多变量数字鲁棒最优控制器的设计及应用

针对线性多变量离散控制系统,给出一种新的鲁棒最优控制器的设计方法．该方法提出了多变量系统的行特征函数的设计新思想,实现等价系统的动态解耦,使闭环控制系统的传递函数矩阵为正规矩阵,达到鲁棒H∞最优稳定;进一步,通过对等价解耦控制系统应用l∞最优控制方法,又能使原闭环控制系统获得最优时域指标．通过在某纸机3种定量和水分控制系统中的在线应用,验证了数字控制器的最优性与鲁棒性．     

基于INA设计方法的多变量PID控制器设计方法的深入研究

基于增大求解方法选择性的目的,本文给出了一种从系统开环传递函数入手求解极限增益和极限频率的计算方法,并以TITO系统为例,给出了详细的推导过程;此外,在详细研究设计方法的基础上,本文以两个典型对象作为研究对象对设置点位置与逆Nyquist阵列（INA）设计方法的多变量PID控制器设计方法的设计性能之间的规律性进行了系列仿真实验研究,并得出：系统开环传递函数矩阵的逆的行Gershgorin带与负实轴的交点（离原点最近的交点）与点（-1,j0）之间的距离越远,系统闭环响应曲线的震荡性越弱,系统的稳定裕量越大。     

一类特殊系统的三对角解耦控制研究

针对一类典型的多变量耦合三对角工业系统,在研究（块）三对角矩阵计算的基础上,提出了一种新的三对角解耦算法。该算法关键在于构造两补偿矩阵,即前串联补偿阵L（s）和后串联补偿阵R（s）,从而使耦合三对角工业系统变为对角系统,实现解耦。考虑到三对角工业系统次对角线上可能存有零传递函数分量,在此讨论了两种L（s）和R（s）的构造算法。经仿真不仅证实了方法的有效性,而且得出了构造的L（s）和R（s）具有多分量相等的特点,这将大大减轻其在工业实现方面的工作量。     

有效传递函数在多变量耦合系统中的应用

针对多变量系统具有多时滞、强铰链耦合的特点,提出了有效开环传递函数解耦策略。由于有效开环传递函数所描述的动力学行为的复杂性,首先采用模型降阶技术,将系统逼近一阶环节+延时(FOPDT)形式;然后运用IMC控制策略实现单位反馈控制。为得到传统PID控制器的典型表达形式,将IMC控制器进行麦克劳林级数展开,通过对相应项系数的比对得到了传统PID控制器。仿真分析表明了该方法能够提高系统动态响应速度、减小稳态误差,实现了多变量耦合系统的理想控制。     

基于Volterra级数的离散MIMO非线性闭环系统的稳定性

基于非线性传递函数矩阵的Volterra级数表示,利用多维Z变换,讨论了一类MIMO离散非线性系统的闭环稳定性,给出了直接利用开环稳定性来判别系统闭环稳定性的新方法,并用实例仿真来验证其有效性。     

单变量控制系统设计的多项式方法程序实现

本程序包是对“单变量控制系统设计的多项式方法”一文理论的具体实现,它对以传递函数或状态空间描述的不同的开环系统,按要求设计出具有某种动态性能的闭环系统。     

基于参数辨识的自适应解耦控制算法的研究

多变量模型的复杂结构、强耦合性、被控对象参数的未知、慢时变等问题要求控制器必须具有良好的自适应性,针对以上问题提出了一种基于改进的广义最小方差闭环自适应解耦控制器实现更好的自适应,其由参数可调的控制器和自适应控制律组成,此控制器通过将闭环系统方程的传递函数矩阵等于期望的对角矩阵来实现解耦,同时改进的辨识算法可进行在线辨识控制器的参数实现同步自适应解耦。通过以CARMA为多变量控制模型,采用该方法进行仿真有效的解决了多变量之间的耦合性。结果表明该方法能够适应相应的变化,跟踪性能较好,且具备良好的解耦能力,进而保证了闭环系统的稳定性,从而验证了此方法能够效提高控制系统的稳定性和鲁棒性。     

一类多变量系统的H∞控制的工程设计方法

从工程应用角度出发,提出一种用H∞控制理论设计一类多变量系统的次优敏感性控制 器的工程设计方法,并证明了其可行性.该方法通过将系统矩阵化为对角占优,利用单独通道 设计思想将多变量系统转化为单变量系统的H∞最优敏感性控制器问题.文末给出了仿真实 例.     

