Two-degree-of-freedom output feedback controllers for discrete-time nonlinear systems

A discrete-time, model-based output feedback control structure for nonlinear processes is developed in the present work. The structure makes use of a closed-loop observer, while at the same time it guarantees that the overall feedback controller possesses integral action. An algebraic transformation is applied on the observer states to insure that the input/output gain of the observer matches the model upon which the static state feedback control law is based. The resulting control algorithm is a two-degree-of-freedom control law, in the sense that the output and the set point are processed in different ways. The control structure is shown not only to have the same properties as the standard model-state feedback structure, but also that it emerges from a model algorithmic control framework. Finally, a simulation example using an exothermic CSTR operating at an open-loop unstable steady state is used to evaluate the closed-loop performance of the proposed method.     

稀土萃取分离过程组分含量区间控制方法

针对稀土萃取过程出口产品的组分含量可以在一定区间范围浮动的要求,提出了一种基于广义预测控制的稀土萃取过程组分含量区间控制方法。首先基于萃取分离过程数据辨识建立组分含量回声状态神经网络（echo state network,ESN）模型;然后针对稀土萃取过程中不同运行工况,采用改进的广义预测控制算法设计组分含量预测控制器,将系统的输出约束纳入求解控制律的优化问题中,使预测控制针对组分含量输出在不同的区域范围采用不同的控制强度,从而实现区间控制同时保证两端出口产品的纯度,最后基于CePr/Nd（铈镨/钕）萃取过程数据的仿真试验验证了该方法的有效性。     

Safe-parking of nonlinear process systems: Handling uncertainty and unavailability of measurements

This work considers the problem of handling actuator faults in nonlinear process systems subject to input constraints, uncertainty and availability of limited measurements. A framework is developed to handle faults that preclude the possibility of continued operating at the nominal equilibrium point using the existing robust or reconfiguration-based fault-tolerant control approaches. The key consideration is to operate the plant using the depleted control action at an appropriate ‘safe-park’ point to prevent onset of hazardous situations as well as enable smooth resumption of nominal operation upon fault-repair. First, we consider the presence of constraints and uncertainty and develop a robust Lyapunov-based model predictive controller that enhances the set of initial conditions from which closed-loop stability is achieved. The stability region characterization provided by the robust predictive controller is subsequently utilized in a safe-parking algorithm that appropriately selects ‘safe-park’ points from the safe-park candidates (equilibrium points subject to failed actuators) to preserve closed-loop stability upon fault-repair. Specifically, a candidate parking point is termed a safe-park point if (1) the process state at the time of failure resides in the stability region of the safe-park candidate (subject to depleted control action and uncertainty) and (2) the safe-park candidate resides within the stability region of the nominal control configuration. Then we consider the problem of availability of limited measurements. An output feedback Lyapunov-based model predictive controller, utilizing an appropriately designed state observer (to estimate the unmeasured states), is formulated and its stability region explicitly characterized. An algorithm is then presented that accounts for the estimation errors in the implementation of the safe-parking framework. The proposed framework is illustrated using a chemical reactor example and demonstrated on a styrene polymerization process.     

不对称系统输入反馈预测控制及可控性分析

研究了生产过程中一类特殊的非线性系统,不对称系统的预测控制方法。在正反方向的控制作用下,这类系统表现出不对称动态特性。此类系统的理论研究特别是控制方法研究十分有限。针对基于正反方向上的线性模型设计的正反模型预测控制方法与传统预测控制方法在结构上的差异进行了分析,说明了由于这种结构上的差异可能导致的模型失配及控制效果不佳,然后采用输入反馈方法对不对称系统正反模型预测控制方法进行了修正,将实际施加给对象的控制作用通过反馈形式纳入到下一步正反方向控制律的求解中。并且在无约束的条件下分析了正反模型预测控制方法的可控性。最后通过pH值控制的仿真实验验证了此两种不对称系统正反模型预测控制方法的控制效果。     

