A simple design method for interval type-2 fuzzy pid controllers

In this study, a design method for single Input interval type-2 fuzzy PID controller has been developed. The most important feature of the proposed type-2 fuzzy controller is its simple structure consisting of a single input variable. The presented simple structure gives an opportunity to the designer to form the type-2 fuzzy controller output in closed form formulation for the first time in literature. This formulation cannot be achieved with present type-2 fuzzy PID controller structures which have employed the Karnik-Mendel type reduction. The closed form solution is derived in terms of the tuning parameters which are chosen as the heights of lower membership functions of the antecedent interval type-2 fuzzy sets. Elaborations are done on the derived closed form output and a simple strategy is presented for a single input type-2 fuzzy PID controller design. The presented interval type-2 fuzzy controller structure still keeps the most preferred features of the PID controller such as simplicity and easy design. We will illustrate how the extra degrees of freedom provided by the antecedent interval type-2 fuzzy sets can be used to enhance the control performance on linear and nonlinear benchmark systems by simulations. Moreover, the type-2 fuzzy controller structure has been implemented on experimental pH neutralization. The simulation and experimental results will illustrate that the proposed type-2 fuzzy controller produces superior control performance and can handle nonlinear dynamics, parameter uncertainties, noise and disturbances better in comparison with the standard PID controllers. Hence, the results and analyses of this study will give the control engineers an opportunity to draw a bridge and connect the type-2 fuzzy logic and control theory.     

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     

Simultaneous closed-loop tuning of cascade controllers based directly on set-point step-response data

This study presents a novel closed-loop tuning method for cascade control systems, in which both primary and secondary controllers are tuned simultaneously by directly using set-point step-response data without resorting to process models. The tuning method can be applied on-line to improve the performance of existing underperforming cascade controllers by retuning controller parameters, using routine operating data. The goal of the proposed design is to obtain the parameters of two proportional-integral-derivative (PID)-type controllers, so that the resulting inner and outer loops behave as similarly as possible to the appropriately specified reference models. The tuning rule and optimization problem related to the proposed design are derived. Based on the rationale behind cascade control, the secondary controller is designed based on disturbance rejection to quickly attenuate disturbances. The primary controller is designed to accurately account for the inner-loop dynamics, without requiring an additional test. In addition, robustness considerations are included in the proposed tuning method, which enable the designer to explicitly address the trade-off between performance and robustness for inner and outer loops independently. Simulation examples show that the proposed method exhibits superior control performance compared with the previous (model-based) tuning methods, confirming the effectiveness of this novel tuning method for cascade control systems.     

Intelligent adaptive control of bioreactors

Supervised model-based self-tuning control of fermentation processes is addressed. The diversity, nonlinearity and time-varying nature of these processes make their control a challenging task. Conventional linear (PID) controllers with fixed parameters cannot meet the increasing performance requirements over the whole operating range. In the approach pursued in this research, a local linear model is identified at the current working point by using a limited amount input–output data obtained through an identification experiment. A linear controller is then tuned on the basis of this model. To minimize the intervention into the process operation, this tuning procedure is only initiated if the performance of the current controller deteriorates. To this end, a supervisory expert system is designed whose tasks are to monitor the process performance, design an appropriate identification experiment, validate the obtained model and tune the controller. The supervisory system is based on a combination of a state automaton with a rule-based fuzzy inference system. Experimental results have demonstrated the feasibility of this approach.     

核动力装置蒸汽发生器水位的分层模糊自适应控制

针对压水堆核动力装置蒸汽发生器的水位控制提出一种分层模糊自适应控制方案，该方案中2个模糊控制器分层连接，每个模糊控制均采用典型模糊控制单元，使得模糊规则个数和可调参数个数大大减少，便于在线学习和实时控制，给出了分层模糊控制器的解析表达式及可调参数的在线学习方法，在快速加负荷和突然甩负荷的仿真实验中，该方案的控制效果明显优于已有的变参数PID控制，验证了该方案的有效性。     

过热汽温二级模糊鲁棒自调整PID控制器设计

许多过程控制对象的模型结构及参数常常具有随设备运行状态改变而产生较大幅度 变化的特性，或者具有某些不确定性，文章探讨了采用增益配置型模糊PID控制器的参数自 调整的鲁棒设计问题，提出利用二级模糊推理结合系统特征在线辨识实现PID参数动态调整 的控制器设计方法，实例仿真表明该控制器能较好地适应对象动态模型的大幅度变化，保持 较优的鲁棒调节性能．     

