Economic model predictive control of nonlinear time‐delay systems: Closed‐loop stability and delay compensation

Closed‐loop stability of nonlinear time‐delay systems under Lyapunov‐based economic model predictive control (LEMPC) is considered. LEMPC is initially formulated with an ordinary differential equation model and is designed on the basis of an explicit stabilizing control law. To address closed‐loop stability under LEMPC, first, we consider the stability properties of the sampled‐data system resulting from the nonlinear continuous‐time delay system with state and input delay under a sample‐and‐hold implementation of the explicit controller. The steady‐state of this sampled‐data closed‐loop system is shown to be practically stable. Second, conditions such that closed‐loop stability, in the sense of boundedness of the closed‐loop state, under LEMPC are derived. A chemical process example is used to demonstrate that indeed closed‐loop stability is maintained under LEMPC for sufficiently small time‐delays. To cope with performance degradation owing to the effect of input delay, a predictor feedback LEMPC methodology is also proposed. The predictor feedback LEMPC design employs a predictor to compute a prediction of the state after the input delay period and an LEMPC scheme that is formulated with a differential difference equation (DDE) model, which describes the time‐delay system, initialized with the predicted state. The predictor feedback LEMPC is also applied to the chemical process example and yields improved closed‐loop stability and economic performance properties. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4152–4165, 2015     

延迟焦化加热炉的自适应状态反馈预测控制和专家控制

An adaptive state feedback predictive control （SFPC） scheme and an expert control scheme are presented and applied to the temperature control of a 1200 kt·a^-1 delayed coking furnace, which is the key equipment for the delayed coking process. Adaptive SFPC is used to improve the performance of temperature control in normal operation. A simplified nonlinear model on the basis of first principles of the furnace is developed to obtain a state space model by linearization. Taking advantage of the nonlinear model, an online model adapting method is presented to accommodate the dynamic change of process characteristics because of tube coking and load changes. To compensate the large inverse response of outlet temperature resulting from the sudden increase of injected steam of a particular velocity to tubes, a monitoring method and an expert control scheme based on heat balance calculation are proposed. Industrial implementation shows the effectiveness and feasibility of the proposed control strategy.     

化学反应器的神经元自适应观测和非线性控制

提出了一种基于神经网络的自适应观测和非线性控制策略,证明了自适应观测器的收敛件和非线性控制系统的稳定性,将其用于连续搅拌釜式放热反应器的浓度控制。根据可在线测量的反应温度,在线估计不可在线测量的反应物浓度和辨识Arrhenius指前因子,并利用重构的状态信息设计出带约束的非线性控制策略。仿真结果表明,观测器/控制器的组合提供了满意的闭环特性,证实了本文方法的有效性。     

A method for robustness analysis of controlled nonlinear systems

This paper presents an approach to analyzing robustness properties of nonlinear systems under feedback control. The core idea is to apply numerical bifurcation analysis to the closed-loop process, using the controller/observer tuning parameters, the set points, and parameters describing model uncertainty (parametric as well as unmodeled dynamics) as bifurcation parameters. By analyzing the Hopf bifurcation and saddle-node bifurcation loci with respect to these parameters, bounds on the controller tuning are identified which can serve as a measure for the robustness of the controlled system. These bounds depend upon the type as well as the degree of mismatch that exists between the plant and the model used for controller design.The method is illustrated by analyzing three control systems which are applied to a continuously operated stirred tank reactor: a state feedback linearizing controller and two output feedback linearizing controllers. While model uncertainty has only a minor effect on the tuning of the state feedback linearizing controller, this does not represent a very realistic scenario. However, when an observer is implemented in addition to the controller and an output feedback linearizing scheme is investigated, it is found that the plant-model mismatch has a much more profound impact on the tuning of the observer than it has on the controller tuning. In addition, two observer designs with different level of complexity are investigated and it is found that a scheme which makes use of additional knowledge about the system will not necessarily result in better stability properties as the level of uncertainty in the model increases. These investigations are carried out using the robustness analysis scheme introduced in this paper.     

