Tuning of multivariable PI-controllers for unknown delay-differential systems

A design method for tuning of multivariable PI-controllers for possibly unknown linear time-invariant delay-differential systems is presented. The plant is assumed to be stable with input and output delays and subject to step disturbances. The multivariable PI-controller may be tuned with the aid of open-loop step responses. The stability and robustness of the control law is discussed and an example is given to show the applicability of the controller.     

Tuning of multivariable PI-controllers for unknown systems with input delay

A design method for on-plant tuning of multivariable PI-controllers for unknown systems is presented. The plant is assumed to be linear, open-loop stable with input delays and subject to step disturbances. The multivariable PI-controller may be tuned with the aid of open-loop step-responses. Finally an example is given to show the applicability of the controller proposed.     

Steady-state feedforward compensation for discrete time multivariable systems

A class of discrete-time feedforward controllers that are designed for steady-state disturbance rejection and command tracking are introduced for linear multivariable systems. The controllers use discretized future set points along time-varying trajectories of the exogenous inputs described by linear models. This is in contrast to the use of the time derivatives of the instantaneous set points in the conventional asymptotic tracking controllers. As a result, apart from numerical noise reduction, the need for real-time generation of the derivative states of the exogenous input models is avoided for the purpose of realization of the feedforward controllers.     

Reduced order controller design for discrete time systems

Robust discrete control system design techniques and model reduction are discussed. A new linear quadratic guussian/loop transfer recovery procedure for discrete time systems is presented. In this technique, a full-state feedback or an output injection feedback is designed which has the desired loop shape, and then recovered by a realizable linear quadratic gaussian controller. To do this, results that show the effects of the weighting matrices (noise intensities) on linear quadratic regulator (Kalman-Bucy filter) return difference and inverse-return difference arc derived and a procedure to recover the linear quadratic regulator loop transfer function is described. The complexity of the resulting controller is then reduced without causing closed-loop instability. Two methods for model reduction are considered. The first is the discrete balanced realization and the second is P frequency weighting technique where it is possible to vary the approximation accuracy with frequency. The controller design and reduction techniques are illustrated by designing a reduced order controller for an 8th order lumped inertia flexible mechanical system.     

Adaptive controller for multivariable delayed systems

A self-tuning controller is presented for the control of multi-input-multi-output discrete systems with multiple time delays. It is established that under suitable offline choice of the performance weights the plant output deviations converge to zero even for non-minimum-phase systems.     

High performance controllers for unknown multivariable systems

Recent work on the design of robust proportional plus integral non-adaptive process controllers for unknown minimum-phase (but possibly unstable) multivariable systems is discussed and extended to predict permissible data inaccuracies and illustrated by application to an open-loop unstable batch process.     

多变量非方系统集中式PI 控制器设计

针对工业过程中含有多时滞的高维多变量非方系统,基于等价传递函数理论,研究其集中式PI控制器设计问题.利用等价传递函数(ETF)与非方被控对象传递函数广义逆之间的关系,提出一种精度更高的ETF参数化算法,并推导出ETF模型的解析通式.所提出的ETF算法既避免了求广义逆的复杂运算,又提高了控制性能,且适用于高维非方系统.仿真实例验证了所提出的ETF算法的有效性和优越性.     

Evolutionary multi-objective optimisation with preferences for multivariable PI controller tuning

Multi-objective optimisation design procedures have shown to be a valuable tool for control engineers. They enable the designer having a close embedment of the tuning process for a wide variety of applications. In such procedures, evolutionary multi-objective optimisation has been extensively used for PI and PID controller tuning; one reason for this is due to their flexibility to include mechanisms in order to enhance convergence and diversity. Although its usability, when dealing with multi-variable processes, the resulting Pareto front approximation might not be useful, due to the number of design objectives stated. That is, a vast region of the objective space might be impractical or useless a priori, due to the strong degradation in some of the design objectives. In this paper preference handling techniques are incorporated into the optimisation process, seeking to improve the pertinency of the approximated Pareto front for multi-variable PI controller tuning. That is, the inclusion of preferences into the optimisation process, in order to seek actively for a pertinent Pareto front approximation. With such approach, it is possible to tune a multi-variable PI controller, fulfilling several design objectives, using previous knowledge from the designer on the expected trade-off performance. This is validated with a well-known benchmark example in multi-variable control. Control tests show the usefulness of the proposed approach when compared with other tuning techniques.     

A model reference adaptive control system for discrete multivariable systems with time delays

This paper presents a new method for designing a model reference adaptive control system for multivariable plants with time delays in the input and output variables. An adaptive algorithm guarantees the asymptotic stability of the error between the plant output and the reference sequence using no anticipative value of the plant output and unknown plant parameter. The validity of the theoretical result is illustrated by a numerical example.     

