Predictive functional control based on fuzzy model forheat-exchanger pilot plant

In this paper, a new method of predictive control is presented. In this approach, a well-known method of predictive functional control is combined with fuzzy model of the process. The prediction is based on fuzzy model given in the form of Takagi-Sugeno type. The proposed fuzzy predictive control has been evaluated by implementation on heat-exchanger plant, which exhibits a strong nonlinear behavior. It has been shown that in the case of nonlinear processes, the approach using fuzzy predictive control gives very promising results. The proposed approach is potentially interesting in the case of batch reactors, heat-exchangers, furnaces, and all the processes that are difficult to model     

Design and Stability Analysis of Fuzzy Model-based Predictive Control – A Case Study

In the paper a fuzzy model based predictive control algorithm is presented. The proposed algorithm is developed in the state space and is given in analytical form, which is an advantage in comparison with optimisation based control schemes. Fuzzy model-based predictive control is potentially interesting in the case of batch reactors, heat-exchangers, furnaces and all the processes with strong nonlinear dynamics and high transport delays. In our case it is implemented to a continuous stirred-tank simulated reactor and compared to optimal PI control. Some stability and design issues of fuzzy model-based predictive control are also given.     

Predictive functional control based on an adaptive fuzzy model of a hybrid semi-batch reactor

In this paper a new approach to the control of a nonlinear, time-varying process is proposed. It is based on a recursive version of the fuzzy identification method and predictive functional control. First, the recursive fuzzy identification method is derived, after which it is used in connection with fuzzy predictive functional control to construct an adaptive fuzzy predictive functional controller. The adaptive FPFC is then tested on a nonlinear, time-varying, semi-batch reactor process and compared with the standard FPFC, which uses non-adaptive fuzzy model. The simulation results are promising; they indicate that the control of time-varying, nonlinear processes with the FPFC can be improved with the use of an adaptive fuzzy model. An improvement in reference tracking and disturbance rejection can be observed, but the main advantage is the reduced number of switchings between hot and cold water. This is an important improvement in the case of real applications.     

基于T-S模糊模型的非线性预测控制策略

提出了一种新的基于T-S模糊模型的非线性预测控制策略. T-S模糊模型用于描述对象的非线性动态特性, 通过将模糊模型的输出反馈回来作为模型输入, 从而构成了模糊多步预报器. 由于T-S模糊模型每条规则的结论部分是一个线性模型, 因此整个模糊模型可以看作一个线性时变系统, 从而将模糊预测控制器中的非线性优化问题转化为一个线性二次寻优问题, 以方便求解. pH中和过程的仿真结果表明其性能优于传统的动态矩阵控制器.     

一种基于T-S模型的模糊预测控制

提出了一种基于T-S模型的模糊预测控制策略。T-S模糊模型用来描述对象的非线性动态特性,通过当前的工况参数实时在线的修正每一时刻的阶跃响应模型参数,将模糊模型作为常规线性预测控制DMC方法的预测模型,从而把T-S模型对复杂的非线性系统的良好描述特性和预测控制的滚动优化算法相结合,来实现利用常规线性预测控制策略对非线性系统的有效控制,有效地解决了复杂工业过程的强非线性问题。pH中和过程的仿真结果表明其性能明显优于传统的PID控制器。     

Design of observer based nonlinear model predictive controller for a continuous stirred tank reactor

Model predictive control (MPC) schemes are now widely used in process industries for the control of key unit operations. Linear model predictive control (LMPC) schemes which make use of linear dynamic model for prediction, limit their applicability to a narrow range of operation (or) to systems which exhibit mildly nonlinear dynamics.

In this paper, a nonlinear observer based model predictive controller (NMPC) for nonlinear system has been proposed. An approach to design NMPC based on fuzzy Kalman filter (FKF) and augmented state fuzzy Kalman filter (ASFKF) has been presented. The efficacy of the proposed NMPC schemes have been demonstrated by conducting simulation studies on the continuous stirred tank reactor (CSTR). The analysis of the extensive dynamic simulation studies revealed that, the NMPC schemes formulated produces satisfactory performance for both servo and regulatory problems. Simulation results also include an inferential control case, where the reactor concentration is not measured but estimated from temperature measurement and used in the NMPC based on FKF and ASFKF formulations.     

