Multivariable adaptive control as a natural extension of SISO adaptive control

The concepts of a potentially structural non-singularity and a structural non-singularity are introduced in this paper. Using these concepts, we derive the result that for almost all cases the plant to be controlled has a diagonal interactor by using an appropriate diagonal proper precompensator. Furthermore, both the precom-pensator and the interactor can be determined only from the structural information of T(s), the relative degrees of each element of T(s), without requiring any parametric information about T(s). Therefore, by assuming that the a priori knowledge of the plant consists of the relative degrees of each element of T(s) as well as the observability index of T(s), we can make MI MO adaptive control be quite a natural extension of SISO adaptive control.     

Multivariable adaptive control: identifiable parameterizations andparameter convergence

The paper presents a direct model reference adaptive control algorithm for multivariable systems that has guaranteed parameter convergence properties. The algorithm requires fewer parameters than existing schemes, and the parameters converge to their nominal values under persistency of excitation conditions. Simple frequency domain conditions on the external inputs are derived to satisfy these conditions. The convergence of the controller parameters to their nominal values guarantees a certain degree of robustness of the algorithms and ensures that the model matching objective is satisfied asymptotically     

Multivariable adaptive control using high-frequency gain matrix factorization

In this note, we extend the application of a less restrictive condition about the high-frequency gain matrix to design stable direct model reference adaptive control for a class of multivariable plants with relative degree greater than one. The new approach is based on a control parametrization derived from a factorization of the high-frequency gain matrix K/sub p/ in the form of a product of three matrices, one of them being diagonal. Three possible factorizations are presented. Only the signs of the diagonal factor or, equivalently, the signs of the leading principal minors of K/sub p/, are assumed known.     

Multivariable adaptive predictive control of a binary distillation column

This paper presents a tutorial review of an adaptive predictive control system (APCS). Special emphasis is given to the key issues involved in the practical application of APCS to real processes. These practical issues are illustrated by actual application of SISO and MIMO control of a pilot scale binary distillation column. The experimental evaluation of this method reveals the simplicity of the adaptive algorithm and its excellent performance in an industrial type environment. The experimental results easily outperformed well-tuned classical PID controllers. A brief review of other applications of adaptive control to chemical processes is also included in this paper.     

Disturbance instabilities in an adaptive system

Two types of disturbance instability of simple adaptive schemes are analyzed. A drift equation shows how stable equilibria are forced to infinity by infrequent but persistent switches of a constant disturbance. The σ-modification proposed by P. Ioannou counteracts these instabilities.     

Multivariable adaptive dynamic surface control based on norm estimation of unknown parameter matrices

In this article, a novel output-feedback adaptive dynamic surface control scheme is proposed for linear time-invariant multivariable plants based on the norm estimation of unknown parameter matrices. Besides avoiding the explosion of complexity problem in traditional multivariable backstepping design, the proposed scheme has the following features: (1) only one parameter needs to be updated on-line regardless of the plant order and input–output dimension, (2) only the Hurwitz condition is required for the high-frequency gain matrix and (3) the ?_∞ performance of the tracking error can be guaranteed. It is shown that all signals of the closed-loop system are semi-globally uniformly bounded. Simulation results are given to illustrate the effectiveness of the proposed scheme.     

Multivariable adaptive predictive control of an aerated lagoon for a wastewater treatment process

The application of an adaptive multivariable predictive model-based control scheme for the control of biotechnological processes is reported. Control design consists of regulating the residual concentrations of two main variables of a multistage wastewater treatment process. Unavailability of measurements leads to the development of an identification technique derived to estimate simultaneously unavailable state variables and time-varying parameters of a nonlinear process. Convergence of the estimation scheme is demonstrated via a theorem and its proof using Lyapunov's method. The estimated variables are used in the explicit design of the control algorithm. Good simulation results have been obtained in regulation, tracking, disturbance rejection and transient behaviour, showing the efficiency of this adaptive control strategy.     

Multivariable dead-beat control

The problem of forcing the state of a linear, multivariable, sampled-data system to zero in a minimum number of time steps is discussed. The solution to the posed problem is given as linear state feedbacks. Numerical aspects of the algorithms for computing these feedbacks are presented. The methods are successfully used to control the temperature profile of a diffusion process in the laboratory.     

