Imperfect model reference adaptive control: deadbeat output error approach

It is well known that while the perfect model matching condition (i.e. unstable plant zeros must be zeros of the reference model) is not met, the model reference adaptive control cannot easily be implemented. In adaptive control systems, since the plant is assumed to be unknown previously, it is a difficult task to choose an adequate reference model such that the perfect model matching condition is guaranteed in every adaptive step. In this paper, a new design algorithm for model reference adaptive control systems is proposed to synthesize an adaptive controller such that the error between the reference model output and the plant output can vanish in a deadbeat manner. In this situation, the stringent matching condition can be relaxed in every adaptive step, so our design algorithm is also suitable for unstable or non-minimum phase systems. Several simulation results are presented to illustrate the good behaviour of our design algorithm.     

电液伺服试验机力控系统负载刚度自适应控制

负载刚度的变化会导致电液伺服力控系统的控制特性发生改变,从而降低系统的稳定性与控制精度.本文以电液伺服万能试验机为研究对象,首先建立了考虑负载刚度的力控系统数学模型,分析了负载刚度的变化对控制特性的影响;其次设计了模型参考自适应(MRAC)控制器,并根据试验机力控系统的设计目标提出了一种具有最小拍响应特性且满足严格正实要求的参考模型;然后利用Simulink对最小拍参考模型MRAC控制器及PID控制器进行了仿真,并在自制的实验平台上采用两种不同刚度的试样分别进行了等速力加载实验,仿真及实验结果表明所设计的控制器能有效的抑制试样刚度的差异所引起的控制特性的变化,使电液伺服力控系统的响应具有良好的一致性.     

Multivariable closed-loop deadbeat control: a polynomial-matrix approach

The closed-loop deadbeat servo problem (CDSP), considered in this paper, consists of the synthesis of a linear, output feedback controller such that the control signal and tracking error both vanish, after a finite period of time, for every reference sequence from a prespecified class and for every initial state of a plant and the controller. The closed-loop structure is determined by studying necessary and sufficient conditions for deadbeat tracking performance. A new theorem asserts that if an open-loop deadbeat control strategy exists for every initial state of the plant and every reference function from a given class, then CDSP is solvable and all desired control laws are found in an explicit parametric form by solving simple, unilateral, linear equations in polynomial matrices. On the basis of this theorem a design algorithm is developed. Asymptotic stability of the closed-loop system exhibiting deadbeat properties is demonstrated. A numerical example is given to illustrate the usefulness and computational efficiency of the new design algorithm presented.     

Deadbeat control of linear multivariable generalized state-spacesystems

The classic idea of deadbeat control is extended to linear multivariable discrete-time generalized state-space systems using algebraic methods. The asymptotic properties of the linear quadratic regulator theory are used to obtain the classes of deadbeat controllers using stabilizing full semistate feedback. The solution is constructed from a `cheap control' problem. Both semistate and output deadbeat control laws are considered. The main design criteria are to drive the semistate and/or outputs of the system to zero in minimum time and that the closed-loop system be internally stable. Unique properties of these types of control laws are discussed. For semistate deadbeat control, all the (dynamic) poles including the ones at infinity are moved to the origin, whereas for output deadbeat, some of the finite transmission zeros are canceled. Numerically reliable algorithms are developed to solve both problems     

A note on parameterization of the class of deadbeat controllers

The problem of parameterizing the class of deadbeat controllers for a given discrete-time system through the minimum number of parameters was solved by Schlegel [1]. This note shows how to utilize the above solution to study some problems in designing deadbeat controllers. First, an algorithm is developed to compute a controller which minimizes-in an average sense-a given objective function. Second, a necessary and sufficient condition is given for the existence of an output deadbeat controller. Finally, the problem of parameterizing the set of deadbeat controllers for those systems transformable to the phase-variable block-canonical form is reconsidered.     

