A design algorithm using external perturbation to improve Iterative Feedback Tuning convergence

Iterative Feedback Tuning constitutes an attractive control loop tuning method for processes in the absence of process insight. It is a purely data driven approach for optimization of the loop performance. The standard formulation ensures an unbiased estimate of the loop performance cost function gradient, which is used in a search algorithm for minimizing the performance cost. A slow rate of convergence of the tuning method is often experienced when tuning for disturbance rejection. This is due to a poor signal to noise ratio in the process data. A method is proposed for increasing the data information content by introducing an optimal perturbation signal in the tuning algorithm. The theoretical analysis is supported by a simulation example where the proposed method is compared to an existing method for acceleration of the convergence by use of optimal prefilters.     

Asymptotic Accuracy of Iterative Feedback Tuning

Iterative feedback tuning (IFT) is a widely used procedure for controller tuning. It is a sequence of iteratively performed special experiments on the plant interlaced with periods of data collection under normal operating conditions. In this note, we derive the asymptotic convergence rate of IFT for disturbance rejection, which is one of the main fields of application.     

Optimal Prefiltering in Iterative Feedback Tuning

Iterative feedback tuning (IFT) is a data-based method for the iterative tuning of restricted complexity controllers. A “special experiment” in which a batch of previously collected output data is fed back at the reference input allows one to compute an unbiased estimate of the gradient of the control performance criterion. We show that, by performing an optimal filtering of the data that are fed back, one can minimize the asymptotic variability of the control performance cost and, hence, minimize the average performance degradation that results from the randomness of the data. The expression of the optimal filter is derived, and a simulation illustrates the benefits that result from using this optimal filter as compared to the use of the classical constant filter.     

气动人工肌肉关节的迭代反馈整定控制及优化

气动人工肌肉关节（PMA）具有低成本、柔顺性和与生物肌肉类似的力学特性等优点，在医疗设备、仿生机器人等领域得到广泛应用.本文针对气动人工肌肉充气变形过程中存在的强非线性、时变性和控制参数难以确定的问题，提出了一种基于迭代反馈整定（IFT）算法的数据驱动优化控制策略，直接基于系统的输入输出数据，定义跟踪性能准则函数并采用Gauss-Newton估计算法实现对PID控制器参数的迭代整定，并通过引入辅助因子获取性能准则函数加权因子的最优值进一步加快了IFT算法的收敛速度.仿真结果表明，该方法相对于Ziegler-Nichols等传统PID参数整定方法可以有效提高控制系统的跟踪性能和鲁棒性.     

FKA算法迭代收敛性分析

《核选择和非线性特征提取的双线性分析》一文提出了一种新颖的核Fisher准则FKC, 并用迭代分析算法FKA求得最优解,但其迭代收敛性缺乏理论上的证明。从理论上对FKA算法的迭代收敛性进行了分析和探讨,并运用Radermacher复杂性分析法进行证明。     

Iterative Toeplitz solvers with local quadratic convergence

We study an iterative, locally quadratically convergent algorithm for solving Toeplitz systems of equations from [R. P. Brent, F. G. Gustavson and D. Y. Y. Yun. “Fast solution of Toeplitz systems of equations and computation of Padé approximations”,J. Algorithms, 1:259–295, 1980]. We introduce a new iterative algorithm that is locally quadratically convergent when used to solve symmetric positive definite Toeplitz systems. We present a set of numerical experiments on randomly generated symmetric positive definite Toeplitz matrices. In these experiments, our algorithm performed significantly better than the previously proposed algorithm.     

Virtual Reference Feedback Tuning for non-minimum phase plants

Model reference control design methods fail when the plant has one or more non-minimum phase zeros that are not included in the reference model, leading possibly to an unstable closed loop. This is a very serious problem for data-based control design methods, where the plant is typically unknown. In this paper, we extend the Virtual Reference Feedback Tuning method to non-minimum phase plants. This extension is based on the idea proposed in Lecchini and Gevers (2002) for Iterative Feedback Tuning. We present a simple two-step procedure that can cope with the situation where the unknown plant may or may not have non-minimum phase zeros.     

基于反馈控制的迭代学习控制器设计

针对具有不确定项或干扰项的重复非线性时变系统,提出了基于反馈控制的迭代学习控制器,其中迭代学习控制器设计为高阶PD型,它以前馈的形式作用于对象,在满足一定的收敛性条件下,证明了该控制器的跟踪误差界是系统初始状态误差界和系统输出干扰项界的线性函数,同时改变反馈增益可以调整系统的最终跟踪误差界,仿真与实验均表明了该方法的有效性。     

Iterative convergence of passage-time densities in semi-Markov performance models

Passage-time densities are important for the detailed performance analysis of distributed computer and communicating systems. We provide a proof and demonstration of a practical iterative algorithm for extracting complete passage-time densities from expressive semi-Markov systems. We end by showing its application to a distributed web-server cluster model of 15.9 million states.     

