Robust controller synthesis for multivariable nonlinear systems with unmeasured disturbances

This work concerns robust controller synthesis using the differential geometric concepts for minimum phase nonlinear systems with unmeasurable disturbances. A pseudo-linearization of the disturbance model at the input-output linearization stage is applied to yield a linear subsystem for controller design. Based on this linear model, a multi-loop controller framework is implemented, whereby μ-synthesis is used to design off-line robust controller in the outer loop while state feedback is implemented in the inner loop. Through proper selection of weights, the outer robust controller is explicitly designed to address both uncertainty and disturbance rejection whereas the inner controller is used for on-line static state feedback. Numerical simulations are used to illustrate robustness of the controller for multi-input multi-output temperature control in two non-isothermal continuous stirred tank reactors in series.     

Computer-aided analysis and design of robust multivariable control systems for chemical processes

A conceptual framework to design robust process control systems is develope d and its realization through an interactive computer-aided design software is presented. The overall design methodology is based on a unified treatment of recent theoretical results in modern control and new computational techniques in symbolic logic manipulation, singular value decomposition and optimization. Several physical examples are given to demonstrate the application of the design approach and the utility of its computer software.     

Perturbation signal design for neural network based identification of multivariable nonlinear systems

The paper focuses on issues in experimental design for identification of nonlinear multivariable systems. Perturbation signal design is analyzed for a hybrid model structure consisting of linear and neural network structures. Input signals, designed to minimize the effects of nonlinearities during the linear model identification for the multivariable case, have been proposed and its properties have been theoretically established. The superiority of the proposed perturbation signal and the hybrid model has been demonstrated through extensive cross validations. The utility of the obtained models for control has also been proved through a case study involving MPC of a nonlinear multivariable neutralization plant.     

PI controller design for a class of distributed parameter systems

In this paper, the regulation problem of convection governed dynamical processes described by linear distributed parameter models with position-independent inputs is addressed by combining the method of characteristics (MC) and the Malek-Zavarei and Jamshidi theorem. In this approach, the MC is used to transform the first order partial differential equations model of such processes into a set of time-delayed ordinary differential equations whose elements are used to generate certain matrices that satisfy linear matrix inequalities that render the proportional integral (PI) control parameters that guarantee the process stability. The performance of the proposed PI controller is tested via numerical simulations in the temperature regulation of a linear heat exchanger and compared to a tightly tuned classical PI controller. The application of the proposed controller is extended to regulate the outlet concentration in a nonlinear non-isothermal plug flow reactor. It is shown that the proposed controller is able to handle the infinite dimensional nature of the process model yielding smooth and unsaturated responses around the predetermined set-point trajectory in the face of load changes, time varying boundary conditions and set-point changes.     

Experiment design for control‐relevant identification of partially known stable multivariable systems

Design of experiments for identification of control‐relevant models is at the heart of robust controller design. In a number of prior publications, experiment designs have been developed that generate input/output data for efficient identification of models satisfying the integral controllability (IC) condition. The design of process inputs for such experiments is often, but not always, based on the concept of independent random rotated inputs, with appropriately proportioned amplitudes. However, prior publications do not account for models that may already be partially known before identification. In this work, this issue is addressed by developing a general experiment design framework for efficient identification of partially known models that must satisfy the IC condition. This framework produces optimal designs by solving appropriately formulated optimization problems, based on a number of rigorous theoretical results. Numerical simulations illustrate the proposed approach and potential future extensions are suggested. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2986–3001, 2016     

A method for simplifying linear multivariable dynamic systems

A method for reducing the order of linear multivariable stable dynamic systems is proposed. The main advantage of this method is that the problem of determining a simplified model is reduced to few matrix manipulations and solution of a few algebraic equations which can be easily programed. The simplified model is obtained so that a quadratic functional of the difference between the output vector and that of the original model is automatically minimized for either step or impulse inputs. Applications of the method include simplification of a dynamic model of a pilot plant for the azeotropic distillation of n-butyl acetate and n-butanol. Very good agreement between the step responses of the original and simplified model is obtained.     

Design of decentralized proportional-plus-integral controllers for multivariable systems

This paper presents a simple method for the design of decentralize proportional-plus-integral controllers for multivariable linear systems where the controllers act directly on the available systems outputs. The proposed design scheme, which includes local as well as hierarchical types of control systems, involves the solution of one nonlinear Riccati matrix equation and one linear Liapunov matrix equation. The practicality and good performance of control systems developed, using this approach, is demonstrated on the mathematical model of a plate absorption column.     

New measures for robustness in linear multivariable feedback systems

New measures for robustness are proposed for linear multivariable control systems. A new theorem is presented to account for the controllability of systems that contain an integrating element, in the presence of additive uncertainties. The theorem leads to the definition of a sufficient condition for robust integral controllability: robustness margin (RM). The ratio of robustness margins for competing control or processs structures can be used to discriminate between these structures. These measures are useful, especially in design stages, since their calculation depends only on steady state information. Applications to several published distillation systems show the merits of these robustness measures.     

Control of multivariable systems containing time delays using a multivariable smith predictor

A multivariable version of the classical Smith predictor is applied to a double effect evaporator containing time delays in the control variables and some of the output variables. As in the classical approach, the multivariable Smith predictor eliminates time delays from the characteristic equation of the closed-loop system. Simulation and experimental results for the pilot-scale evaporator are quite promising and demonstrate the feasibility of the multivariable Smith predictor for practical control problems.     