Two-channel adaptive hybrid control of the air-to-fuel ratio and torque of automobile engines

Combined feedforward/feedback control algorithm for highly nonlinear systems was proposed on the basis of the approximating hybrid model. The designed MIMO controller enables simultaneous control of the air-to-fuel ratio and torque for injector automobile engines. The theoretical results were validated experimentally with physical cars.     

Multivariable weighted predictive control

A multivariable Weighted Predictive Control (MV WPC) algorithm is presented and properties of the multivariable closed-loop system are discussed. Simulation studies for industrial processes show that satisfactory closed-loop performance can be achieved by tuning the design parameters in the WPC algorithm. A series of tuning guidelines for a successful design are also proposed.     

Multivariable control of double-effect distillation configurations

Heat-integrated double effect distillation column design is promising from the viewpoint of energy conservation. However, the control of the system is very difficult in the sense that the system is nonlinear, multivariable and interacting. A new model-based control scheme developed by Han and Park (AIChE J. 1993, 39 (5), 787) to deal with these difficulties has been applied to these heat-integrated distillation configurations (feed-split configuration, heavy-split configuration). Our simulation results indicate that the control scheme is able to overcome the severity of interactions and shows good control performance for a heat integrated double-effect distillation column with high purity specification.     

基于Kp=S1D1U1分解的多变量鲁棒模型参考自适应控制

针对具有噪声的多变量系统,利用高频增益矩阵K。_p=S_1D_1U_1分解,提出了一种多变量鲁棒直接型模型参考自适应控制．通过重新证明一些同单变量系统鲁棒自适应控制理论相似的性质,及重新定义规范化信号,找出了闭环系统的所有信号与规范化信号之间的关系,严格地分析了闭环系统的稳定性和鲁棒性．     

Exponential stability of linear equations arising in adaptive identification

The stability, properties are examined of various time-varying linear differential equations which arise in model reference adaptive identification schemes. Necessary and sufficient conditions for exponential stability are presented.     

轴流压缩系统失稳现象的主动控制

为了开展对压缩系统旋转失速和喘振两类失稳现象的主动控制研究,进一步改善压缩系统防喘振控制的效果,选取了轴流压缩系统的四阶失稳模型,将容腔出口节流阀作为主动控制的作动机构,用非线性控制理论中的backstepping方法,设计抑制压缩系统失稳现象的主动控制律,应用于失稳模型,通过仿真,验证了在变转速条件下,旋转失速、喘振以及旋转失速和喘振先后发生时的控制效果.肯定了失稳主动控制比传统的防喘振控制和单纯的喘振主动控制的优越性,并通过仿真,考察了控制律对于系统特性参数和结构参数变化的鲁棒性.结论:研究压缩系统失稳的主动控制,无论在理论和实用都有重要意义.     

Multivariable constrained process control via Lyapunov R-functions

This paper proposes a smooth control Lyapunov function with maximal controlled domain of attraction for the state-feedback control of constrained uncertain linear systems describing the dynamics of multivariable processes. Constructive algorithms are shown to build such a control Lyapunov function within a merging procedure due to the so-called R-functions. Robustness with respect to polytopic model uncertainties and disturbance rejection are also discussed. The controlled dynamics of two chemical reactions are simulated to show the benefits of the proposed strategy.     

Optimal multi-variable control of gas turbine engines

This paper focuses on the practical problems of gas turbine engine local-optimal multi-variable control design and implementation. An algorithm for real-time resolution of the optimization problem is proposed for the non-linear optimal control design of the engine. The example of the turbo-jet engine multi-variable control presented shows that the method developed is highly efficient.     

EGR control of pressure-wave supercharged IC engines

This paper addresses the problem of exhaust gas recirculation occurring when pressure-wave superchargers are used as boosting devices for IC engines.

During hard accelerations, critical situations arise whenever large amounts of exhaust gas are recirculated over the charger from the exhaust to the intake manifolds of the engine. Such recirculations cause the engine torque to drop sharply and thus severely affect the driveability of the vehicle. In order to prevent such situations, the actuators such as throttles, valves, etc., have to be controlled in a coordinated way. Such a control system and its model-based design and verification on an engine test bench are described here in detail.