Output feedback robust model predictive control with unmeasurable model parameters and bounded disturbance☆

The output feedback model predictive control (MPC), for a linear parameter varying (LPV) process system including unmeasurable model parameters and disturbance (all lying in known polytopes), is considered. Some previously developed tools, including the norm-bounding technique for relaxing the disturbance-related constraint handling, the dynamic output feedback law, the notion of quadratic boundedness for specifying the closed-loop stability, and the el ipsoidal state estimation error bound for guaranteeing the recursive feasibility, are merged in the control design. Some previous approaches are shown to be the special cases. An example of continuous stirred tank reactor (CSTR) is given to show the effectiveness of the proposed approaches.     

Detection and management of actuator faults in controlled particulate processes using population balance models

This paper presents a methodology for the design of an integrated fault detection and fault-tolerant control (FD-FTC) architecture for particulate processes described by population balance models (PBMs) with control constraints, actuator faults and a limited number of process measurements. The architecture integrates model-based fault detection, state estimation, nonlinear feedback and supervisory control on the basis of an appropriate reduced-order model that captures the dominant dynamics of the process and is obtained through application of the method of weighted residuals. The architecture comprises a family of control configurations together with a fault detection filter and a supervisor. For each configuration, a stabilizing output feedback controller with well-characterized stability properties is designed through the combination of a state feedback controller and a state observer that uses the available measurements of principal moments of the particle size distribution (PSD) and the continuous-phase variables to provide appropriate state estimates. A fault detection filter that simulates the behavior of the fault-free, reduced-order model is designed, and its discrepancy from the behavior of the actual process state estimates is used as a residual for fault detection. Finally, a switching law based on the stability regions of the constituent control configurations is derived to reconfigure the control system in a way that preserves closed-loop stability in the event of fault detection. Appropriate fault detection thresholds and control reconfiguration criteria that account for model reduction and state estimation errors are derived for the implementation of the FD-FTC architecture on the particulate process. Finally, the methodology is applied to the problem of constrained, actuator fault-tolerant stabilization of an unstable steady-state of a continuous crystallizer.     

Multi-objective nonlinear model predictive control through switching cost functions and its applications to chemical processes

This paper proposes a switching multi-objective model predictive control (MOMPC) algorithm for constrained nonlinear continuous-time process systems. Different cost functions to be minimized inMPC are switched to satisfy different performance criteria imposed at different sampling times. In order to ensure recursive feasibility of the switching MOMPC and stability of the resulted closed-loop system, the dual-mode control method is used to design the switching MOMPC controller. In this method, a local control law with some free-parameters is constructed using the control Lyapunov function technique to enlarge the terminal state set of MOMPC. The correction termis computed if the states are out of the terminal set and the free-parameters of the local control laware computed if the states are in the terminal set. The recursive feasibility of the MOMPC and stability of the resulted closed-loop system are established in the presence of constraints and arbitrary switches between cost functions. Finally, implementation of the switching MOMPC controller is demonstrated with a chemical process example for the continuous stirred tank reactor.     

Estimator-based control of reactive distillation system: Application of an extended Kalman filtering

This paper demonstrates that a state estimator can be successfully designed and implemented in a feedback control system of reactive distillation. The work of the state estimator is to provide the state compositions that are required to be used in the controller for necessary action. The control performance of a system that relies on the state estimator is examined and compared to a system that takes direct measurement from the process assuming the availability of a perfect online analyzer. It is found that the estimator-based system is robust against a moderate measurement errors and erroneous initial conditions. If the state estimator is designed from a highly erroneous process model, noisy measurements and approximate initial conditions, the use of estimator together with an online analyzer (for easily measured states) is recommended to achieve an effective control of a reactive distillation system.     