变风量空调系统恒温解耦控制优化

在室内恒温控制问题的研究中,变风量空调系统的房间送风量、冷冻水流量和风机转速三个输入变量与房间温度、送风温度和静压三个输出变量之间存在着不同程度的耦合关系,每个房间的温度控制会受到不同程度的干扰,严重时会影响到整个系统的稳定性.为解决上述问题,根据变风量空调系统的房间、表冷器、风机等各个子系统模型,通过寻找一个合适的开环传递函数矩阵,实现对系统的解耦控制,通过使解耦矩阵的对角元素为1,得到简化的解耦矩阵.比通常利用对角化方法和状态反馈矩阵方法直接求得的解耦矩阵要简单.运行空调实验结果表明控制回路之间干扰不明显,解耦控制效果良好.     

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.     

The stability of linear multivariable systems

A general criterion is presented for establishing the stability of a multivariable system from the stability of the simplified system consisting of its diagonal elements. This new criterion includes all known criteria of stability based on the diagonal system elements such as Rosenbrock's (1974), Nwokah's (1980) anil Koussiouris's (1980). For the class of matrices satisfying this criterion an equivalent result in terms of eigenloci can also be stated     

Non‐diagonal controllers in MIMO quantitative feedback design

This paper discusses multivariable quantitative feedback design through the use of controllers with off‐diagonal elements. Controller design for multivariable plants with significant uncertainty is simpler and potentially less conservative if some sort of dominance is achieved (by reducing the interaction effect of off‐diagonal plant elements) before a diagonal (decentralized) controller design is attempted. Traditional approaches for achieving dominance are not applicable when plant uncertainty must be considered. This paper discusses parallel and series implementations and for the latter, a pseudo‐Gauss elimination approach to the design has been developed. The interaction is measured using the Perron–Frobenius root of an interaction matrix. In some applications, it is possible to trade off individual plant cases against each other in order to reduce to the worst‐case interaction over the entire plant set. Copyright © 2002 John Wiley & Sons, Ltd.     

The Popov criterion and the inverse Nyquist method†

Kosonbrock's inverse Nyquist array (I.N.A.) theory for linear multivariable control Bystema with constant feedback elements is extended, to include systems lip to m nonlinear feedback elements, where the system has m inputs and m outputs. This extension is achieved by considering the Popov criterion for the most general case and through two further theorems. It shows that, as in the ease of Rosenbrock's I.N.A. theory, when certain auxiliary conditions are met with the help of suitable controllers, the design of multivariable controllers containing many non-linear feedbacks, can be based on the m frequency response loci corresponding to the diagonal entries of the open-loop inverse transfer function matrix. This leads to a simple design technique identical to the I.N.A. design method, suitable for use with a computer-aided design facility which permits a designer to use his intuitive understanding of transfer functions based on classical theory. The I.N.A. theory has been extended by Rosenbrock to cover systems having non-linear, time-varying feedback elements very recently.     

Equivalent transfer function method for PI/PID controller design of MIMO processes

In this paper, a novel engineering oriented control system design method for multivariable processes is presented. By employing the concepts of energy transmission ratio and effective relative gain, an equivalent transfer function matrix for closed loop control system can be obtained. Based on the equivalent transfer function matrix, both off-diagonal decoupling controllers and main loop diagonal controllers can be easily designed using the existing PI/PID tuning rules. The main advantages of the method are that: (1) the overall control system performance is better compared with the existing decoupling control methods; (2) it is very simple which can be easily understood and implemented by field control engineers; and (3) the control system is robust, it can still work with satisfactory performance even under significant model mismatches. Several multivariable industrial processes with different interaction characteristics are employed to demonstrate the simplicity and effectiveness of the design method.     