Dynamic output feedback control of a flexible air-breathing hypersonic vehicle via T–S fuzzy approach

By utilising Takagi–Sugeno (T–S) fuzzy set approach, this paper addresses the robust H_∞ dynamic output feedback control for the non-linear longitudinal model of flexible air-breathing hypersonic vehicles (FAHVs). The flight control of FAHVs is highly challenging due to the unique dynamic characteristics, and the intricate couplings between the engine and fight dynamics and external disturbance. Because of the dynamics’ enormous complexity, currently, only the longitudinal dynamics models of FAHVs have been used for controller design. In this work, T–S fuzzy modelling technique is utilised to approach the non-linear dynamics of FAHVs, then a fuzzy model is developed for the output tracking problem of FAHVs. The fuzzy model contains parameter uncertainties and disturbance, which can approach the non-linear dynamics of FAHVs more exactly. The flexible models of FAHVs are difficult to measure because of the complex dynamics and the strong couplings, thus a full-order dynamic output feedback controller is designed for the fuzzy model. A robust H_∞ controller is designed for the obtained closed-loop system. By utilising the Lyapunov functional approach, sufficient solvability conditions for such controllers are established in terms of linear matrix inequalities. Finally, the effectiveness of the proposed T–S fuzzy dynamic output feedback control method is demonstrated by numerical simulations.     

Efficient control of a 3-link planar rigid manipulator using self-regulated fractional-order fuzzy PID controller

A self-regulated fractional-order fuzzy proportional–integral–derivative (SRFOFPID) controller is proposed to control a highly non-linear, complex and coupled 3-link planar rigid robotic manipulator in a virtual industrial environment. Industrial environment was simulated by introducing different kind of disturbances in the system and sensor noise. Proposed SRFOFPID controller is a direct non-linear adaptive controller having self-regulating feature and has been realized using fractional-order operators i.e. integrator and differentiator in self-regulated integer-order fuzzy PID (SRIOFPID) controller. Gains of SRFOFPID and SRIOFPID controllers are optimized using Backtracking Search Algorithm by minimizing an amalgamation of integral absolute error signal and integral absolute change in control signal as cost function. Performance of SRFOFPID and SRIOFPID controllers are assessed and compared with reference path under virtually simulated industrial environment. Presented intensive simulation studies revealed that both the controllers offered decent reference trajectory tracking performance under nominal operating conditions while SRFOFPID controller offered exceptionally robust performance under industrial scenario and uncertainties. Finally, the stability analysis of overall closed loop system is performed using small gain theorem and necessary and sufficient bounded-input and bounded-output stability conditions are established.     

基于感知模糊自适应蚁群算法的非线性PID控制

随着系统复杂度的提高和对象不确定性因素的增加,为克服线性PID动态性能和稳态性能差的缺陷,分析了非线性PID控制器各控制参数对误差的理想变化过程,构造非线性PID控制器。由于增益参数大量增加,传统参数优化方法不再适用,在分析蚁群算法的基础上,提出了基于感知自适应蚁群算法,并加入模糊自适应信息素更新机制,用于优化非线性PID控制器的设计方法。通过仿真实验将该控制器与基于蚁群算法的非线性PID控制器和基于蚁群算法、Z-N法的PID控制器进行对比,并对控制性能和收敛性能进行了分析,结果表明该算法有效克服了传统蚁群算法收敛速度较慢、容易陷入局部最优而停滞的缺陷,该控制器具有更好的动态性能和稳态性能。     

Statistically optimized FOPID for output force control of SEAs

Fractional order PID (FOPID) controllers have recently found an increasing application in different fields of control. Comparing to traditional PID algorithms, FOPID controllers provide more flexibility and better performances. The simple and non-model-based structure of FOPID controllers has boosted their usage in real-world applications. However, due to having two more control parameters than regular PID controllers and the non-linear structure of FOPID controllers, the tuning procedure of these controllers is still a challenge. The authors of the present paper have recently proposed a Taguchi-based gain tuning algorithm for tuning of control parameters of FOPID controller. The present paper is an experimental evaluation of the proposed method. A custom made SEA, FUM-LSEA, is used as the test bed in this study. Deriving a dynamic model of the FUM-LSEA, feed-forward terms are added to the controller to compensate for disturbances from motions of the output block. Optimal gains and orders of the controller are obtained through a set of experiments suggested by the Taguchi method. The Taguchi optimized controller is also compared to a Ziegler–Nichols tuned controller. The experimental results indicate 45% improvements in force tracking error.     