Performance of control strategies to track the trajectories of batch reactors

We propose a modified globally linearizing control (MGLC) structure and a nonlinear feedforward-feedback control (NFF/FB) structure to track trajectories of processes in a batch reactor. The MGLC structure performs trajectory tracking perfectly when the model inversion can be obtained by linearization of state feedback. Otherwise, the NFF/FB structure is recommended. The performance of the control laws that we developed are compared with other control laws designed with the same technique. The proposed control law based on the MGLC structure exhibits robust performance whereas that based on NFF/FB structure produces decreased sensitivity to process noise.     

Optimization of nonlinear process based on sequential extreme learning machine

In this paper, a new approach to the optimal control with constraints is proposed to achieve a desired end product quality for nonlinear processes based on new kernel extreme learning machine (KELM). The contributions of the paper are as follows: (1) In existing ILC algorithm, the model was built only between manipulated input variables U and output variables Y without considering the state variables. However, the states variables X_state are important in the industrial processes, which are usually constrained. In this paper, the variables are divided into state variables X_state, manipulated input variables U and output Y in the process of modeling. Then ΔU can be obtained by batch-to-batch iterative learning control separately. Kernel algorithm is added to ELM. (2) Constraints of state variables X_state and the input variables U are considered in the current version. PSO is used to solve the optimization problem. (3) Kernel trick is introduced to improve accuracy of ELM modeling. New KELM algorithm is proposed in the current version. The input trajectory for the next batch is accommodated by searching for the optimal value through the error feedback at a minimum cost. The particle swarm optimization algorithm is used to search for the optimal value based on the iterative learning control (ILC). The proposed approach has been shown to be effective and feasible by applying bulk polymerization of the styrene batch process and fused magnesium furnace.     

MULTIVARIABLE CONTROL OF CATALYTIC CRACKING PROCESSES

Simple, explicit and physically intuitive Feedforward and Feedback control policies are designed for Fluidized Catalytic Cracking Processes. The Feedforward (FF) control algorithm compensates for changes in the feed rate and feed coking tendency by the use of the air flow and catalyst circulation rates as control variables to maintain the conversion and the reactor temperature at fixed levels. Through steady state and dynamic simulations the FF controller is shown to be very effective. To improve the dynamic response of the process and to account for the process/model mismatch a feedback (FB) controller is also designed to complement the FF action. The FB action is designed by use of the transformation related to the physical modes which correspond to the extensive variables of the process. It is shown that the required control structure consists of two loops. One uses the air flow rate to control the total sensible heat content of the reactor and regenerator solid phases. The other loop controls the regenerator enthalpy by changes in the catalyst circulation rate. The air flow rate controller includes an integral action to avoid reactor temperature offsets, while the catalyst circulation rate controller requires a nonlinear static observer to predict the coke concentration on the regenerated catalyst from dense bed and flue gas regenerator temperatures. The performance of the controller for changes on the oil feed rate, caking tendency of the feed, as well as for reactor temperature set point changes is faster and smoother than Kurihara's scheme.     

Explicit distributed model predictive control design for chemical processes under constraints and uncertainty

In multivariable industrial processes, the common distributed model predictive control strategy is usually unable to deal with complex large-scale systems efficiently, especially under system constraints and high control performance requirements. Based on this situation, we use the distributed idea to divide the large-scale system into multiple subsystems and transform them into the state space form. Combined with the output tracking error term, we build an extended non-minimal state space model that includes output error and measured output and input. When dealing with system constraints, the new constraint matrix is divided into range and kernel space by using the explicit model predictive control algorithm, which reduces the difficulty of solving constraints in the extended system and further improves the overall control performance of the system. Finally, taking the coke furnace pressure control system as an example, the proposed algorithm is compared with the conventional distributed model predictive control algorithm using non-minimal state space, and the simulation results show the feasibility and superiority of this method.     

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.     

