A continuous stirred tank heater simulation model with applications

This article presents a first principles simulation of a continuous stirred tank heater pilot plant at the University of Alberta. The model has heat and volumetric balances, and a very realistic feature is that instrument, actuator and process non-linearities have been carefully measured, for instance to take account of the volume occupied by heating coils in the tank. Experimental data from step testing and recordings of real disturbances are presented. The model in Simulink and the experimental data are available electronically, and some suggestions are given for their application in education, system identification, fault detection and diagnosis.     

改进块式递推偏最小二乘建模方法及应用

针对传统偏最小二乘(PLS)模型的在线更新问题,提出了带有自适应遗忘因子的块式递推PLS建模方法.通过Hotelling-T2和Q统计量确定遗忘因子的大小,并且进行模型递推更新,确保模型跟踪过程特性的变化.将所提出的方法应用于管坯斜轧穿孔能耗过程,表现出较强的模型在线更新能力.测试结果表明,带有自适应遗忘因子的块式递推PLS方法的性能优于传统的迭代偏最小二乘方法的性能.     

Adaptive extremum-seeking control of a continuous stirred tank bioreactor with Haldane's Kinetics

In this paper, we present an adaptive extremum seeking control scheme for a continuous stirred tank bioreactor with Haldane's kinetics. The proposed adaptive extremum seeking approach uses the kinetic model of the bioreactor to construct a seeking algorithm that drives the system states to the desired set-points that extremize the value of an objective function. Lyapunov's stability theorem is used in the design of the extremum seeking controller and the development of the parameter updating laws. Simulation experiments are given to show the effectiveness of the proposed approach.     

A robust control scheme for nonlinear non-isothermal uncertain jacketed continuous stirred tank reactor

A Non-isothermal Jacketed Continuous Stirred Tank Reactor (CSTR) is extensively used in chemical as well as in other process industries to manufacture different products. The dynamics of non-isothermal CSTR are highly nonlinear and open-loop unstable in nature. Moreover, it may have parametric uncertainties, disturbances and un-modeled side reactions which may cause the reactor temperature to deviate from the reference value. This deviation may degrade quality of the product because the chemical reaction inside the CSTR depends on reactor temperature. For such a nonlinear, unstable and uncertain process, designing a control scheme with the ability to reject the effects of disturbances along with a good reference tracking capability is a challenging control engineering problem. In this work, a novel robust sliding mode control technique named as Improved Integral Sliding Mode Control (IISMC) has been presented for uncertain non-isothermal jacketed CSTR process. Moreover, a variety of recently developed sliding mode control techniques such as Classical Integral Sliding Mode Control (CISMC) and Super Twisted Algorithm based Sliding Mode Control (STA-SMC) have also been devised and compared with the proposed approach in order to investigate the effectiveness of the proposed scheme. A Lyapunov based analysis has also been provided to assure the robust stability of the closed loop process. Furthermore, in order to extend the state feedback approach to the output feedback scheme, two robust observers; High Gain Observer (HGO) and Extended High Gain Observer (EHGO), are also designed for the very process. They have also been compared with each other and have been investigated for robust stability using Lyapunov based approach. Finally, an output feedback control scheme using IISMC and EHGO has been presented and its performance has been examined and compared with the IISMC based state feedback approach. The simulation results show that the proposed control scheme effectively rejects the uncertainties and disturbances without leading the process to instability and offers good reference tracking capabilities.     

Adaptive extremum seeking control of continuous stirred tank bioreactors with unknown growth kinetics

In this paper, we present an adaptive extremum seeking control scheme for continuous stirred tank bioreactors. We assume limited knowledge of the growth kinetics. An adaptive learning technique is introduced to construct a seeking algorithm that drives the system states to the desired set-points that maximize the value of an objective function. Lyapunov's stability theorem is used in the design of the extremum seeking controller structure and the development of the parameter learning laws. Simulation results are given to show the effectiveness of the proposed approach.     

Simulink在全混流反应器中的应用

尝试一种进行化工过程仿真的新方法，利用Matlab的仿真工具箱Sireulink，对全混流反应器进行可视化建模和仿真计算，以一个一级不可逆放热反应为例，进行稳态模拟及动态模拟，根据模拟结果提出反应器最优操作状态，并对动态模拟的各稳态操作点进行详细分析，同时提出了避免不稳定性的方法。结果表明，使用Simulink所建立的模型，具有很好的开放性和可移植性，还能轻松地分析过程动态特性，是进行建模仿真的好工具。     

Output feedback adaptive extremum seeking control of a continuous stirred tank bioreactor with Monod's kinetics

An adaptive extremum seeking controller is presented for the optimization of the production rate of a continuous stirred tank bioreactor with Monod's kinetics. This controller is saturated outside a domain of interest and a reduced-order observer is designed to estimate the substrate concentration in the bioreactor. It is shown that once a persistence of excitation condition is satisfied, the convergence of the parameter estimates to their true values is guaranteed. Semi-global asymptotic stability for the output feedback closed-loop system is proved based on Lyapunov's theorem. Simulation results are shown to illustrate the performance of the proposed approach.     