基于迭代继电反馈的多变量PID控制器自整定

PID控制是工业过程中最常用的控制方法,但在实际生产过程中,被控过程往往是多变量、有耦合的,常规PID控制器参数往往整定不良、性能欠佳,对运行工况的适应性较差。为此,将迭代反馈理论和继电整定方法有机结合起来,提出一种适用于存在耦合的多变量系统PID控制器的参数整定方法。运用该方法整定PID参数,不需要被控对象的数学模型,而且具有速度快、效果好等优点。     

调节性能最优的继电反馈PID整定公式

针对实际控制系统中恒值控制系统较多的情况,以调节性能最优为目标,利用计算机辅助分析工具和数据拟合软件,建立了继电反馈自整定所使用的PID参数整定公式.同时,针对2类常用过程模型的仿真试验,设计了一种新的整定公式并拟合得到4套整定公式,且分别用4个算例验证了4套整定公式的有效性.将新整定公式与已提出的2种整定公式进行比较,结果证明了新公式的优越性.     

基于路由更新链的BGP收敛性改进机制*

提出一种BGP收敛性改进机制。首先构建路由更新链,以记录所有最优路由发生变化的节点ID;在充分尊重最小路由通告时间间隔(MRAI)的前提下,通过更新和传递路由更新链使得各节点及时了解源节点、中间节点和邻居节点的路由变化;利用路由更新链中的ID信息,各节点能够快速全面地排除本地所有无效路由,加快了BGP收敛。性能分析说明了该机制比现有方法开销更小、效率更高。     

Iterative Learning Control for uncertain systems: Robust monotonic convergence analysis

In this paper, we present a novel Robust Monotonic Convergence (RMC) analysis approach for finite time interval Iterative Learning Control (ILC) for uncertain systems. For that purpose, a finite time interval model for uncertain systems is introduced. This model is subsequently used in an RMC analysis based on μ analysis. As a result, we can handle additive and multiplicative uncertainty models in the RMC problem formulation, analyze RMC of linear time invariant MIMO systems controlled by any linear trial invariant ILC controller, and formulate additional straightforward RMC conditions for ILC controlled systems. To illustrate the derived results, we analyze the RMC properties of linear quadratic (LQ) norm optimal ILC.     

Iterative extensions of the Sturm/Triggs algorithm: convergence and nonconvergence

We give the first complete theoretical convergence analysis for the iterative extensions of the Sturm/Triggs algorithm. We show that the simplest extension, SIESTA, converges to nonsense results. Another proposed extension has similar problems, and experiments with "balanced" iterations show that they can fail to converge or become unstable. We present CIESTA, an algorithm which avoids these problems. It is identical to SIESTA except for one simple extra computation. Under weak assumptions, we prove that CIESTA iteratively decreases an error and approaches fixed points. With one more assumption, we prove it converges uniquely. Our results imply that CIESTA gives a reliable way of initializing other algorithms such as bundle adjustment. A descent method such as Gauss-Newton can be used to minimize the CIESTA error, combining quadratic convergence with the advantage of minimizing in the projective depths. Experiments show that CIESTA performs better than other iterations.     

An Iterative Method for Optimal Feedback Control and Generalized HJB Equation

In this paper, a new iterative method is proposed to solve the generalized Hamilton-Jacobi-Bellman (GHJB) equation through successively approximate it. Firstly, the GHJB equation is converted to an algebraic equation with the vector norm, which is essentially a set of simultaneous nonlinear equations in the case of dynamic systems. Then, the proposed algorithm solves GHJB equation numerically for points near the origin by considering the linearization of the non-linear equations under a good initial control guess. Finally, the procedure is proved to converge to the optimal stabilizing solution with respect to the iteration variable. In addition, it is shown that the result is a closed-loop control based on this iterative approach. Illustrative examples show that the update control laws will converge to optimal control for nonlinear systems.      

An Optimal Approach to Online Tuning Method for PID Type Iterative Learning Control

The proportional-integral-derivative (PID) controller is widely used in process control engineering. However, the parameter updating of PID controller has     

New Approach on the Automatic Tuning of Multivariable PI Controllers Using Relay Feedback

A new algorithm for automatic tuning of multivariable PI controllers for multi-input multi-output processes is presented. The tuning procedure consists of four stages. In the first, the critical point of each possible loop is identified using the conventional relay feedback test. In this phase, a set of critical frequencies is formed. In the second stage, among the process critical frequency set, a design frequency is chosen. The choice of this design frequency is done with respect to the interaction problem in the multivariable system. In the third stage, the process steady state and frequency response matrices at the design frequency are estimated with good accuracy. In the fourth stage, the information about the process is used to tune the multivariable PI controller. For the multivariable PI controller, a new design technique is derived taking into account the decoupling condition at the low- and high-frequency range of the process. The proposed method is applied to various typical processes and experimented on using a laboratory-scaled model of a paper machine head-box. The experimental test has shown good results where significant performance improvement over the existing tuning methods is demonstrated.