基于非线性静态反馈解耦的三容系统PI控制

三容系统实验台是模拟多容器流程系统的多输入多输出、时变、强耦合、非线性的实验系统。采用一种基于非线性静态反馈的解耦方法进行三容实验系统的液位控制,当系统满足一定的务件时,可以寻找到一个输出与等效新输入之间的线性微分方程关系,然后再选择合适的状态反馈形式即可使该非线性系统解耦。经解耦,三容系统可分解为两个相互独立的单输入单输出线性子系统,对每个这样的子系统可以采用PI控制。给出了应用的实验结果和与没有使用解耦的PI控制方法的比较：     

Gain-scheduled L-one control for linear parameter-varying systems with parameter-dependent delays

This paper deals with the problem of gain-scheduled L-one control for linear parameter-varying (LPV) systems with parameter-dependent delays. The attention is focused on the design of a gain-scheduled L-one controller that guarantees being an asymptotically stable closed-loop system and satisfying peak-to-peak performance constraints for LPV systems with respect to all amplitude-bounded input signals. In particular, concentrating on the delay-dependent case, we utilize parameter-dependent Lyapunov functions (PDLF) to establish peak-to-peak performance criteria for the first time where there exists a coupling between a Lyapunov function matrix and system matrices. By introducing a slack matrix, the decoupling for the parameter-dependent time-delay LPV system is realized. In this way, the sufficient conditions for the existence of a gain-scheduled L-one controller are proposed in terms of the Lyapunov stability theory and the linear matrix inequality (LMI) method. Based on approximate basis function and the gridding technique, the corresponding controller design is cast into a feasible solution problem of the finite parameter linear matrix inequalities. A numerical example is given to show the effectiveness of the proposed approach.     

A parametric frequency domain approach to decoupling with coupled rows

This contribution considers the incomplete decoupling of non-minimum phase and non-decouplable systems by static state feedback, where a stable diagonal decoupling is not possible. By introducing a coupled row in the reference transfer matrix, so that one output is affected by several reference inputs, an incompletely decoupled but internally stable closed loop system is obtained. This decoupling problem is solved using a parametric approach to the design of state feedback controllers in the frequency domain. Explicit expressions are derived for the design parameters of the state feedback controller achieving the decoupled reference transfer matrix. A simple example demonstrates the proposed design procedure.     

多变量多时滞系统的前馈补偿解耦及IMC-PID控制

多变量系统控制器设计中遇到的主要难题是多时滞和强铰链耦合问题;对于非奇异方阵系统,根据解耦理论通过串级前馈时滞补偿器将原系统解耦为多个单变量小时滞系统,运用模型降阶技术,将解耦后的复杂单变量小时滞系统逼近为FOPDT(一阶环节+延时)形式,采用IMC控制策略实现多个单变量系统单位反馈控制,运用了麦克劳林级数展开式,通过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有效性地补偿系统时滞,同时现实解耦;解决了多变量多时滞系统控制器设计复杂性的难题,有一定的工程参考价值。     

Transfer matrix approach to the triangular block decoupling problem

The triangular block decoupling problem for linear multivariable systems is studied via the transfer matrix approach. This approach clearly separates the problem of admissible control laws from the one of desired decoupled system specifications. Necessary and sufficient triangular decoupling conditions are given for various control laws. These conditions are expressed in a very simple way in terms of linear dependance among the transfer matrix rows. It turns out that when the problem is solvable, this can be done by static state feedback on a minimal realization of the system. Furthermore it is shown that whenever triangular block decoupling is possible, it is also attainable with stability.     

A Design Of Multiloop Predictive Self‐Tuning Pid Controllers

In this paper, a new design scheme of multiloop predictive self‐tuning PID controllers is proposed for multivariable systems. The proposed scheme firstly uses a static pre‐compensator as an approximately decoupling device, in order to roughly reduced the interaction terms of the controlled object. The static matrix pre‐compensator is adjusted by an on‐line estimator. Furthermore, by regarding the approximately decoupled system as a series of single‐input single‐output subsystems, a single‐input single‐output PID controller is designed for each subsystem. The PID parameters are calculated on‐line based on the relationship between the PID control and the generalized predictive control laws. The proposed scheme is numerically evaluated on a simulation example.     