Versal matrix families,normal forms and higher order bifurcations in dynamic chemical systems

Characterization of the possible dynamic phenomena which arise when a steady state loses stability due to parametric variations is important in process and control system design and is useful for dynamic model identification and evaluation. The linearized system Jacobian Jordan block structure at bifurcation implies corresponding possibilities for nonlinear dynamic phenomena near bifurcation. The linearized system characteristic equation and the theory of versal representation of matrix families are applied to identify the number of system parameters which must be varied simultaneously to achieve different eigenvalue configurations. The theory of normal forms is used to illustrate the topological equivalence, near bifurcation, of the original system and the normal form representation which contains a relatively small number of nonlinear differential equations. This theory is used to organize and interpret studies of dynamics in two chemical reaction systems: (i) consecutive-competitive reactions in an isothermal CSTR with multivariable proportional feedback control; and (ii) coupled oscillations in two interacting CSTR's with autocatalytic reactions.     

CONTROL AND ESTIMATION FOR PERTURBED NONLINEAR PROCESSES WITH DEADTIME

Feedback linearization techniques are used to deal with the nonlinear controller designs which have attracted many researchers' attention in recent years. The approach has been applied successfully to solve a number of practical nonlinear control problems, but typically requires on-line full state measurement which is usually not the case in real chemical process industries. In this paper, we address the problem of synthesizing nonlinear state feedback controllers for time-delay nonlinear systems which are perturbed by disturbances. On-line estimation of the unmeasurable disturbances and unavailable state variables is introduced to facilitate the implementation of coordinate transformations and state feedback and prediction. Two kinds of dynamic compensators are then proposed to handle the process deadtime. Finally numerical simulations in a CSTR example demonstrate the promising performance of the overall nonlinear control structure in disturbance rejection.     

AN EXOTHERMIC CONTINUOUS STIRRED TANK REACTOR IS FEEDBACK EQUIVALENT TO A LINEAR SYSTEM

This brief paper demonstrates the concept of linear feedback equivalence for an exothermic eontinu-ous stirred tank reactor with first order kinetics. Feedback control is achieved by finding a transformation for the nonlinear system which carries this system into a linear controllable system in Brunovsky canonical form. A linear state feedback controller is then designed which achieves control over a broad range of operating conditions. This example demonstrates how recent developments in nonlinear control theory can be applied to chemical systems without relying on the usual methods of local linearization.     

Robust continuous velocity control of convective spatially distributed systems

In this work a robust nonlinear scheme is proposed to control spatially distributed convective systems described by first-order hyperbolic partial differential equations by manipulating the flow velocity. The proposed scheme is designed after the method of characteristics is used to establish key structural properties of the system dynamics. The resulting feedback control, which can be seen as a proportional integral controller with variable integration time, does not require measurements for several axial points nor infinite dimensional state estimations. The proposed controller is applied successfully to two heat exchange simulation examples and a nonisothermical plug flow reactor. It is shown that it is robust in the face of uncertain parameters and load disturbances. Finally, the performance of the robust controller is compared to other control applications.     

