Analysis of direct action fuzzy PID controller structures

The majority of the research work on fuzzy PID controllers focuses on the conventional two-input PI or PD type controller proposed by Mamdani (1974). However, fuzzy PID controller design is still a complex task due to the involvement of a large number of parameters in defining the fuzzy rule base. This paper investigates different fuzzy PID controller structures, including the Mamdani-type controller. By expressing the fuzzy rules in different forms, each PLD structure is distinctly identified. For purpose of analysis, a linear-like fuzzy controller is defined. A simple analytical procedure is developed to deduce the closed form solution for a three-input fuzzy inference. This solution is used to identify the fuzzy PID action of each structure type in the dissociated form. The solution for single-input-single-output nonlinear fuzzy inferences illustrates the effect of nonlinearity tuning. The design of a fuzzy PID controller is then treated as a two-level tuning problem. The first level tunes the nonlinear PID gains and the second level tunes the linear gains, including scale factors of fuzzy variables. By assigning a minimum number of rules to each type, the linear and nonlinear gains are deduced and explicitly presented. The tuning characteristics of different fuzzy PID structures are evaluated with respect to their functional behaviors. The rule decoupled and one-input rule structures proposed in this paper provide greater flexibility and better functional properties than the conventional fuzzy PHD structures.     

直接蒸汽加热器温控系统的仿真研究

针对直接蒸气加热器出口温度具有非线性、时生性、大滞后等特点,建立了直接蒸汽加热器温控系统的数学模型.提出了一种模糊PID温度控制方案,它将常规PID控制和模糊控制二者优点相结合,利用模糊控制规则对PID参数进行自整定,有效提高了系统的抗干扰能力和适应参数变化的能力,保证了加热器出口温度的精确控制.MATLAB仿真结果证明了该方案的正确性和实用性.     

Integration of PSO and GA for optimum design of fuzzy PID controllers in a pendubot system

In this paper, a novel auto-tuning method is proposed to design fuzzy PID controllers for asymptotical stabilization of a pendubot system. In the proposed method, a fuzzy PID controller is expressed in terms of fuzzy rules, in which the input variables are the error signals and their derivatives, while the output variables are the PID gains. In this manner, the PID gains are adaptive and the fuzzy PID controller has more flexibility and capability than the conventional ones with fixed gains. To tune the fuzzy PID controller simultaneously, an evolutionary learning algorithm integrating particle swarm optimization (PSO) and genetic algorithm (GA) methods is proposed. The simulation results illustrate that the proposed method is indeed more efficient in improving the asymptotical stability of the pendubot system. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Hybrid control of a pneumatic artificial muscle (PAM) robot arm using an inverse NARX fuzzy model

We investigated the possibility of applying a hybrid feed-forward inverse nonlinear autoregressive with exogenous input (NARX) fuzzy model-PID controller to a nonlinear pneumatic artificial muscle (PAM) robot arm to improve its joint angle position output performance. The proposed hybrid inverse NARX fuzzy-PID controller is implemented to control a PAM robot arm that is subjected to nonlinear systematic features and load variations in real time. First the inverse NARX fuzzy model is modeled and identified by a modified genetic algorithm (MGA) based on input/output training data gathered experimentally from the PAM system. Second the performance of the optimized inverse NARX fuzzy model is experimentally demonstrated in a novel hybrid inverse NARX fuzzy-PID position controller of the PAM robot arm. The results of these experiments demonstrate the feasibility and benefits of the proposed control approach compared to traditional PID control strategies. Consequently, the good performance of the MGA-based inverse NARX fuzzy model in the proposed hybrid inverse NARX fuzzy-PID position control of the PAM robot arm is demonstrated. These results are also applied to model and to control other highly nonlinear systems.     

