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.     

基于ELM的一类不确定性纯反馈非线性系统的Backstepping自适应控制

针对一类不确定性纯反馈非线性动力学系统,在中值定理、Backstepping控制的基础上,提出一种基于极限学习机（ELM）的自适应神经控制方法。ELM随机确定单隐层前馈网络（SLFNs）的隐含层参数,仅需调整网络的输出权值,能以极快的学习速度获得良好的推广性。在每一步的Backstepping设计中,应用ELM网络对子系统的未知非线性项进行在线逼近,通过Lyapunov稳定性分析设计的权值参数自适应调节律,可以保证闭环非线性系统所有信号半全局最终一致有界,系统的输出收敛于期望轨迹的很小邻域内。将所设计的控制方法应用于化工过程中的连续搅拌反应釜（CSTR）非线性系统实例中,仿真结果表明了控制方法的有效性。     

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.     

Modeling and control of Wiener-type processes

We develop a simple relay feedback method to identify Wiener-type nonlinear processes. It separates the identification problem of the nonlinear static function from that of the linear dynamic subsystem to simplify the identification procedure significantly. Owing to the separation, the unmeasurable output of the linear dynamic subsystem can be obtained in a straightforward manner. Then, determining the model structure of the nonlinear static function becomes very simple and the estimates are robust to additive output noises. We can identify the whole activated region of the nonlinear static function as well as the ultimate information of the linear dynamic subsystem from only one relay feedback test. More information on the linear dynamic subsystem can be estimated by well-established linear system identification methods from additional tests. We use a nonlinear control strategy to compensate the nonlinear dynamics of the Wiener process so that the design parameters can be determined by usual tuning rules developed for linear processes and a high control performance can be achievable as in linear processes.     

Suboptimal control of nonlinear dynamic systems via moving model

Suboptimal feedback control with a quadratic performance index is considered for nonlinear dynamic systems. The systems are represented by a moving model which is derived by using block pulse functions. This approach permits the linear feedback control law to be applied to nonlinear systems. The suboptimal feedback control of a nonisothermal CSTR with control constraints is presented to illustrate the considerable promise that the method exhibits.     

Feedback linearizing control of a fluidized bed reactor

The design of an adaptive nonlinear controller for the control of a fluidized bed reactor is derived by using exact linearization techniques. Reset action and parameter adaptation are used to make more robust the precise compensation of nonlinear terms, which is called for in the linearization technique. A nonlinear antiwindup mechanism is introduced to handle reset windup problem and to provide fast response without large overshoot. Simulation results show that the proposed adaptive controller guarantees good setpoint tracking. The developed estimation algorithm allows accurate estimation of the parameters for which the regressor component is not zero.     

A simple adaptive control strategy for temperature trajectory tracking in batch processes

In this paper, a simple adaptive control strategy is suggested for temperature tracking control of batch processes. A nonlinear controller, which is in structure very simple and consists of a single parameter, is proposed. To enable this controller to control a batch process adaptively, a simple parameter tuning algorithm is derived based on the Lyapunov stability theorem. The proposed adaptive control scheme is directly operational, which does not depend on process model and the only a priori process information required is the system response direction. To demonstrate the effectiveness and applicability of the proposed scheme, illustrative examples are provided. Extensive simulation results reveal that the proposed adaptive control strategy appears to be a simple and effective approach to batch process control, which provides robust control despite the wide range of operating conditions and nonlinear dynamics of the system.     

Soft sensor model derived from Wiener model structure: modeling and identification

The processes of building dynamic and static relationships between secondary and primary variables are usually integrated in most of nonlinear dynamic soft sensor models. However, such integration limits the estimation accuracy of soft sensor models. Wiener model effectively describes dynamic and static characteristics of a system with the structure of dynamic and static submodels in cascade. We propose a soft sensor model derived from Wiener model structure, which is an extension of Wiener model. Dynamic and static relationships between secondary and primary variables are built respectively to describe the dynamic and static characteristics of system. The feasibility of this model is verified. Then the expression of discrete model is derived for soft sensor system. Conjugate gradi-ent algorithm is applied to identify the dynamic and static model parameters alternately. Corresponding update method for soft sensor system is also given. Case studies confirm the effectiveness of the proposed model, alternate identification algorithm, and update method.     