Bounded robust control of constrained multivariable nonlinear processes

This work focuses on control of multi-input multi-output (MIMO) nonlinear processes with uncertain dynamics and actuator constraints. A Lyapunov-based nonlinear controller design approach that accounts explicitly and simultaneously for process nonlinearities, plant-model mismatch, and input constraints, is proposed. Under the assumption that all process states are accessible for measurement, the approach leads to the explicit synthesis of bounded robust multivariable nonlinear state feedback controllers with well-characterized stability and performance properties. The controllers enforce stability and robust asymptotic reference-input tracking in the constrained uncertain closed-loop system and provide, at the same time, an explicit characterization of the region of guaranteed closed-loop stability. When full state measurements are not available, a combination of the state feedback controllers with high-gain state observes and appropriate saturation filters, is employed to synthesize bounded robust multivariable output feedback controllers that require only measurements of the outputs for practical implementation. The resulting output feedback design is shown to inherit the same closed-loop stability and performance properties of the state feedback controllers and, in addition, recover the closed-loop stability region obtained under state feedback, provided that the observer gain is sufficiently large. The developed state and output feedback controllers are applied successfully to non-isothermal chemical reactor examples with uncertainty, input constraints, and incomplete state measurements. Finally, we conclude the paper with a discussion that attempts to put in perspective the proposed Lyapunov-based control approach with respect to the nonlinear model predictive control (MPC) approach and discuss the implications of our results for the practical implementation of MPC, in control of uncertain nonlinear processes with input constraints.     

自适应鲁棒迭代学习控制在陶瓷机械手中的应用

针对一类不确定非线性系统,结合自适应鲁棒控制和迭代学习控制方法,提出了自适应鲁棒迭代学习混合控制策略。学习控制策略用于处理周期性不确定,自适应鲁棒控制策略用于处理具有未知上界的非周期性不确定。所提出的控制方案保证跟踪误差在有限的迭代步骤内收敛到任意指定的误差区域。最后将此控制策略应用于陶瓷机械手的控制,仿真结果表明此方法的有效性。     

Nonlinear adaptive switching control for a class of non-affine nonlinear systems

An improved nonlinear adaptive switching control method is presented to relax the assumption on the higher order nonlinear terms of a class of discrete-time non-affine nonlinear systems. The proposed control strategy is composed of a linear adaptive controller, a neural network (NN) based nonlinear adaptive controller and a switching mechanism. An incremental model is derived to represent the considered system and an improved robust adaptive law is chosen to update the parameters of the linear adaptive controller. A new performance criterion of the switching mechanism is designed to select the proper controller. Using this control scheme, all the signals in the system are proved to be bounded. Numerical examples verify the effectiveness of the proposed algorithm.     

区间二型模糊免疫PID在环己烷无催化氧化温度控制系统中的应用

环己烷无催化氧化过程具有非线性、多变量耦合、大时滞等特点,使用常规比例积分微分(PID)控制方案无法达到理想的控制性能。提出了一种区间二型模糊免疫PID控制器,其本质上是一种基于免疫PID的非线性控制器,利用区间二型模糊逻辑系统来逼近免疫反馈律中的非线性函数,以提升控制器处理和逼近复杂不确定非线性系统的能力。将所提出的控制器应用于环己烷无催化氧化温度控制系统,仿真结果表明该方法是有效的。     

区间二型模糊免疫PID在环己烷无催化氧化温度控制系统中的应用

环己烷无催化氧化过程具有非线性、多变量耦合、大时滞等特点,使用常规比例积分微分(PID)控制方案无法达到理想的控制性能。提出了一种区间二型模糊免疫PID控制器,其本质上是一种基于免疫PID的非线性控制器,利用区间二型模糊逻辑系统来逼近免疫反馈律中的非线性函数,以提升控制器处理和逼近复杂不确定非线性系统的能力。将所提出的控制器应用于环己烷无催化氧化温度控制系统,仿真结果表明该方法是有效的。     

一类非线性不确定时滞系统鲁棒预测控制

针对一类非线性不确定时滞系统,结合Lyapunov稳定性定理和H∞理论,得到系统渐进稳定和状态反馈H∞控制器存在的充分条件,并且给出了此类非线性不确定时滞系统的鲁棒H∞状态反馈控制律设计方案.最后通过具体数值仿真说明了设计方案的有效性.     

