of high order iterative learning control (ILC) algorithms are considered. An error equation is formulated, and using statistical models of the load and measurement disturbances an equation for the covariance matrix of the control error vector is derived. The results are exemplified by analytic derivation of the covariance matrix for a second order ILC algorithm.     

受扰动2-D线性时变系统的迭代学习控制

利用2-D系统理论的Roesser模型,给出了受扰动的线性时变离散系统迭代学习控制(ILC)问题的一种解决方法.对系统所受的已知扰动,给出其学习律参数的选取范围以及仅经一次迭代就能实现输出完全跟踪期望轨迹的参数选取方法;对系统所受的未知扰动,首先对SISO系统提出其学习律存在的条件及参数选取方法,进而推广到MIMO系统中,提出MIMO系统学习律的参数选取方法.最后给出两个数值例子进一步说明所得结果的有效性.     

Integrated predictive iterative learning control based on updating reference trajectory for point-to-point tracking

A novel control technique is proposed by combining iterative learning control (ILC) and model predictive control (MPC) with updating-reference trajectory for point-to-point tracking problem of batch process. In this paper, a batch-to-batch updating-reference trajectory, which passes through the desired points, is firstly designed as the tracking trajectory within a batch. The updating control law consists of P-type ILC part and MPC part, in which P-type ILC part can improve the performance by learning from previous executions and MPC part is used to suppress the model perturbations and external disturbances. Convergence properties of the integrated predictive iterative learning control (IPILC) are analyzed theoretically, and the sufficient convergence conditions of output tracking error are also derived for a class of linear systems. Comparing with other point-to-point tracking control algorithms, the proposed algorithm can perform better in robustness. Furthermore, updating-reference relaxes the constraints for system outputs, and it may lead to faster convergence and more extensive range of application than those of fixed-reference control algorithms. Simulation results on typical systems show the effectiveness of the proposed algorithm.     

A convex optimization approach to robust iterative learning control for linear systems with time-varying parametric uncertainties

In this paper, we present a new robust iterative learning control (ILC) design for a class of linear systems in the presence of time-varying parametric uncertainties and additive input/output disturbances. The system model is described by the Markov matrix as an affine function of parametric uncertainties. The robust ILC design is formulated as a min–max problem using a quadratic performance criterion subject to constraints of the control input update. Then, we propose a novel methodology to find a suboptimal solution of the min–max optimization problem. First, we derive an upper bound of the worst-case performance. As a result, the min–max problem is relaxed to become a minimization problem in the form of a quadratic program. Next, the robust ILC design is cast into a convex optimization over linear matrix inequalities (LMIs) which can be easily solved using off-the-shelf optimization solvers. The convergences of the control input and the error are proved. Finally, the robust ILC algorithm is applied to a physical model of a flexible link. The simulation results reveal the effectiveness of the proposed algorithm.