Triangularization technique for the design of multivariable control systems

This paper presents a novel technique for the design of multivariable control systems. A stable and proper precompensator is to be determined for a multivariable plant such that the compensated plant transfer function matrix is tringular and diagonally dominnnt in a non-standard way. As a consequence of the triangular-diagonal-dominance property, only the diagonal elements need to be considered in an overall closed-loop design. In effect, the technique provides a systematic procedure to reduce a multivariable design problem to independent scalar design problems.     

Achieving diagonal interactor matrix for multivariable linear systems with uncertain parameters

The notion of interactor matrix or equivalently the Hermite normal form, is a generalization of relative degree to multivariable systems, and is crucial in problems such as decoupling, inverse dynamics, and adaptive control. In order for a system to be input-output decoupled using static state feedback, the existence of a diagonal interactor matrix must first be established. For a multivariable linear system which does not have a diagonal interactor matrix, dynamic precompensation or dynamic state feedback is required for achieving a diagonal interactor matrix for the compensated system. Such precompensation often depends on the parameters of system, and is thus difficult to implement with accuracy when the system is subject to parameter uncertainty. In this paper we characterize a class of linear systems which can be precompensated to achieve a diagonal interactor matrix without the exact knowledge of the system parameters. More precisely, we present necessary and sufficient conditions on the transfer matrix of the system under which there exists a diagonal dynamic precompensator such that the compensated system has a diagonal interactor matrix. These conditions are associated with the so-called (non)generic singularity of certain matrix related to the system structure but independent of the system parameters. The result of this paper is expected to be useful in robust and adaptive designs.     

Quantitative non‐diagonal controller design for multivariable systems with uncertainty

The loop coupling reduction of multivariable systems under the presence of plant uncertainty is currently a most discussed topic. Following the ideas suggested by Horowitz, in this paper the role played by the non‐diagonal controller elements is analysed in order to state a design methodology. Thus, the definition of a coupling matrix and a quality function of the non‐diagonal elements come into use to quantify the amount of loop interaction and to design the controllers, respectively. This yields a criterion that makes possible to propose a sequential design methodology of the fully populated matrix controller, in the quantitative feedback theory (QFT) robust control frame. Finally, a real example with the heat exchanger of a pasteurization plant is included to show the practical use of this technique. Copyright © 2002 John Wiley & Sons, Ltd.     

On the robustness of multivariable linear feedback systems

One of the useful indicators of the robustness of a multivariable linear feedback system is the largest singular value of the nominal closed-loop transfer matrix. It is shown that while comparing different, not necessarily diagonal, closed-loop transfer matrices which have the same diagonal elements, the diagonal closed-loop transfer matrix has the greatest robustness. For plants with not "too" large parameter uncertainty, this result also guarantees the maximization of disturbance rejection, and the minimization of the control signal "power" at the plant's input.     

H∞ Controller design for spectral MIMO models by convex optimization

A new method for robust fixed-order H_∞ controller design by convex optimization for multivariable systems is investigated. Linear Time-Invariant Multi-Input Multi-Output (LTI-MIMO) systems represented by a set of complex values in the frequency domain are considered. It is shown that the Generalized Nyquist Stability criterion can be approximated by a set of convex constraints with respect to the parameters of a multivariable linearly parameterized controller in the Nyquist diagram. The diagonal elements of the controller are tuned to satisfy the desired performances, while simultaneously, the off-diagonal elements are designed to decouple the system. Multimodel uncertainty can be directly considered in the proposed approach by increasing the number of constraints. The simulation examples illustrate the effectiveness of the proposed approach.     

Computer aided design of multivariable nonlinear control systems using frequency domain techniques

The application of frequency domain methods to the study of a class of multivariable nonlinear feedback systems is considered within the context of a comprehensive interactive graphics design procedure and a new computational method is outlined for the determination of limit cycle operation which emphasises the effects of off diagonal system elements. It is shown how compensation can be applied using classical graphical design methods to avoid critical regions in the frequency domain. Two examples of use are given.