离散时间系统的滑模控制器设计与仿真研究

针对不确定性离散时间系统,分析和设计了一类变结构控制器。当存在外界干扰和不确定性时,系统状态也是全局有界稳定的。一个新的切换面作为系统的输出信号被提出,特别用来设计滑模控制器。系统状态一旦进入到准滑动模态,就对设备参数变化和外界干扰显示出强的鲁棒性,因为控制器的设计完全考虑了边界层的影响。外推法被用来估计不确定离散时间系统的不确定值。两种方法均有效地消除了系统的抖振,确保了系统的稳定性,且保证了变结构控制系统良好的品质。最后,仿真结果证实了所提出方法的有效性。     

高维多变量系统集中式PI 控制器设计

针对高维多变量系统,基于等价传递函数理论研究全矩阵结构的PI控制器设计问题.同时考虑对象的稳态增益和响应速度两个因素,提出一种新的等价传递函数参数化方法;利用等价传递函数与被控过程的传递函数逆阵之间的关系,推导出等价传递函数的解析通式;在此基础上,结合经典的PID控制技术进行多变量系统集中式PI控制方法研究.最后通过典型工业过程实例,验证了所提出设计方法的简单性和有效性.     

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.     

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for pieccwise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ perfomiance and the controller can be obtained by solving a set of bilinear lnatrLx inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global qnadnmc Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.     

未知多变量非线性系统自适应模糊预测控制

对一类未知多变量非线性系统提出了直接自适应模糊预测控制方法,此方法首先对被控对象提出了线性时变子模型加非线性子模型的预测模型,然后直接用模糊逻辑系统组成的向量来设计预测控制器,并基于时变死区函数对控制器中的未知向量和广义误差估计值中的未知矩阵进行自适应调整．文中证明了此方法可使广义误差向量估计值收敛到原点的一个邻域内．     

A third-order sliding mode controller for nonlinear multivariable systems

This paper proposes a third-order sliding mode controller for nonlinear multivariable systems with uncertain parameters and subject to external disturbances. The controller achieves fast convergence rate, high tracking accuracy, and a reduced level of chattering. The stability of the controller and its global ultimately uniform convergence is proved by the Lyapunov stability theory. Simulation results on a single inverted pendulum system are given to illustrate the effectiveness of the proposed control scheme by comparing it with methods such as a second-order supertwisting controller, a third-order supertwisting controller, and an integral terminal third-order sliding mode controller.     

Unconstrained quasi-continuous representation of multivariable discrete systems

Substituting (1, 1) P'adé approximants for sampling delays from numerical integration in time-discretized linear multivariable system equations yields quasi-continuous (q-c) mathematical representations of the discrete system. The q-c models can indicate distortion resulting from discretization of a continuous system in the form of perturbations of the system parameter matrices and an overall time delay. Corresponding compensations tend to restore a discretized system to its continuous form prior to discretization. Analyses of characterizing transition matrices, stability, sampling frequency and accuracy of illustrative examples of closed-loop realizable numerical integration points to merits of convenience and accuracy in ‘ low pass ’ applications.     

Observers for linear discrete multivariable systems with inaccessible inputs

The problem of observing the state vector of a discrete-time multivariable system subjected to inaccessible inputs is considered. Using a polynomial-type approximation for these inputs, a set of necessary and sufficient conditions that can be readily applied to determine the existence of an observer is obtained. Computer simulation results for a third-order two-input two-output system are included.     

时滞状态反馈下离散时滞系统H∞控制器失效时间分析

针对控制器存在短暂失效的情形,研究一类时变时滞离散系统在时滞状态反馈控制下的H_∞控制器失效时间分析问题.本文的目标是寻求控制器正常工作时间与失效时间的比率应满足的条件以确保系统指数镇定且具有加权l_2增益.为此,基于切换的思想,所考虑的系统被转化为一个仅含有两个子系统的切换系统,其中一个子系统是控制器失效时的不稳定子系统,另一个是控制器未失效时的稳定子系统.通过使用多Lyapunov函数及平均驻留时间方法,给出问题可解的充分条件及时滞状态反馈H_∞切换控制器的设计方案.仿真算例表明了所得结果的有效性.     

Constrained discrete-time PI controller design for output PDFs of stochastic systems with time delays

This article presents a new proportional-integral (PI) tracking control strategy for non-Gaussian stochastic systems based on a square root B-spline model for the output probability density functions (PDFs). Following the square root B-spline approximation to the measured output PDF, a non-linear discrete-time dynamical model can be established between the control input and the weights related to the PDFs. It is noted that the PDF tracking is transformed to a constrained dynamical tracking control problem for weight dynamics. For the non-linear discrete-time weight model including time-delay terms and exogenous disturbances, convex linear matrix inequality optimisation algorithms are used to design a generalised PI controller such that stabilisation, state constraint and tracking performance can be guaranteed simultaneously. Furthermore, in order to enhance the robustness, the peak-to-peak measure index is applied to optimise the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.     

Design of PI controller for multivariable feedback control system using the inverse-Nyquist-array method

The paper presents an application of the Rosenbrock inverse-Nyquist-array method in the design of PI controller for a multivariable control system. The proposed grapho-analytical procedure enables all controller parameters to be readily, determined when an application of conventional PI controllers within the control loops of multivariable control system yields a good general performance. The incorporation of an integral action term to each loop of the control system improves the system accuracy eliminating any steady-state error, when step changes in the reference values of the control loops are employed. For purpose of illustration of the design technique, the example based on a model of a 30-plate distillation column is considered.