Weighted minimum variance controller for nonsquare multivariable systems

A weighted minimum variance controller is described for nonsquare multivariable systems. The controller is a generalization of the scalar case which can ensure stability even when the system is open-loop unstable and nonminimum phase. Moreover, as the control weighting tends to zero, asymptotic stability is guaranteed.     

随机系统的多模型直接自适应解耦控制器

针对多变量离散时间随机系统, 提出了一种采用广义最小方差性能指标的多模型直接自适应解耦控制器. 该多模型控制器由多个固定控制器和两个自适应控制器构成. 固定控制器用以覆盖系统参数的可能变化范围, 自适应控制器用以保证系统的稳定性和提高暂态性能. 该多模型控制器利用矩阵的伪交换性和拟Diophantine方程性质, 基于广义最小方差性能指标, 将随机系统辨识算法和最优控制器设计相结合, 直接辨识出控制器的参数, 通过广义最小方差性能指标中加权多项式的选取,不但实现了多变量系统的动态解耦控制, 而且消除了稳态误差、配置了闭环极点. 文末给出了全局收敛性分析. 仿真结果表明该方法明显优于常规自适应控制器.     

一种多变量隐式极点配置自校正控制器及其应用A

本文提出了一种极点配置自校正控制器.该控制器不仅能控制开环不稳定或非最小相位 系统,而且能控制具有任意、未知或变化传输延时结构的多变量系统.该控制器采用隐式方式 来实现即利用输入输出数据直接辨识控制器的参数.这样不仅避免在线解矩阵方程,而且增 加算法的鲁棒性.仿真和实时控制多变量电加热系统的结果表明该控制器具有好的控制性能.     

基于CARIMA模型的多变量极点配置自校正直接算法及其鲁棒性

本文根据 CARIMA 模型,采用双线性一步松驰算法和多项式矩阵展开交换法,给出一种适用于非最小相位系统的多变量极点配置自校正直接算法,并研究了其鲁棒性.此法计算量小,对初值选择不敏感,系统跟踪调节性能好,鲁棒性强,是一种有应用前景的极点配置直接算法。     

Direct adaptive pole placement with application to nonminimum phase systems

This note presents the first direct adaptive control structure for nonminimum phase systems where controller parameter identification can be posed as a standard linear parameter estimation problem. In particular, a linear equation error model is formulated for estimating both the controller parameters and some additional auxiliary parameters. The key idea involves insertion of the Bezout polynomial identity into the polynomial design equation which arises in arbitrary pole placement.     

Direct adaptive control with integral action for nonminimum phase systems

This note presents a direct adaptive control scheme for nonminimum phase systems where controller parameters are estimated from the recursive least-squares algorithm. Some additional auxiliary parameters are obtained from the proposed polynomial identity,, and a local convergence is guaranteed without any extra conditions. Integral action is incorporated into the adaptive controller to eliminate the steady-state error, and to satisfy a condition of the unique solution for the polynomial identity as well.     

A self-tuning decoupling controller for a class of multivariablesystems and global convergence analysis

A simple multivariable self-tuning controller is presented which decouples a class of multivariable systems and specifically handles multivariable systems with a different delay associated with each output. The global convergence of this adaptive control algorithm is established. It is shown that the system input-output vectors are always sample-mean-square bounded and the conditional mean-square-generalized tracking error achieves its global minimum, even for nonminimum phase systems, for an appropriate cost function     

多模型自适应控制的分层递阶构造与覆盖性质分析

针对一类非最小相位系统,设计一种多模型自适应控制器.该控制器由固定控制器模型、常规自适应模型和可重新赋值自适应模型构成.固定控制器模型采用分层递阶结构用来减少模型集的数目,根据切换指标选出的上一层最优控制器,动态设计本层固定控制器模型实现对其参数变化范围的覆盖.该控制器采用直接自适应算法,通过加权多项式的选取,消除了稳态误差.文末对系统的覆盖性、模型数目等进行了分析.仿真结果表明当采用相同数目的模型时,其控制效果明显优于常规多模型控制器.     

On the design of single-loop single-input-output feedback control systems in the complex-frequency domain

This paper is concerned with single-loop, single-input-output, feedback control systems consisting of a plant, controller, and feedback sensor each modeled by a rational transfer function. The plant can be unstable, nonminimum phase, and even improper. The objective is the determination of the controller transfer function for which the system is asymptotically stable and design objectives are met. This has always been the goal in feedback system design. What is novel about the approach presented here is that the family of all stabilizing controller transfer functions is parameterized in terms of a rational functionK (s). The design method allows for complete freedom in the selection of all closed-loop system poles (except those associated with hidden modes). This is accomplished through the choice of the denominator polynomial forK (s). The remaining design freedom lies in the selection of the numerator ofK (s). This freedom is utilized to shape the system sensitivity function and to achieve specified steady-state error coefficients. A numerical example in which the plant is unstable and nonminimum phase is presented to illustrate the above points. The final design is compared with alternative designs and the tradeoffs are clearly displayed.     