ROBUST CONTROL OF BATCH REACTORS

The design of robust nonlinear feedback controller is analysed for a trajectory tracking in a single-input single-output nonlinear state variable system x = f(x) + g(x)u, y=cx which arises in nonlinear chemical processes particularly in batch reactor control problems. Simulation results for the batch reactor temperature tracking problem show the effectiveness of the control scheme and its robustness to modelling errors. The method is also applicable to multi-input multi-output system where the number of inputs is equal to that of outputs. The controller design is also analyzed for situations wrier: the kinetics, the activation energy and Ihe heat of reaction are unknown and also only limited measurement of state-variables are available. The method of Youcef-Toumi and Ito (1987) is applied to such problems and the effectiveness of control system is shown by simulation.     

化工过程强非线性系统的变模型自适应预测控制

提出一种变模型自适应预测控制算法 ;基于非线性状态空间模型 ,通过每步在当前工作点 (非平衡点 )线性化获得线性化子模型 ,以此进行状态反馈预测控制 ,线性化子模型随工作点变化 ,且不限于平衡点。通过pH值控制的对比仿真实验 ,证明其对强非线性过程的控制效果优于传统的多模型预测控制。最后分析讨论了该控制算法存在的几个重要问题 ,并指出与之相关的未来研究方向     

A MODEL-BASED DIRECT ADAPTIVE PI CONTROLLER FOR NONLINEAR PROCESS CONTROL

This article proposes a model-based direct adaptive proportional-integral (PI) controller for a class of nonlinear processes whose nominal model is input-output linearizable but may not be accurate enough to represent the actual process. The proposed direct adaptive PI controller is composed of two parts: the first is a linearizing feedback control law that is synthesized directly based on the process's nominal model and the second is an adaptive PI controller used to compensate for the model errors. An effective parameter-tuning algorithm is devised such that the proposed direct adaptive PI controller is able to achieve stable and robust control performance under uncertainties. To show the robust stability and performance of the direct adaptive PI control system, a rigorous analysis involving the use of a Lyapunov-based approach is presented. The effectiveness and applicability of the proposed PI control strategy are demonstrated by considering the time-dependent temperature trajectory tracking control of a batch reactor in the presence of plant/model mismatch, unanticipated periodic disturbances, and measurement noises. Furthermore, for use in an environment that lacks full-state measurements, the integration of a sliding observer with the proposed control scheme is suggested and investigated. Extensive simulation results reveal that the proposed model-based direct adaptive PI control strategy enables a highly nonlinear process to achieve robust control performance despite the existence of plant/model mismatch and diversified process uncertainties.     

Distributed model predictive control of switched nonlinear systems with scheduled mode transitions

A method for the design of distributed model predictive control (DMPC) systems for a class of switched nonlinear systems for which the mode transitions take place according to a prescribed switching schedule is presented. Under appropriate stabilizability assumptions on the existence of a set of feedback controllers that can stabilize the closed‐loop switched, nonlinear system, a cooperative DMPC architecture using Lyapunov‐based model predictive control (MPC) in which the distributed controllers carry out their calculations in parallel and communicate in an iterative fashion to compute their control actions is designed. The proposed DMPC design is applied to a nonlinear chemical process network with scheduled mode transitions and its performance and computational efficiency properties in comparison to a centralized MPC architecture are evaluated through simulations. © 2013 American Institute of Chemical Engineers AIChE J, 59:860‐871, 2013     

A self-tuning control method for Wiener nonlinear systems and its application to process control problems

Many chemical processes can be modeled as Wiener models, which consist of a linear dynamic subsystem follow-ed by a static nonlinear block. In this paper, an effective discrete-time adaptive control method is proposed for Wiener nonlinear systems with uncertainties. The parameterization model is derived based on the inverse of the nonlinear function block. The adaptive control method is motivated by self-tuning control and is derived from a modified Clarke criterion function, which considers both tracking properties and control efforts. The un-certain parameters are updated by a recursive least squares algorithm and the control law exhibits an explicit form. The closed-loop system stability properties are discussed. To demonstrate the effectiveness of the obtained results, two groups of simulation examples including an application to composition control in a continuously stirred tank reactor (CSTR) system are studied.