A robust least squares based approach to min‐max model predictive control

This article deals with the model predictive control (MPC) of linear, time‐invariant discrete‐time polytopic (LTIDP) systems. The 2‐fold aim is to simplify the treatment of complex issues like stability and feasibility analysis of MPC in the presence of parametric uncertainty as well as to reduce the complexity of the relative optimization procedure. The new approach is based on a two degrees of freedom (2DOF) control scheme, where the output r(k) of the feedforward input estimator (IE) is used as input forcing the closed‐loop system ∑_f. ∑_f is the feedback connection of an LTIDP plant ∑_p with an LTI feedback controller ∑_g. Both cases of plants with measurable and unmeasurable state are considered. The task of ∑_g is to guarantee the quadratic stability of ∑_f, as well as the fulfillment of hard constraints on some physical variables for any input r(k) satisfying an “a priori” determined admissibility condition. The input r(k) is computed by the feedforward IE through the on‐line minimization of a worst‐case finite‐horizon quadratic cost functional and is applied to ∑_f according to the usual receding horizon strategy. The on‐line constrained optimization problem is here simplified, reducing the number of the involved constraints and decision variables. This is obtained modeling r(k) as a B‐spline function, which is known to admit a parsimonious parametric representation. This allows us to reformulate the minimization of the worst‐case cost functional as a box‐constrained robust least squares estimation problem, which can be efficiently solved using second‐order cone programming.     

Constrained predictive control for multivariable systems with application to power systems

Generalized predictive control (GPC) and dynamic performance predictive control (DPC) algorithms are introduced for industrial applications. Constraints on plant input rate, plant absolute input and plant absolute output can be implemented and are demonstrated on an application of these algorithms. A standard quadratic programming algorithm performs the calculation of the optimal control. A MATLAB/Simulink toolbox environment has been developed where controllers can be designed, linear and non-linear plant models can be embedded, discrete- and continuous-time loop parts can be mixed and simulation results can be managed and evaluated by graphical and statistical tools. This package utilises a graphical user interface. Finally, a case study design example is presented where a linear gas turbine model for power generation is examined with constrained GPC and DPC, and the advantages and drawbacks of the approach are the discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

Pulse-width predictive control for LTV systems with application to spacecraft rendezvous

This work presents a Model Predictive Controller (MPC) that is able to handle Linear Time-Varying (LTV) plants with Pulse-Width Modulated (PWM) control. The MPC is based on a planner that employs a Pulse-Amplitude Modulated (PAM) or impulsive approximation as a hot-start and then uses explicit linearization around successive PWM solutions for rapidly improving the solution by means of quadratic programming. As an example, the problem of rendezvous of spacecraft for eccentric target orbits is considered. The problem is modeled by the LTV Tschauner–Hempel equations, whose state transition matrix is explicit; this is exploited by the algorithm for rapid convergence. The efficacy of the method is shown in a simulation study.     

An efficient artificial bee colony algorithm with application to nonlinear predictive control

In this paper a constrained nonlinear predictive control algorithm, that uses the artificial bee colony (ABC) algorithm to solve the optimization problem, is proposed. The main objective is to derive a simple and efficient control algorithm that can solve the nonlinear constrained optimization problem with minimal computational time. Indeed, a modified version, enhancing the exploring and the exploitation capabilities, of the ABC algorithm is proposed and used to design a nonlinear constrained predictive controller. This version allows addressing the premature and the slow convergence drawbacks of the standard ABC algorithm, using a modified search equation, a well-known organized distribution mechanism for the initial population and a new equation for the limit parameter. A convergence statistical analysis of the proposed algorithm, using some well-known benchmark functions is presented and compared with several other variants of the ABC algorithm. To demonstrate the efficiency of the proposed algorithm in solving engineering problems, the constrained nonlinear predictive control of the model of a Multi-Input Multi-Output industrial boiler is considered. The control performances of the proposed ABC algorithm-based controller are also compared to those obtained using some variants of the ABC algorithms.     

Robust multi-parametric model predictive control for LPV systems with application to anaesthesia

We present a multi-parametric model predictive controller (mpMPC) for discrete-time linear parameter-varying (LPV) systems based on the solution of the mpMPC problem for discrete-time linear time-invariant (LTI) systems. The control method yields a controller that adapts to parameter changes of the LPV system. This is accomplished by an add-on unit to the implementation of the mpMPC for LTI systems. No modification of the optimal mpMPC solution for LTI systems is needed. The mpMPC for LPV systems is entirely based on simple computational steps performed on-line. This control design method could improve the performance and robustness of a mpMPC for LPV systems with slowly varying parameters. We apply this method to process systems which suffer from slow variation of system parameters due, for example, to aging or degradation. As an illustrative example the reference tracking control problem of the hypnotic depth during intravenous anaesthesia is presented: the time varying system matrix mimics an external disturbance on the hypnotic depth. In this example the presented mpMPC for LPV systems shows a reduction of approximately 60% of the reference tracking error compared to the mpMPC for LTI systems.     