基于T-S模糊模型与粒子群优化的非线性预测控制

引言模型预测控制属于一种基于模型的多变量的控制算法,发展至今已在化工过程控制方面得到了广泛的应用[1-5]。状态反馈预测控制[6-8]是模型预测控制技术的一种,基于状态空间模型,采用实测状态     

Control of milk pasteurization process using model predictive approach

A milk pasteurization process, a nonlinear process and multivariable interacting system, is difficult to control by the conventional on–off controllers since the on–off controller can handled the temperature profiles for milk and water oscillating over the plant requirements. The multi-variable control approach with model predictive control (MPC) is proposed in this study. The proposed algorithm was tested for control of a milk pasteurization process in four cases of simulation such as set point tracking, model mismatch, difference control and prediction horizons, and time sample. The results for the proposed algorithm show the well performance in keeping both the milk and water temperatures at the desired set points without any oscillation and overshoot and giving less drastic control action compared to the cascade generic model control (GMC) strategy.     

A DIRECT NONLINEAR ADAPTIVE CONTROL OF STATE FEEDBACK LINEARIZABLE SYSTEMS

A direct nonlinear adaptive control of state feedback linearizable single-input single-output systems is proposed in the case when parametric uncertainties are represented linearly in the unknown parameters. The main feature of the proposed nonlinear adaptive control system is that the linearizing coordinate transformation and the state feedback are updated by parametric adaptive law, derived using the second method of Lyapunov. The proposed adaptive control scheme is relatively straightforward and simple in the sense that it does not use the concept of augmented error. This adaptive control scheme is numerically applied to an exothermic chemical reactor system and is compared with the nonadaptive stale feedback linearization which has an integral action. The simulation shows that the proposed adaptive control scheme can be applied effectively to highly nonlinear, uncertain chemical systems.     

Model predictive control for multivariable unstable processes with constraints on manipulated variables

The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steady states. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input-multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control. Linear Quadratic Regulator (LQR) with integral action.     

基于LPV模型的燃料电池空气进气系统控制

质子交换膜燃料电池是一种通过氢气和氧气的电化学反应将化学能直接转化为电能的装置。提出一种改进的四阶燃料电池进气系统模型,分析了系统的约束性。针对系统模型所具有的非线性特性,提出建立线性变参数（LPV）模型用于对系统的控制。针对状态变量不可测的问题引入卡尔曼滤波器,同时通过可观性分析得出系统所需测量的最佳变量。在符合约束条件下设计基于线性变参数模型的状态空间模型预测控制器,控制空压机的工作电压保证氢气燃料的充分反应。仿真结果表明,基于LPV模型的模型预测控制器能够对空气进气系统进行有效的控制,且满足空压机喘振和阻塞边界等约束条件,与单模型预测控制相比具有更好的控制效果。     

基于自适应模糊神经网络的非线性系统模型预测控制

针对非线性动态系统的控制问题,提出了一种基于自适应模糊神经网络(adaptive fuzzy neural network, AFNN)的模型预测控制(model predictive control, MPC)方法。首先,在离线建模阶段,AFNN采用规则自分裂技术产生初始模糊规则,采用改进的自适应LM学习算法优化网络参数;然后,在实时控制过程,AFNN根据系统输出和预测输出之间的误差调整网络参数,从而为MPC提供一个精确的预测模型;进一步,AFNN-MPC利用带有自适应学习率的梯度下降寻优算法求解优化问题,在线获取非线性控制量,并将其作用到动态系统实施控制。此外,给出了AFNN-MPC的收敛性和稳定性证明,以保证其在实际工程中的成功应用。最后,利用数值仿真和双CSTR过程进行实验验证。结果表明,AFNN-MPC能够取得优越的控制性能。     

基于广义预测控制为主的综合控制算法构成控制器的开发与应用

提出一种以广义预测控制算法为主,以由Smith预估参数组成的无模型控制律为辅,以多变量状态反馈为前馈的综合控制算法控制器,其中广义预测控制算法在PC机中实现并通过与DCS通讯完成数据交换,而Smith预估控制、无模型控制率、多变量状态反馈算法均在DCS中实现。此种控制器克服了广义预测控制抗干扰能力弱的缺点,在加热炉控制应用中其优越性得到充分体现,解决了加热炉自动控制的难题,保证了工艺指标。