Selection of control configurations for economic model predictive control systems

Economic model predictive control (EMPC) is a feedback control method that dictates a potentially dynamic (time‐varying) operating policy to optimize the process economics. The objective function used in the EMPC system may be a general nonlinear function that describes the process/system economics. As this function is not derived on the sole basis of classical control considerations (stabilization, tracking, and optimal control action calculation) but rather on the basis of economics, selecting the appropriate control configuration, and quantifying the influence of a given input on an economic cost is an important task for the proper design and computational efficiency of an EMPC scheme. Owing to these considerations, an input selection methodology for EMPC is proposed which utilizes the relative degree and the sensitivity of the economic cost with respect to an input to identify and select stabilizing manipulated inputs with the most dynamic and steady‐state influence on the economic cost function to be assigned to EMPC. Other considerations for input selection for EMPC are also discussed and integrated into a proposed input selection methodology for EMPC. The control configuration selection method for EMPC is demonstrated using a chemical process example. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3230–3242, 2014     

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。     

基于神经网络和多模型的非线性自适应PID控制及应用

针对一类未知的单输入单输出离散非线性系统,提出了基于神经网络和多模型的非线性自适应PID控制方法。该方法由线性自适应PID控制器、神经网络非线性自适应PID控制器以及切换机构组成。采用线性自适应PID控制器可保证闭环系统所有信号有界;采用神经网络非线性自适应PID控制器可改善系统性能;通过引入合理的切换机制,能够在保证闭环系统稳定的同时,提高系统性能。理论分析表明,该方法能够保证闭环系统所有信号有界,如果适当地选择神经网络的结构和参数,系统的跟踪误差将收敛于任意给定的紧集。将所提出的方法应用于连续搅拌反应釜,仿真结果验证了所提出方法的有效性。由于该方法基于增量式数字PID控制器,在工业过程中有着广阔的应用前景。     

Adaptive extremum-seeking control of convection-reaction distributed reactor with limited actuation

In this paper, we pose and solve an adaptive extremum control problem to optimize the productivity of a van de Vusse reaction taking place in a tubular reactor governed by a set of nonlinear hyperbolic partial differential equations. Estimation and control algorithms that take into account control input constraints are developed by using a Lyapunov-based procedure, ensuring stability and convergence under a persistency of excitation condition. Here, we assume that the temperature information along the reactor is the only available on-line measurement to estimate the unmeasured objective function at the reactor exit. Numerical application of the proposed method shows that the resulting feedback algorithm steers the system to its optimum using a non-distributed jacket temperature actuation. The time evolution of the cost function is compared with an idealized distributed version of the algorithm presented previously.     

Improved system identification method for Hammerstein-Wiener processes

We propose a new system identification method for Hammerstein-Wiener processes, in which an input static nonlinear block, a linear dynamic block, and an output static nonlinear block are connected in a series. The proposed method can estimate the model parameters in a very simple way without solving the full-dimensional nonlinear optimization problem by activating the process with a specially designed test signal, composed of a relay feedback signal, a binary signal and a multi-step signal. The proposed method analytically identifies the output nonlinear static function and the input nonlinear static function from the relay signal and the multi-step signal, respectively. The linear dynamic subsystem is identified from the relay feedback signal and the binary signal with existing well-established linear system identification methods. We demonstrate with a simple example that the proposed method can be successfully applied to identify the Hammerstein-Wiener-type nonlinear process.     

Nonlinear adaptive control algorithm for a multicomponent batch distillation column

In this article, a nonlinear adaptive control strategy is proposed for a multicomponent batch distillation column. The hybrid control scheme consists of a generic model controller (GMC) and a nonlinear adaptive state estimator (ASE). In the first part of the study, an adaptive observer is designed aiming to estimate the partially known parameters based on the measured compositions in the presence of process/predictor mismatch. The open-loop dynamic behavior of the developed ASE estimator is investigated under initialization error, disturbance, and uncertain parameters. In the subsequent part, the adaptive GMC-ASE controller (GMC control structure in conjunction with ASE estimator) has been synthesized for the example distillation column. A simulation-based comparative study has been conducted between the derived nonlinear GMC-ASE control algorithm and a gain-scheduled proportional integral (GSPI) law in terms of constant composition control. The proposed adaptive control scheme is shown to be quite promising due to the exponential error convergence capability of the ASE estimator in addition to the high-quality performance of the GMC controller.     