Model predictive control of constrained LPV systems

This article considers robust model predictive control (MPC) schemes for linear parameter varying (LPV) systems in which the time-varying parameter is assumed to be measured online and exploited for feedback. A closed-loop MPC with a parameter-dependent control law is proposed first. The parameter-dependent control law reduces conservativeness of the existing results with a static control law at the cost of higher computational burden. Furthermore, an MPC scheme with prediction horizon ‘1’ is proposed to deal with the case of asymmetric constraints. Both approaches guarantee recursive feasibility and closed-loop stability if the considered optimisation problem is feasible at the initial time instant.     

Frequency-interval control configuration selection for multivariable bilinear systems

Control configuration selection is the procedure of choosing the appropriate input and output pairs for the design of decoupled (SISO or block) controllers for multivariable systems. This step is an important prerequisite for a successful industrial control strategy. The focus of this paper is on the problem of control configuration selection for a class of nonlinear systems which is known as bilinear systems. First, new frequency-interval gramians are presented for bilinear systems. These gramians are devised in particular for many applications in which one is interested in analysis and control of a system within a frequency-interval. It is shown that these gramians are the solutions to the so-called frequency-interval generalized Lyapunov equations. These gramians are used in the interaction measure for control configuration selection of MIMO bilinear systems. Most of the results on control configuration selection, which have been proposed so far, can only support linear systems. The proposed gramian-based interaction measure supports bilinear processes, can show the input–output interactions for any frequency-interval of interest, and can be used to propose a richer sparse or block diagonal controller structure.     

Achieving vector relative degree for nonlinear systems with parametric uncertainties

Several algorithms for adaptive control, as well as for static state feedback decoupling, feedback linearization, or inversion of nonlinear multivariable systems require that the systems have full vector relative degree, in order to be applied. In this paper, we provide a parameter-independent method of achieving full vector relative degree for nonlinear multivariable systems which do not have it. We determine conditions under which a diagonal dynamic precompensation is sufficient to achieve vector relative degree for multivariable nonlinear systems, and describe a simple algorithm which determines such compensation.     

Decoupling Controller with Disturbance Observer for LTI MIMO Systems

In this paper, a decoupling multivariable control strategy for linear time‐invariant (LTI) multi‐input/multi‐output (MIMO) systems is proposed. The strategy includes a multivariable disturbance observer (MDOB) and a decoupling controller. This MDOB is introduced to improve the system performances when the system encounters severe external disturbances. H₂ optimal scheme is utilized to design the MDOB filter. The controller is developed based on an inverse control method, through which the design process can be simplified. Simulation results certify the effectiveness of the proposed control strategy.     

多变量解耦控制的工业过程运行层次控制方法

基于多变量解耦控制技术,提出了一种工业过程运行的层次控制方法,用于实现表征过程整体运行性能的工艺指标.底层回路控制系统采用多回路PI/PID控制技术进行设计,用于将关键工艺参数控制在给定的工作点.针对中被控过程和底层回路控制系统构成的文义对象,采用扩展的单位反馈解耦方法设计上层回路设定控制器,该回路设定控制器能够克服系...     

Discretization and event triggered digital output feedback control of LPV systems

This paper investigates the problem of discretization and digital output feedback control design for continuous-time linear parameter-varying (LPV) systems subject to a time-varying networked-induced delay. The proposed discretization procedure converts a continuous-time LPV system into an equivalent discrete-time LPV system based on an extension of the Taylor series expansion and using an event-based sampling. The scheduling parameters are continuously measured and modeled as piecewise constant. A new transmission of the measured output to the controller is triggered by significant changes in the parameters, yielding time-varying transmission intervals. The obtained discretized model has matrices with polynomial dependence on the time-varying parameters and an additive norm-bounded term representing the discretization residual error. A two step strategy based on linear matrix inequality conditions is then proposed to synthesize a digital static scheduled output feedback control law that stabilizes both the discretized and the LPV model. The conditions can also be used to provide robust (i.e., independent of the scheduling parameter) static output feedback controllers. The viability of the proposed design method is illustrated through numerical examples.     

一类MIMO非线性系统的稳定干扰解耦控制

基于非线性系统的微分几何理论相对阶概念,研究了一类M IMO非线性系统的干扰解耦问题(DDP),定义了M IMO系统关于干扰的向量相对阶,给出了该类非线性系统通过静态状态反馈的干扰解耦可解的充分必要条件,并进一步讨论了解耦系统反馈镇定问题,给出了解耦系统可镇定的充分条件,仿真结果验证了该方法的有效性.     