Computer-aided multivariable control system design for processes with time delays

A computer-aided control system design package is described which handles processes with multiple time delays and allows subsequent design of interaction compensators. The package synthesizes control system designs for complex problems in a short time while also providing dynamic simulation for the purpose of evaluating controller performance. Example problems are presented along with a case study on sensitivity to errors in the delays.     

A scheduled controller for a nonlinear process of Wiener type based on IMC framework and local models

In this paper, we present an efficient, practical gain scheduled controller for a nonlinear process of Wiener type, pH problem. The main idea is to use locally linearized first-order models to approximate the real process in the neighborhood of steady points, thus resulting in a conventional PI controller within IMC framework. The scheduling variable is chosen to be the measured pH value which is supposed to be at steady state. Once locally linearized first-order models at several steady points are obtained, a simple linear interpolation is carried out for those points in between them. The results show that the practical scheme used can perform satisfactorily.     

Design of a multivariable internal model controller based on singular value decomposition

In this article, a novel internal model control (IMC) approach based on singular value decomposition (SVD) is proposed for the control of multiple‐input–multiple‐output (MIMO) systems with multiple time delays. This approach achieves decoupling using a compensation term and improves the robustness using SVD in the inverse of the steady‐state gain matrix of process. Meanwhile, a novel filter is designed for decoupling and fast response speed of multivariable systems with multiple delays. The design of the controller can be extended to non‐square systems where there are more inputs than outputs. Examples are included to illustrate the effectiveness of the method. © 2012 Canadian Society for Chemical Engineering     

Internal model control design for input‐constrained multivariable processes

Multivariable plants under input constraints such as actuator saturation are liable to performance deterioration due to control windup and directionality change. A two‐stage internal model control (IMC) antiwindup design for open loop stable plants is presented. The design is based on the solution of two low‐order quadratic programs at each time step, which addresses both transient and steady‐state behaviors of the system. For analyzing the robust stability of such systems against any infinity‐norm bounded uncertainty, stability test have also been developed. In particular, we note that the controller input‐output mappings satisfy certain integral quadratic constraints. Simulated examples show that the two‐stage IMC has superior performance when compared with other existing optimization‐based antiwindup methods. The stability test is illustrated for a plant with left matrix fraction uncertainty. A scenario where the proposed two‐stage IMC competes favorably with a long prediction horizon model predictive control is described. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Decoupling internal model control for multivariable systems with multiple time delays

In this paper, the decoupling internal model control (IMC) with stability is investigated for multivariable stable processes with multiple time delays. All the stabilizing IMC controllers which solve this decoupling problem and the resulting closed-loop systems are characterized in terms of the open-loop system's time delays and non-minimum phase zeros. It shows that the inclusion of some time delays and non-minimum phase zeros might be necessary to make a decoupling solution realizable and stabilizing. Based on this characterization, a control design method for best achievable performance is presented. However, owing to the high complexity of the theoretical controller, a practical controller design procedure is developed with the help of the proposed model reduction algorithm. Examples are given to illustrate our analysis and design. Significant performance improvement over the existing multivariable Smith predictor control has been achieved with the proposed approach.     

化工过程非方瘦系统的串级控制系统结构设计

化工过程一般为多变量系统,其中输出变量个数多于输入变量个数的非方多变量系统称为瘦系统,现有的非方系统控制结构设计一般采用方形化处理方法,只能形成一个输入变量与一个输出变量配对的单回路控制,要么作为工艺控制指标的重要变量不能成为被控变量,要么次要变量未纳入反馈控制,无法满足控制要求。本文介绍了非方系统的平均频域相对增益阵,对瘦系统进行了变量配对分析,提出了一种瘦系统串级控制系统结构设计方法。这种方法在不添加输入变量的同时有效利用了所有的输出变量反馈,使系统反馈信息更完备,构造了重要变量与次要变量结合的串级控制系统。最后通过实例分析说明了瘦系统的串级控制系统结构设计方法不仅能够得到合理的变量配对,而且系统控制性能良好,尤其在进行干扰抑制的过程中体现出了快速性和高效性。     

一类多变量系统的自抗扰非线性动态解耦控制

针对一类多变量系统控制中的耦合问题,提出了一种基于自抗扰技术的非线性动态解耦控制(ADRC)方法。该方法不依赖于系统的精确数学模型,分别在控制器耦合矩阵部分已知和未知的情形下,在局部静态解耦的基础上,将各子系统的模型摄动、外扰和包括输入变量相互作用在内的动态耦合视为各通道上的扰动总和,通过引入虚拟控制和状态量,设计扩张状态观测器(ESO)估计总扰动并进行反馈补偿,进而再对各解耦子对象分别设计非线性单输入单输出ADRC以保证闭环系统稳定。最后以蒸馏塔模型的过程控制仿真验证了该方法具有良好的动态解耦效果,对模型不确定性和外部扰动具有较好的鲁棒性和适应能力。     

Methods for performance monitoring and diagnosis of multivariable model-based control systems

Methods for performance monitoring and diagnosis of multivariable closed loop systems have been proposed aiming at application to model predictive control systems for industrial processes. For performance monitoring, the well-established traditional statistical process control method is empolyed. To meet the underlying premise that the observed variable is univariate and statistically independent, a temporal and spatial decorrelation procedure for process variables has been suggested. For diagnosis of control performance deterioration, a method to estimate the model-error and disturbance signal has been devised. This method enables us to identify the cause of performance deterioration among the controller, process, and disturbance. The proposed methods were evaluated through numerical examples.