An optimal adaptive robust PID controller subject to fuzzy rules and sliding modes for MIMO uncertain chaotic systems

In this paper, an optimal adaptive robust PID controller based on fuzzy rules and sliding modes is introduced to present a general scheme to control MIMO uncertain chaotic nonlinear systems. In this control scheme, the gains of the PID controller are updated by using an adaptive mechanism, fuzzy rules, the gradient search method, and the chain rule of differentiation in order to minimize the sliding surfaces of sliding mode control. More precisely, sliding mode control is used as a supervisory controller to provide sufficient control inputs and guarantee the stability of the control approach. To ascertain the parameters of the proposed controller and avoid trial and error, the multi-objective genetic algorithm is employed to augment the performance of proposed controller. The chaotic system of a Duffing-Holmes oscillator and an industrial robotic manipulator are the case studies to evaluate the performance of the proposed control approach. The obtained results of this study regarding both systems are compared with the outcomes of two notable studies in the literature. The results and analysis prove the efficiency of the proposed controller with regard to MIMO uncertain systems having challenging external disturbances in terms of stability, minimum tracking error and optimal control inputs.     

Teaching–learning based optimization algorithm based fuzzy-PID controller for automatic generation control of multi-area power system

This paper deals with the design of a novel fuzzy proportional–integral–derivative (PID) controller for automatic generation control (AGC) of a two unequal area interconnected thermal system. For the first time teaching–learning based optimization (TLBO) algorithm is applied in this area to obtain the parameters of the proposed fuzzy-PID controller. The design problem is formulated as an optimization problem and TLBO is employed to optimize the parameters of the fuzzy-PID controller. The superiority of proposed approach is demonstrated by comparing the results with some of the recently published approaches such as Lozi map based chaotic optimization algorithm (LCOA), genetic algorithm (GA), pattern search (PS) and simulated algorithm (SA) based PID controller for the same system under study employing the same objective function. It is observed that TLBO optimized fuzzy-PID controller gives better dynamic performance in terms of settling time, overshoot and undershoot in frequency and tie-line power deviation as compared to LCOA, GA, PS and SA based PID controllers. Further, robustness of the system is studied by varying all the system parameters from −50% to +50% in step of 25%. Analysis also reveals that TLBO optimized fuzzy-PID controller gains are quite robust and need not be reset for wide variation in system parameters.     

模糊PID控制器的设计及其仿真

对非线性大滞后等特殊的系统,存在常规PID控制器控制效果不甚理想的问题,为此结合模糊控制和常规PID控制二者的优点提出了模糊PID(Fuzzy-PID)控制方法.首先建立模糊规则、进行模糊推理,确定PID控制器的参数,再由PID控制器直接控制对象,实现实时控制的目的.将所设计的模糊PID控制器应用于具有大时滞,对大惯性的皮革温度收缩测定仪温度控制系统检测其性能,计算机仿真试验结果表明:Fuzzy-PID控制器与常规PID控制器相比较,确实提高了仪器温度控制系统的自适应能力和鲁棒性,改善了系统的动态性能和静态性能,能使非线性、大滞后等特殊的系统达到了良好的控制效果.     

模糊自适应PID控制的研究及应用仿真

传统PID控制器参数的整定是在获取对象数学模型的基础上,根据某一整定规则来确定的,难以适应复杂多变的控制系统。针对其参数整定不良、性能欠佳,对被控过程的适应性差等缺点采用模糊控制与自适应PID控制结合起来,设计了模糊自适应PID控制器。利用模糊推理方法实现对PID参数的在线自整定,进一步完善PID控制器的性能,提高系统的控制精度。仿真结果表明该模糊自适应PID控制器既具有PID控制器高精度的优点,又具有模糊控制器快速、适应性强的特点,使被控对象具有良好的动、稳态特性,有较好的工程应用前景。     

模糊PID复合控制在变频空调中应用研究

空调房间温度控制是一复杂的控制过程,传统的模糊或PID控制很难得到较好的控制效果,模糊控制和PID控制适当结合控制空调房间温度可使控制效果大大提高。本文建立了房间温度控制模型,介绍了模糊和PID控制并联结合方式并对各复合控制器进行了设计。对设计的变频空调控制系统进行了仿真,结合仿真图,从鲁棒性和稳定性方面分析了设计的各模糊和PID复合控制器控制效果。     

基于遗传优化的模糊PID控制在智能除草中的应用研究*

针对当前智能除草控制系统的非线性、时滞性及喷施精度过低等问题,设计了一种基于超代遗传算法(HG-GA)优化的模糊PID控制方案。在该方案中,针对智能除草装置的特点,设计了对应的模糊PID控制器,并对控制器的各因子进行遗传优化,从而提高系统的控制效果,同时加快了优化速度。实验结果表明这是一种有效的控制策略,尤其是在处理非线性及外部干扰方面有更好的鲁棒性。     