Hybrid Fuzzy Modelling for Model Predictive Control

Model predictive control (MPC) has become an important area of research and is also an approach that has been successfully used in many industrial applications. In order to implement a MPC algorithm, a model of the process we are dealing with is needed. Due to the complex hybrid and nonlinear nature of many industrial processes, obtaining a suitable model is often a difficult task. In this paper a hybrid fuzzy modelling approach with a compact formulation is introduced. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for the hybrid fuzzy modelling purposes is presented. An efficient method for identifying the hybrid fuzzy model is also proposed. A MPC algorithm suitable for systems with discrete inputs is treated. The benefits of the MPC algorithm employing the hybrid fuzzy model are verified on a batch-reactor simulation example: a comparison between the proposed modern intelligent (fuzzy) approach and a classic (linear) approach was made. It was established that the MPC algorithm employing the proposed hybrid fuzzy model clearly outperforms the approach where a hybrid linear model is used, which justifies the usability of the hybrid fuzzy model. The hybrid fuzzy formulation introduces a powerful model that can faithfully represent hybrid and nonlinear dynamics of systems met in industrial practice, therefore, this approach demonstrates a significant advantage for MPC resulting in a better control performance.     

Partially decoupled approach of extended non-minimal state space predictive functional control for MIMO processes

This paper presents a partially decoupled design of the state space predictive functional control for MIMO processes. The multivariable process is first treated into MISO process by a simple Cramer's rule solution to linear equations which provides a balance between model complexity and control system design, and then the derived MISO process based extended state space predictive functional control is presented. The overall design of the controller enables the controller to consider both the process state dynamics and the output dynamics, thus improved control performance for tracking set-points and disturbance rejection is resulted. The proposed controller is tested on both model match and model mismatch cases to demonstrate its superiority. In addition, a closed-form of transfer function representation that facilitates frequency analysis of the control system is provided to give further insight into the proposed method.     

Robust model predictive control of discrete nonlinear systems with time delays and disturbances via T–S fuzzy approach

In this paper, robust fuzzy model predictive control of a class of nonlinear discrete systems subjected to time delays and persistent disturbances is investigated. Based on the modeling method of delay difference inclusions, nonlinear discrete time-delay systems can be represented by T–S fuzzy systems comprised of piecewise linear delay difference equations. Moreover, Lyapunov–Razumikhin function (LRF), instead of Lyapunov–Krasovskii functional (LKF), is employed for time-delay systems due to its ability to reflect system original state space and its advantages in controller synthesis and computation. The robust positive invariance and input-to-state stability with respect to disturbance under such circumstances are investigated. A robust constraint set is adopted that the system state is converged to this set round the desired point. In addition, the controller synthesis conditions are derived by solving a set of matrix inequalities. Simulation results show that the proposed approach can be successfully applied to the well-known continuous stirred tank reactor (CSTR) systems subjected to time delay.     

Model predictive control of resonant systems using Kautz model

The scope of this paper broadly spans in two areas: system identification of resonant system and design of an efficient control scheme suitable for resonant systems. Use of filters based on orthogonal basis functions (OBF) have been advocated for modelling of resonant process. Kautz filter has been identified as best suited OBF for this purpose. A state space based system identification technique using Kautz filters, viz. Kautz model, has been demonstrated. Model based controllers are believed to be more efficient than classical controllers because explicit use of process model is essential with these modelling techniques. Extensive literature search concludes that very few reports are available which explore use of the model based control studies on resonant system. Two such model based controllers are considered in this work, viz. model predictive controller and internal model controller. A model predictive control algorithm has been developed using the Kautz model. The efficacy of the model and the controller has been verified by two case studies, viz. linear second order underdamped process and a mildly nonlinear magnetic ball suspension system. Comparative assessment of performances of these controllers in those case studies have been carried out.     

一种新的预测控制算法：模糊预测控制算法*

将模糊控制与预测控制相结合，提出了一种基于被控对象一般形式的时间离散模型的模糊预测控制算法，并对控制算法的有效性进行了分析，仿真研究结果表明，该模糊预测控制算法既适用于线性对象，也可用于非线性对象的控制。     

Recurrent neuro-fuzzy networks for nonlinear process modeling

A type of recurrent neuro-fuzzy network is proposed in this paper to build long-term prediction models for nonlinear processes. The process operation is partitioned into several fuzzy operating regions. Within each region, a local linear model is used to model the process. The global model output is obtained through the centre of gravity defuzzification which is essentially the interpolation of local model outputs. This modeling strategy utilizes both process knowledge and process input/output data. Process knowledge is used to initially divide the process operation into several fuzzy operating regions and to set up the initial fuzzification layer weights. Process I/O data are used to train the network. Network weights are such trained so that the long-term prediction errors are minimized. Through training, membership functions of fuzzy operating regions are refined and local models are learnt. Based on the recurrent neuro-fuzzy network model, a novel type of nonlinear model-based long range predictive controller can be developed and it consists of several local linear model-based predictive controllers. Local controllers are constructed based on the corresponding local linear models and their outputs are combined to form a global control action by using their membership functions. This control strategy has the advantage that control actions can be calculated analytically avoiding the time consuming nonlinear programming procedures required in conventional nonlinear model-based predictive control. The techniques have been successfully applied to the modeling and control of a neutralization process.     