Output regulation boundary control of first-order coupled linear MIMO hyperbolic PIDE systems

ABSTRACT

The work addresses the output regulation problem for coupled linear multiple input multiple output (MIMO) hyperbolic partial integro-differential equation systems with disturbances affecting the systems through the space and boundary input. The exosystems are extended to generate ramp signals and general family of polynomial signals. The system decomposition is applied through the state transformation and yields a decoupled equivalent system. Based on the decoupled form, the backstepping transformation is applied and then in the new coordinate, the full state and output-feedback regulators are designed, respectively. For the state feedback regulator, the corresponding regulator equation is obtained and its solvability conditions are provided to facilitate the regulator design and feasibility. The design of observer-based regulator is based on the decoupling of the observer error system into a PDE subsystem and an ODE subsystem so that the backstepping approach achieves stabilisation by eigenvalue assignment leading to design of observer stabilizing gains.     

Experimental evaluation of a multivariable adaptive nonlinear predictive controller

A new multivariable adaptive nonlinear predictive controller is designed using a general nonlinear input-output model and variable transformations. The controller is similar in form to typical linear predictive controllers can be tuned analogously or by specifying a single parameters for each controlled variable. In addition, the design procedure is computationally efficient. The new controller is compared to a multi-loop proportional-integral (PI) controller with one-way static decoupling and to an adaptive linear predictive controller through tests on a simulated nonlinear distillation column. The new controller performed well in an experimental application to a multicomponent distillation column.     

一种预测优化解耦补偿器的研究设计

提出一种通过对象输出预测实现对角优化解耦的补偿器设计方法,给出了该补偿器 的解耦算式.此预测优化解耦补偿器有别于传统的动态或静态解耦补偿方法,适用于具有非 最小相位特性的众多多变量系统的解耦补偿,具有较好的稳定性和可实现性.同时给出了仿 真实验结果.     

A multivariable MRAC scheme with application to a nonlinear aircraft model

This paper revisits the multivariable model reference adaptive control (MRAC) problem, by studying adaptive state feedback control for output tracking of multi-input multi-output (MIMO) systems. With such a control scheme, the plant-model matching conditions are much less restrictive than those for state tracking, while the controller has a simpler structure than that of an output feedback design. Such a control scheme is useful when the plant-model matching conditions for state tracking cannot be satisfied. A stable adaptive control scheme is developed based on LDS decomposition of the high-frequency gain matrix, which ensures closed-loop stability and asymptotic output tracking. A simulation study of a linearized lateral-directional dynamics model of a realistic nonlinear aircraft system model is conducted to demonstrate the scheme. This linear design based MRAC scheme is subsequently applied to a nonlinear aircraft system, and the results indicate that this linearization-based adaptive scheme can provide acceptable system performance for the nonlinear systems in a neighborhood of an operating point.     

离散LPV重复过程的l2-l∞ 动态输出反馈控制

探究离散线性参数变化(LPV) 重复过程的l₂-l_∞ 动态输出反馈控制问题. LPV 重复过程是一类复杂的时变2D 系统. 对于整个参数变化空间, 传统方法是基于二次稳定框架设计过程的控制器, 具有较大的保守性. 这里利用参数依赖Lyapunov 函数, 设计离散LPV 重复过程的参数依赖鲁棒l₂-l_∞  动态输出反馈控制器, 可确保闭环离散LPV 重复过程沿通道渐近稳定, 且具有一定的l₂-l_∞  扰动抑制水平. 最后, 仿真结果验证了所提出方法的有效性.

     

Control of ball mill grinding circuit using model predictive control scheme

Ball mill grinding circuits are essentially multivariable systems with high interaction among process variables. Traditionally grinding circuits are controlled by detuned multi-loop PI controllers that minimize the effect of interaction among the control loops. Detuned controllers generally become sluggish and a close control of the circuit is not possible. Model Predictive Controllers (MPC) can handle such highly interacting multivariable systems efficiently due to its coordinated approach. Moreover, MPC schemes can handle input and output constraints more explicitly and operation of the circuits close to their optimum operating conditions is possible. Control studies on a laboratory ball mill grinding circuit are carried out by simulation with detuned multi-loop PI controllers, unconstrained and constrained model predictive controllers and their performances are compared.     

Decoupling and arbitrary pole placement in linear systems using output feedback

Linear multivariable systems are considered which can be decoupled by state-variable feedback, but arbitrary pole placement and decoupling cannot be achieved simultaneously. These systems cannot be decoupled using output feedback. A compensator is presented which allows decoupling and arbitrary pole placement in the augmented system using output feedback.