Quantitative design and analysis of fuzzy proportional-integralderivative control a step towards autotuning

In this paper, a thorough mathematical analysis is proposed for designing and tuning fuzzy proportional-integral-derivative (FZ-PID) control in order to achieve a better performance and simpler design. The quantitative model of FZ-PID, derived for the mathematical analysis and gain design, consists of a nonlinear relay and a nonlinear proportional-integral-derivative (PID) controller. This nonlinear model can be treated as of a PID nature around the equilibrium state under certain approximations. Through direct comparison with the conventional PID control, the connection between the scaling gains and the control actions is expressed in an explicit mathematical form. This theoretical analysis reveals that FZ-PID leads to more damping and hence less oscillation than do its conventional counterparts. This could be one of the reasons why fuzzy logic control can achieve a robust performance. A less coupled gain structure is further proposed to decouple the influence of the scaling gains and to disclose the major contribution of each gain to the different aspects of the control performance. Consequently, the systematic design and tuning method of the conventional PID control can be applied to the initial gain design and the fine tuning of the FZ-PID control. The simulation results confirm the effectiveness of the method proposed. This research is actually an important step towards the possible autotuning of the fuzzy controller.     

New methodology for analytical and optimal design of fuzzy PIDcontrollers

Describes a methodology for the systematic design of fuzzy PID controllers based on theoretical fuzzy analysis and, genetic-based optimization. An important feature of the proposed controller is its simple structure. It uses a one-input fuzzy inference with three rules and at most six tuning parameters. A closed-form solution for the control action is defined in terms of the nonlinear tuning parameters. The nonlinear proportional gain is explicitly derived in the error domain. A conservative design strategy is proposed for realizing a guaranteed-PID-performance (GPP) fuzzy controller. This strategy suggests that a fuzzy PID controller should be able to produce a linear function from its nonlinearity tuning of the system. The proposed PID system is able to produce a close approximation of a linear function for approximating the GPP system. This GPP system, incorporated with a genetic solver for the optimization, will provide the performance no worse than the corresponding linear controller with respect to the specific performance criteria. Two indexes, linearity approximation index (LAI) and nonlinearity variation index (NVI), are suggested for evaluating the nonlinear design of fuzzy controllers. The proposed control system has been applied to several first-order, second-order, and fifth-order processes. Simulation results show that the proposed fuzzy PID controller produces superior control performance to the conventional PID controllers, particularly in handling nonlinearities due to time delay and saturation     

Hierarchical fuzzy control

In a conventional rule based fuzzy control system, the rules are of the following form: if (condition) then (action), and all rules are essentially in a random order. The number of rules increases exponentially as the number of the system variables, on which the fuzzy rules are based, is increased. In this paper, the rules are structured in a hierarchical way so that the total number of rules will be a linear function of the system variables. The hierarchical fuzzy control algorithm developed in this paper is applied to control the feedwater flow to a steam generator of a power plant. The simulation results show that the hierarchical fuzzy controller yields superior performance over the conventional PID controller.     

Structural analysis of fuzzy controllers with nonlinear input fuzzy sets in relation to nonlinear PID control with variable gains

The popular linear PID controller is mostly effective for linear or nearly linear control problems. Nonlinear PID controllers, however, are needed in order to satisfactorily control (highly) nonlinear plants, time-varying plants, or plants with significant time delay. This paper extends our previous papers in which we show rigorously that some fuzzy controllers are actually nonlinear PI, PD, and PID controllers with variable gains that can outperform their linear counterparts. In the present paper, we study the analytical structure of an important class of two- and three-dimensional fuzzy controllers. We link the entire class, as opposed to one controller at a time, to nonlinear PI, PD, and PID controllers with variable gains by establishing the conditions for the former to structurally become the latter. Unlike the results in the literature, which are exclusively for the fuzzy controllers using linear fuzzy sets for the input variables, this class of fuzzy controllers employs nonlinear input fuzzy sets of arbitrary types. Our structural results are thus more general and contain the existing ones as special cases. Two concrete examples are provided to illustrate the usefulness of the new results.     