具有通用性能指标的多变量自校正控制器*

本文讨论了一类多变量自校正控制器,给出了最优控制律及给定闭环极点时,确定加权多项式阵P(z~(-1)),Q(z~(-1))和消除静差求解加权多项式阵R(z~(-1))的算式。当系统参数未知且缓变时,应用递推最小二乘法即可求得所需的控制器参数。     

自校正控制非最小相位的电加热系统

本文提出了一种简单的多变量极点配置自校正解耦控制器。该控制器不仅避免了在线求解矩阵方程和矩阵求逆运算而且实现了自适应解耦控制。该自适应控制器已被成功地应用来控制双输入双输出非最小相位的电加热炉。     

Multivariable direct adaptive decoupling controller using multiple models and a case study

In this paper, a multivariable direct adaptive controller using multiple models without minimum phase assumption is presented to improve the transient response when the parameters of the system jump abruptly. The controller is composed of multiple fixed controller models, a free-running adaptive controller model and a re-initialized adaptive controller model. The fixed controller models are derived from the corresponding fixed system models directly. The adaptive controller models adopt the direct adaptive algorithm to reduce the design calculation. At every instant, the optimal controller is chosen out according to the switching index. The interaction of the system is viewed as the measured disturbance which is eliminated by the choice of the weighing polynomial matrix. The global convergence is obtained. Finally, several simulation examples in a wind tunnel experiment are given to show both effectiveness and practicality of the proposed method. The significance of the proposed method is that it is applicable to a non-minimum phase system, adopting direct adaptive algorithm to overcome the singularity problem during the matrix calculation and realizing decoupling control for a multivariable system. Supported by the National Natural Science Foundation of China (Grant Nos. 60504010, 60864004), the National High-Tech Research and Development Program of China (Grant No. 2008AA04Z129), the Key Project of Chinese Ministry of Education (Grant No. 208071), and the Natural Science Foundation of Jiangxi Province (Grant No. 0611006)     

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.     

A multivariable generalized self-tuning controller with decoupling design

This note describes a multivariable generalized self-tuning controller with decoupling which combines the classical pole-zero placement strategy with the optimal strategy for self-tuning control. The controller uses techniques of updating weighting polynomial matrices on line and eliminating the tracking errors without use of an integrator, and decouples the multivariable system.     

A unified method for the design of nonovershooting linear multivariable state-feedback tracking controllers

We consider the use of linear multivariable feedback control to achieve a nonovershooting step response. A method is given for designing a linear time invariant state feedback controller to asymptotically track a constant step reference with zero overshoot and arbitrarily small rise time, under some mild assumptions. We present a unified design method that can be applied to continuous and discrete time systems, square and non-square systems, minimum and nonminimum phase systems, and also strictly proper and nonstrictly proper systems.     

The use of a quadratic performance index to design multivariable control systems

A quadratic performance index is considered as a generalized criterion for designing linear multivariable control systems. A method is developed for expressing the characteristic polynomial of the optimal system as an explicit function of the weighting matrix elements of the performance index. Since these elements are actually the design parameters it then becomes possible to obtain some general properties of the optimal systems as well as to select the weighting matrix elements, such that more conventional criteria on the system transient response are satisfied. The results are applied to the design of two multivariable systems; in one case, the plant is initially unstable and, in the second case, it is desired to have the system response follow that of a linear model.     

On the control of non-linear processes: An IDA–PBC approach

A high performance non-linear controller that exploits the properties of port-Hamiltonian systems to precisely define the interconnections and energy dissipations of non-linear processes is presented for a large class of chemical processes. The controller is derived from classical interconnection and damping assignment–passivity based control theory but an additional degree of freedom is introduced in the controller design by the use of “non-exact matching” closed-loop storage functions. By a proper closed-loop interconnection assignment the proposed controller achieves total decoupling between outputs and since no inversion of the process dynamics is made in the design it is equally applicable to minimum phase and nonminimum phase system. The controller design methodology is presented and stability conditions are stated. As illustrative example the proposed method is used to design controllers for a multiple-input/multiple-output non-isothermal continued stirred tank reactor that exhibits nonminimum phase behavior.     

多输入预报自校正前馈控制器及其在高频焊管焊接过程控制中的应用

本文针对高频焊管焊接过程的控制,提出了一种适用于具有多种扰动对象的多输入预报自校正前馈控制器,其特点是综合了广义最小方差控制的最优性、极点配置控制的鲁棒性和多输入前馈控制的抗扰性等优点。该控制器采用间接算法实现,在线选择二次型性能指标中加权项。它不仅可以消除可测干扰的影响,消除稳态跟踪误差,而且即使用于非最小相位系统也具有全局收敛特性。理论分析和仿真实验表明,提出的控制器具有良好的控制性能,可以适应焊接过程环境的变化,从而获得满意的控温效果。     

Generalized minimum variance control of MIMO systems—A stability result

This note describes a generalized minimum variance (GMV) control algorithm for square systems. The controller embeds an integral action on the error vector. It is shown how an appropriate yet simple choice of some design parameters guarantees overall asymptotic stability for open loop asymptotically stable and possibly nonminimum phase plants.     

多变量系统控制器的参数满意优化设计

为了将满意优化拓展到多变量系统中以解决多变量控制系统线性二次型(LQ)控制器设计中加权系数阵确定难的问题,提出多变量系统满意优化设计方法,通过设计满意度函数,构造出多变量系统的满意优化数学模型,并用改进遗传算法实现二级倒立摆系统LQ控制器满意优化设计.仿真结果显示,系统具有更满意的综合性能指标.证实了该方法的有效性和实用性.本文的研究对多变量系统优化设计具有一定的参考价值.