Stability analysis of a multi-model predictive control algorithm with application to control of chemical reactors

We study a stabilizing multi-model predictive control strategy for controlling nonlinear process at different operating conditions. The control algorithm is a receding horizon scheme with a quasi-infinite horizon objective function that has finite and infinite horizon cost components. The finite horizon cost consists of free input variables that direct the system towards a terminal region which contains the desired operating point. The infinite horizon cost has an upper bound and steers the system to the desired operating point. The system is represented by a sequence of piecewise linear models. Based on the condition of the system states, the sequence of piecewise linear models is updated and the controller’s objective function switches form quasi-infinite to infinite horizon objective function. This results in a hybrid control structure. A recent approach in the analysis of hybrid systems that uses multiple Lyapunov functions is employed in the stability analysis of the closed-loop system. The stabilizing hybrid control strategy is illustrated on two examples and their closed-loop stability properties are studied.     

A variable‐structure gradient RBF network with its application to predictive ship motion control

The prediction of dynamic behavior of the nonlinear time‐varying process plays an important role in predictive control applications. Although neural network algorithms have been intensively researched in modeling and controlling nonlinear systems in recent years, most of them mainly focused on the static dynamics. In this paper, a variable‐structure gradient radial basis function (RBF) network is implemented for nonlinear real‐time model predictive control, which is achieved by the proposed gradient orthogonal model selection (GOMS) algorithm. By learning the gradient message of real‐time updated data in a sling window, the structure and the connecting parameters of the network can be adaptively adjusted to adapt to the time‐varying dynamics. The proposed algorithm is evaluated with Mackey‐Glass chaotic time series prediction. Moreover, the variable structure network achieved by GOMS algorithm is applied as a multi‐step predictor in a ship course‐tracking control study, results demonstrate the applicability and effectiveness of the proposed GOMS algorithm and the variable‐RBF‐network based predictive control strategy. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Probabilistic prediction methods for nonlinear systems with application to stochastic model predictive control

The performance of modern control methods, such as model predictive control, depends significantly on the accuracy of the system model. In practice, however, stochastic uncertainties are commonly present, resulting from inaccuracies in the modeling or external disturbances, which can have a negative impact on the control performance. This article reviews the literature on methods for predicting probabilistic uncertainties for nonlinear systems. Since a precise prediction of probability density functions comes along with a high computational effort in the nonlinear case, the focus of this article is on approximating methods, which are of particular relevance in control engineering practice. The methods are classified with respect to their approximation type and with respect to the assumptions about the input and output distribution. Furthermore, the application of these prediction methods to stochastic model predictive control is discussed including a literature review for nonlinear systems. Finally, the most important probabilistic prediction methods are evaluated numerically. For this purpose, the estimation accuracies of the methods are investigated first and the performance of a stochastic model predictive controller with different prediction methods is examined subsequently using multiple nonlinear systems, including the dynamics of an autonomous vehicle.     

Robust disturbance modeling for model predictive control with application to multivariable ill-conditioned processes

In this paper the disturbance model, used by MPC algorithms to achieve offset-free control, is optimally designed to enhance the robustness of single-model predictive controllers. The proposed methodology requires the off-line solution of a min-max optimization problem in which the disturbance model is chosen to guarantee the best closed-loop performance in the worst case of plant in a given uncertainty region. Application to a well-known ill-conditioned distillation column is presented to show that, for ill-conditioned processes, the use of a disturbance model that adds the correction term to the process inputs guarantees a robust performance, while the disturbance model that adds the correction term to the process outputs (used by industrial MPC algorithms) does not.     

Model predictive control with adaptive disturbance prediction and its application to fatty acid distillation column control

This paper describes the results of a joint university-industry study to control a fatty acid distillation sequence, which is plagued with severe disturbance problems. In order to solve the disturbance problem, a model predictive control algorithm is modified in terms of disturbance prediction. Assuming that the dynamics of the unmeasured disturbances is generated by an auto-regressive form, the dynamics of the disturbance can be adaptively identified by using time series data of prediction errors and inputs. Using an identified disturbance model with a process model, future outputs are predicted. Control actions are determined so that the predicted output is as close to the target value as possible. This modified model predictive control aglorithm is applied to a ratio control scheme for three distillation columns. The control system developed has been in use sucessfully for more than six years to produce commercial products.