有限拍控制研究

设计了一种新的有限拍控制方法.由于控制器结构的改变,改善了开环系统的性质,使具有不稳定极点的被控对象也可以应用有限拍控制,扩大了有限拍控制的应用范围.     

Deadbeat output regulators for decouplable recursive non-linear systems

The deadbeat output regulator problem is formulated and solved in a straight-forward way for a class of decouplable multivarialbe recursive non-linear systems. It is shown that the decoupling control sequences drive each regulated output to zero and remain at zero thereafter in a minimum number of control iterations; this number is equal to the relative degree of the corresponding output. In addition, we show that the internal stability of a deadbeat closed-loop system is guaranteed only if the system is minimum phase.     

Output deadbeat control discrete-time multivariate systems

An algorithm is presented to compute output deadbeat controls for linear multivariable systems. The algorithm, based on quadratic optimization with no cost on control (cheap control), is numerically stable and covers the most general cases. The resulting controls are internally stable and are shown to drive the outputs of the system to zero in minimum time using state feedback. The central part of the algorithm is the construction of the nonunique state-cost matrix. Two alternatives are presented having different complexities and resulting in solutions having different properties     

State deadbeat control of nonlinear systems: Construction via sets

A geometric generalization of the discrete-time linear deadbeat control problem is studied. The proposed method to generate a deadbeat tracker for a given nonlinear system is constructive and makes use of sets that can be computed iteratively. For demonstration, derivations of the deadbeat feedback law and tracker dynamics are provided for an example system. Based on the method, a simple algorithm that computes the deadbeat gain for a linear system with scalar input is given.     

Multipurpose deadbeat controllers for multivariable systems

A simple and direct deadbeat control design algorithm for discrete-time multivariable systems is introduced. Our brief was to synthesize a realizable controller to achieve the following objectives: (1) input-output decoupling, (2) deadbeat tracking of any prespecified class of changeable deterministic reference signals and (3) changeable deterministic disturbances rejection where the changeable reference signals and disturbances can be different at each channel. Since the internal stability requirement is satisfied, our design algorithm can easily handle both unstable and non-minimum phase systems. Some constraints on the transfer function are also derived to make sure that the derived controller is realizable. Since all solutions can be described in parametric form, some of the performance criteria can be combined.     

基于多模型的非线性系统自适应最小方差控制

对于一类典型的离散时间非线性系统, 提出了一种基于多模型的自适应最小方差控制方法. 通过在平衡点附近建立线性模型, 用径向基函数神经元网络来补偿建模误差和未建模动态, 形成了非线性系统的多模型表示. 采用了具有积分性质的切换指标函数作为切换法则和最小方差的控制方法构成了多模型自适应控制器. 仿真实验的结果表明了这种方法的有效性.     

Simultaneous deadbeat tracking controller synthesis

A direct and simple design algorithm for the problem of simultaneously deadbeat tracking a prespecified class of inputs by only one controller is presented. This novel approach is based on polynomial algebra and the principle of system realizability. Without solving linear polynomial diophantine equations, the proposed procedure consists of solving a set of linear equations depending on system dynamics, and yields the deadbeat controller in a compact form well suited for system with inaccessible states and changeable reference signals. Since all solutions are described in a parametric form, some performance criteria can be easily incorporated as well. Examples are presented to illustrate the usefulness and computational easiness of this simple design algorithm.     

An indirect stochastic adaptive scheme with on-line choice ofweighting polynomials

An indirect adaptive control algorithm combining a quadratic cost measure of the Clarke-Gawthrop type and the classical control strategy of pole placement is presented. It updates the weighting polynomials of the cost function online in such a way that the closed-loop poles are located at prespecified positions. The convergence and stability of the adaptive control algorithm is also given without the assumption that the system is minimum phase     

On the general solution of the state deadbeat control problem

In this note, the state deadbeat control problem is considered. It is shown that, after appropriate change of basis of input and state spaces, the general solution of the state deadbeat control problem can be expressed completely by the rows of the powers of system matrix. This result yields a very simple procedure for the calculation of a state feedback deadbeat control gain. It also provides the number of free parameters which could be used for further design purposes. The results are illustrated by an example at the end of the note     