自适应模糊滑模控制在化工过程中的应用

为有效处理多变量、非线性及非最小相位系统的复杂化工过程,提出了一种新型的自适应模糊滑模控制,该方法针对滑模控制鲁棒性好但存在抖振的问题,采用模糊控制柔化控制信号,而与滑模控制的结合可以充分利用系统信息,简化模糊控制;在此基础上提出一种新的自适应调整比例因子来进行模糊变论域,柔化了控制信号并减小了滑模控制器输出的抖振。并给出模糊滑模控制的算法和稳定性分析,得到简化后的通用模糊规则库,可通过比例因子在线调节输入量的论域,使构成的控制系统具有很强的鲁棒性、较好的自适应能力和较高的控制精度。最后对于非线性单输入单输出(SISO)和多输入多输出(MIMO)化工模型进行仿真研究,结果表明即使工况点发生大的变化或受到较大干扰时,仍具有良好的抗扰动能力和很强的鲁棒性。     

Optimization for ASP flooding based on adaptive rationalized Haar function approximation

This paper presents an adaptive rationalized Haar function approximation method to obtain the optimal injection strategy for alkali-surfactant-polymer (ASP) flooding. In this process, the non-uniform control vector parameterization is introduced to convert original problem into a multistage optimization problem, in which a new normalized time variable is adopted on the combination of the subinterval length. Then the rationalized Haar function approximation method, in which an auxiliary function is introduced to dispose path constraints, is used to transform the multistage problem into a nonlinear programming. Furthermore, an adaptive strategy proposed on the basis of errors is adopted to regulate the order of Haar function vectors. Finally, the nonlinear programming for ASP flooding is solved by sequential quadratic programming. To illustrate the performance of proposed method, the experimental comparison method and control vector parameterization (CVP) method are introduced to optimize the original problem directly. By contrastive analysis of results, the accuracy and efficiency of proposed method are confirmed.     

NONLINEAR PI CONTROLLER FOR pH PROCESS

The control of pH is one of the most difficult challenges in the process industry because of the severe nonlinearities and high precision required in manipulating the flow rate. The Wiener model, which consists of a linear dynamic element followed by a nonlinear static element, is used for representing such nonlinear processes. Piecewise continuous polynomials are used for mapping the nonlinear static gain accurately. A nonlinear PI controller was designed based on the Wiener model. Simulation results on the nonlinear mathematical model are presented to highlight the superior performance of the Wiener model based nonlinear PI controller in comparison to that of the local linear PI controller. The performance of the nonlinear PI controller was further improved upon by using the method of inequalities to obtain a single set of PI controller settings that takes into account the parametric variations in the linear dynamic element at different operating points. Simulation and experimental results are presented to support the work.     

NONLINEAR PI CONTROLLER FOR pH PROCESS

The control of pH is one of the most difficult challenges in the process industry because of the severe nonlinearities and high precision required in manipulating the flow rate. The Wiener model, which consists of a linear dynamic element followed by a nonlinear static element, is used for representing such nonlinear processes. Piecewise continuous polynomials are used for mapping the nonlinear static gain accurately. A nonlinear PI controller was designed based on the Wiener model. Simulation results on the nonlinear mathematical model are presented to highlight the superior performance of the Wiener model based nonlinear PI controller in comparison to that of the local linear PI controller. The performance of the nonlinear PI controller was further improved upon by using the method of inequalities to obtain a single set of PI controller settings that takes into account the parametric variations in the linear dynamic element at different operating points. Simulation and experimental results are presented to support the work.     

基于ANFIS与多模型的一类非线性系统的自适应控制方法

针对一类不确定的离散时间零动态不稳定非线性系统,提出了一种基于自适应神经模糊推理系统(ANFIS)与多模型的非线性自适应控制方法。该方法由线性鲁棒自适应控制器,基于ANFIS的非线性自适应控制器以及切换机制组成。线性控制器用来保证闭环系统输入输出信号有界,非线性控制器用来改善系统性能。切换机制通过对上述两种控制器的切换,保证闭环系统输入输出有界的同时,改善系统性能。在采用ANFIS作为系统未建模动态补偿器时,首先用一个连续、单调、可逆的一一映射把可能无界的未建模动态的定义域转化成一个有界闭集,保证了ANFIS的万能逼近特性成立的前提条件。而且,ANFIS能减小BP神经网络收敛速度慢和容易陷入局部极小的问题,改善了控制效果。建立了保证系统稳定性的引理,并给出了闭环系统的稳定性和收敛性分析。通过仿真比较,说明了所提方法的有效性。