Predictive Functional Control Based on Fuzzy Model: Design and Stability Study

In the paper the design methodology and stability analysis of parallel distributed fuzzy model based predictive control is presented. The idea is to design a control law for each rule of the fuzzy model and blend them together. The proposed control algorithm is developed in state space domain and is given in analytical form. The analytical form brings advantages in comparison with optimization based control schemes especially in the sence of realization in real-time. The stability analysis and design problems can be viewed as a linear matrix inequalities problem. This problem is solved by convex programming involving LMIs. In the paper a sufficient stability condition for parallel distributed fuzzy model-based predictive control is given. The problem is illustrated by an example on magnetic suspension system.     

基于啤酒发酵过程的时变轨迹输出反馈鲁棒模糊预测控制

考虑到实际生产中状态不易测量和设定值变化的情况以及系统本身的非线性特性,针对啤酒发酵过程温度控制系统提出了一种时变轨迹下输出反馈鲁棒模糊预测控制方法。在啤酒发酵罐温度系统的机理模型的基础上,建立包括不确定性和未知干扰的状态空间模型;通过设计模糊集,建立为具有加权系数的T-S模糊状态空间模型;并在状态变量的中引入输出跟踪误差,建立新型多自由度状态空间模型;并运用鲁棒模型预测控制方法优化参数不确定性问题,结合李雅普诺夫稳定性理论推导出线性矩阵不等式形式的稳定性条件,通过求解线性矩阵不等式中参数来计算对应子模型控制律,并对所设计的输出反馈控制器给定权值。通过仿真结果验证了提出方法的有效性和可行性。     

PEMFC的模糊辨识和非线性预测控制

质子交换膜燃料电池(PEMFC)是21世纪最有前景的发电技术之一。该文针对PEMFC等一类具有严重非线性的复杂被控对象,提出一种基于模糊模型的非线性预测控制算法对PEMFC系统进行建模与控制。在建模与控制过程中,采用模糊聚类和线性辨识方法在线建立PEMFC控制系统的T-S模糊预测模型,然后基于分支定界法的基本原理对控制量进行离散寻优,从而实现PEMFC的非线性预测控制。仿真和实验结果证明了该算法的有效性和优越性。     

Predictive Functional Control Based on Fuzzy Model: Comparison with Linear Predictive Functional Control and PID Control

The implementation of the fuzzy predictive functional control (FPFC) on the magnetic suspension system is presented in the paper. The magnetic suspension system was in our case the pilot plant for magnetic bearing and is an open-loop unstable process, therefore a lead compensator was used to stabilize it. The high quality control requirements were a-periodical step response and zero steady-state error. Adding the integrator to a feedback causes overshoot. The solution to the problem was cascade control with fuzzy predictive functional controller in the outer loop. To cope with the unknown model parameters and the nonlinear nature of the magnetic system, a fuzzy identification based on FNARX model was used. After successful validation the obtained fuzzy model was used for controller design. The FPFC is compared with a cascade linear predictive functional control (PFC) and PID control. The results we obtained with the FPFC are very promising and hardly comparable with conventional control techniques.     

Fuzzy Control for Nonlinear Uncertain Electrohydraulic Active Suspensions With Input Constraint

This paper presents a Takagi-Sugeno (T-S) model-based fuzzy control design approach for electrohydraulic active vehicle suspensions considering nonlinear dynamics of the actuator, sprung mass variation, and constraints on the control input. The T-S fuzzy model is first applied to represent the nonlinear uncertain electrohydraulic suspension. Then, a fuzzy state feedback controller is designed for the obtained T-S fuzzy model with optimized H _infin performance for ride comfort by using the parallel-distributed compensation (PDC) scheme. The sufficient conditions for the existence of such a controller are derived in terms of linear matrix inequalities (LMIs). Numerical simulations on a full-car suspension model are performed to validate the effectiveness of the proposed approach. The obtained results show that the designed controller can achieve good suspension performance despite the existence of nonlinear actuator dynamics, sprung mass variation, and control input constraints.     

Observers for Takagi-Sugeno fuzzy systems

We focus on the analysis and design of two different sliding mode observers for dynamic Takagi-Sugeno (TS) fuzzy systems. A nonlinear system of this class is composed of multiple affine local linear models that are smoothly interpolated by weighting functions resulting from a fuzzy partitioning of the state space of a given nonlinear system subject to observation. The Takagi-Sugeno fuzzy system is then an accurate approximation of the original nonlinear system. Our approach to the analysis and design of observers for Takagi-Sugeno fuzzy systems is based on extending sliding mode observer schemes to the case of interpolated multiple local affine linear models. Thus, our main contribution is nonlinear observer analysis and design methods that can effectively deal with model/plant mismatches. Furthermore, we consider the difficult case when the weighting functions in the Takagi-Sugeno fuzzy system depend on the estimated state.