Double objective optimal multivariable ripple-free deadbeat control

This paper presents novel results on optimal multivariable deadbeat control. Given a discrete-time, stable, linear, time invariant plant model, we give a simple parameterization of all stabilizing ripple-free deadbeat controllers of a given order. The free parameter is then optimized in the sense that a quadratic index is kept minimal. The optimality criterion has the advantage of accounting for both tracking performance and magnitude of the control effort. The proposed design procedure is simple to use and allows the tuning of the controller with a scalar weighting factor. Simulation results are included to illustrate the effectiveness of the proposed design algorithm.     

不确定性系统的自适应鲁棒跟踪控制

针对存在未知干扰和未建模动态等不确定性的系统的自适应鲁棒跟踪控制问题进行了 探讨.首选将l1优化控制器的有限拍设计方法结合给出了最优鲁棒稳态跟踪控制器的设计方法． 然后利用集员辨识的思想,将名义模型的参数和未建模动态及干扰的大小作为未知参数,提出了 一种递推参数估计方法.最后将上述研究结果结合起来提出了一种自适应鲁棒跟踪控制策略,证 明了自适应算法的全局收敛性并给出了鲁棒跟踪性能指标的一下较紧的上界.与现有的结果相 比,本文提出的自适应控制具有非保守的鲁棒稳定性,具有渐近最优的鲁棒跟踪性能.     

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.     

Self-tuning control application to a nuclear power plant

The aim of this paper is to investigate the application possibilities of a self-tuning control method to a pressurized-water reactor (PWR) nuclear power plant. A self-tuning control algorithm which incorporates pole assignment into the generalized minimum variance strategy with a particular form of cost function is employed. This algorithm enables closed-loop system stability characteristics to be readily specified and facilitates reference following. The control system design is based on a second-order linear model with unknown, time-varying parameters. To ensure that this low-order model describes the complex real dynamics well enough for control purposes, control parameters are updated on-line with a recursive estimation sequences of the extended least-squares method. Weighting polynomials are also adjusted on-line to keep closed-loop poles at the desired location and to satisfy the zero steady-state condition and disturbance rejection. The purpose of this control system is to hold the average coolant temperature in the reactor as near as possible to a desired but changing reference value in the load-following mode of the nuclear power plant. The position of the control rods is an appropriate control variable. Simulation results are very successful and show the possibilities of the adaptive control application to actual plants.     

广义最小方差自校正重置PID控制器及其在压力系统中的应用研究

针对压力系统的纯延迟、大惯性、非线性、时变等特点,本文将重置控制和以广义最小方差为性能指标的自校正PID控制相结合,提出一种广义最小方差自校正重置PID控制方法。该方法首先根据被控对象的数学模型,以广义最小方差为目标设计广义最小方差控制器,通过选择该控制器的分母多项式,求解Diophantine方程,得到具有PID结构形式的广义最小方差控制器,再在该控制器的积分项中引入重置控制,构成广义最小方差重置PID控制;对于模型未知或参数慢时变的被控对象,通过采用带遗忘因子的递推最小二乘法构建系统的自适应机制,增强控制系统的自适应能力和鲁棒性。最后,将该控制方法应用于压力容器的恒值控制中,获得了比较满意的控制效果。     

基于数据自适应评判的离散2-D系统零和博弈最优控制

提出了基于一种迭代自适应评判设计(ACD)算法解决一类离散时间Roesser型2-D系统的二人零和对策问题. 文章主要思想是采用自适应评判技术迭代的获得最优控制对使得性能指标函数达到零和对策的鞍点. 所提出的ACD可以通过输入输出数据进行实现而不需要系统的模型. 为了实现迭代ACD算法, 神经网络分别用来近似性能指标函数和计算最优控制率. 最后最优控制策略将应用到空气干燥过程控制中以证明其有效性.