Hybrid fuzzy control of robotics systems

This paper presents a new approach towards optimal design of a hybrid fuzzy controller for robotics systems. The salient feature of the proposed approach is that it combines the fuzzy gain scheduling method and a fuzzy proportional-integral-derivative (PID) controller to solve the nonlinear control problem. The resultant fuzzy rule base of the proposed controller can be decomposed into two layers. In the upper layer, the gain scheduling method is incorporated with a Takagi-Sugeno (TS) fuzzy logic controller to linearize the robotics system for a given reference trajectory. In the lower layer, a fuzzy PID controller is derived for all the locally linearized systems by replacing the conventional PI controller by a linear fuzzy logic controller, which has different gains for different linearization conditions. Within the guaranteed stability region, the controller gains can be optimally tuned by genetic algorithms. Simulation studies on a pole balancing robot and a multilink robot manipulator demonstrate the effectiveness and robustness of the proposed approach.     

基于Smith预估模糊PID的主汽温控制系统

针对生物质电厂主汽温具有非线性、时变性、大滞后、随机干扰量大等特性导致的工况复杂、控制难度大的问题,提出了一种基于Smith预估补偿的模糊PID串级控制方案.主控制器采用模糊推理的方法实现PID参数的在线自整定,利用Smith预估器实现对温控系统的纯滞后补偿.详细阐述温控系统的硬件配置和软件实现,实际运行结果表明该方案有效提高了系统的抗干扰能力和适应参数变化的能力,具有鲁棒性强、动态响应快及稳态精度高的优点.     

高压超临界萃取装置的模糊PID控制方法

高压超临界萃取控制参数具有时变、非线性的特点,对其进行精确控制具有很大难度.PID控制广泛应用于工业过程控制,但常规PID控制器参数对运行工况的适应性差.模糊控制具有不依赖系统数学模型、调节速度快、鲁棒性好等优点,但稳态精度欠佳.将PID控制与模糊控制相结合,设计了模糊PID反馈控制器,形成了模糊PID复合控制方法.以...     

模糊控制与PID控制的对比及其复合控制

在对PID控制与模糊控制进行对比的基础上提出了一种模糊PID复合控制方案.首先,分别设计了一个常规PID控制器和一个基本模糊控制器;然后,对两种控制方案进行了仿真对比研究,并对它们的优缺点进行了评价;最后,为了将两种方案取长补短、优势互补,设计了一种模糊PID复合型控制器.该复合控制器根据偏差范围的大小,通过模糊控制与...     

Online tuning fuzzy PID controller using robust extended Kalman filter

Fuzzy PID controllers have been developed and applied to many fields for over a period of 30 years. However, there is no systematic method to design membership functions (MFs) for inputs and outputs of a fuzzy system. Then optimizing the MFs is considered as a system identification problem for a nonlinear dynamic system which makes control challenges. This paper presents a novel online method using a robust extended Kalman filter to optimize a Mamdani fuzzy PID controller. The robust extended Kalman filter (REKF) is used to adjust the controller parameters automatically during the operation process of any system applying the controller to minimize the control error. The fuzzy PID controller is tuned about the shape of MFs and rules to adapt with the working conditions and the control performance is improved significantly. The proposed method in this research is verified by its application to the force control problem of an electro-hydraulic actuator. Simulations and experimental results show that proposed method is effective for the online optimization of the fuzzy PID controller.     

A novel fractional order fuzzy PID controller and its optimal time domain tuning based on integral performance indices

A novel fractional order (FO) fuzzy Proportional-Integral-Derivative (PID) controller has been proposed in this paper which works on the closed loop error and its fractional derivative as the input and has a fractional integrator in its output. The fractional order differ-integrations in the proposed fuzzy logic controller (FLC) are kept as design variables along with the input–output scaling factors (SF) and are optimized with Genetic Algorithm (GA) while minimizing several integral error indices along with the control signal as the objective function. Simulations studies are carried out to control a delayed nonlinear process and an open loop unstable process with time delay. The closed loop performances and controller efforts in each case are compared with conventional PID, fuzzy PID and PI^λD^μ controller subjected to different integral performance indices. Simulation results show that the proposed fractional order fuzzy PID controller outperforms the others in most cases.