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。     

非完整移动机械手鲁棒自适应模糊控制

考虑系统存在的参数、外界扰动和未建模动态等不确定性,研究非完整移动机械手的鲁棒自适应控制器设计方法.基于用旋量理论建立的非完整移动机械手的动力学模型,设计了移动平台子系统的运动控制器,然后应用非线性反步控制技术和模糊逻辑系统的通用逼近性,用参数化线性模糊逻辑系统逼近非完整移动机械手动力学模型中的不确定项,基于Lyapu...     

Developments of fuzzy PID controllers

Abstract: This paper describes the development and tuning methods for a novel self-organizing fuzzy proportional integral derivative (PID) controller. Before applying fuzzy logic, the PID gains are tuned using a conventional tuning method. At supervisory level, fuzzy logic readjusts the PID gains online. In the first tuning method, fuzzy logic at the supervisory level readjusts the three PID gains during the system operation. In the second tuning method, fuzzy logic only readjusts the proportional PID gain, and the corresponding integral and derivative gains are readjusted using the Ziegler–Nichols tuning method while the system is in operation. For the compositional rule of inferences in the fuzzy PID and the self-organizing fuzzy PID schemes two new approaches are introduced: the min implication function with the mean of maxima defuzzification method, and the max-product implication function with the centre of gravity defuzzification method. The fuzzy PID controller, the self-organizing fuzzy PID controller and the PID controller are all applied to a non-linear revolute-joint robot arm for step input and path tracking experiments using computer simulation. For the step input and path tracking experiments, the novel self-organizing fuzzy PID controller produces a better output response than the fuzzy PID controller; and in turn both controllers exhibit better process output than the PID controller.     

具有PID反馈增益的自主水下航行器反步法变深控制

本文针对海底地形测绘时自主水下航行器(autonomous underwater vehicle,AUV)的变深控制问题,提出具有PID增益调节的AUV深度控制方法,基于反馈增益的反步法设计控制器,避免了采用传统反步法导致控制器中存在虚拟控制量的高阶导数问题;基于李雅普诺夫稳定性理论设计控制器参数消除了部分非线性项,得到的控制器的线性部分为状态变量的线性组合,具有PID控制器参数调节的形式;针对存在建模不精确、外界干扰和测量噪声时的闭环系统鲁棒性进行分析,保证了误差系统在扰动作用时的一致最终有界性.最后通过仿真实验验证了本文设计的控制器的有效性.     

Design and implementation of a fuzzy supervisor for on-line compensation of nonlinearities: An instability avoidance module

Unstable behavior of a control loop is the most feared situation in control engineering. Since PID controllers are linear in nature, but still used in 90% of control loops in the process industry, their use in nonlinear processes increases the risk of closed-loop unstable response. This paper presents the design of an instability avoidance module for SISO PID control loops to automatically adjust the controller's tuning parameters when undesired oscillatory behavior is monitored. This module is a Fuzzy-based Supervisor composed of a dynamic parameter identification module that operates on-line, and a Fuzzy Inference System (FIS) with fuzzy rules to modify PID tuning. Tests in nonlinear process models are performed, demonstrating that this Fuzzy Supervisor—Type 1 (non-intrusive) provides the PID controller the ability to adapt its tuning to eliminate observed oscillatory behavior.     

模糊免疫PID算法在温度控制系统中的应用研究

该文针对温度控制系统非线性、大滞后、参数时变的特征,设计了模糊免疫PID控制器。该控制器结合了模糊逻辑、免疫机理以及PID调节的各种优点,既具有模糊控制的非线性作用,又具有免疫控制的自适应能力,同时还具有PID控制的广泛适用性。文章介绍了模糊免疫PID控制器的控制原理和设计方法,在Matlab中编写函数仿真,结果表明该控制器能够实现持续干扰情况下的闭环鲁棒稳定,并使系统呈现良好的动态和静态性能。     

Real-time control of a water-gas shift reactor by a model-based fuzzy gain scheduling technique

A model-based fuzzy gain scheduling technique is proposed. Fuzzy gain scheduling is a form of variable gain scheduling which involves implementing several linear controllers over a partitioned process space. A higher-level rule-based controller determines which local controller is executed. Unlike conventional gain scheduling, a controller with fuzzy gain scheduling uses fuzzy logic to dynamically interpolate controller parameters near region boundaries based on known local controller parameters. Model-based fuzzy gain scheduling (MFGS) was applied to PID controllers to control a laboratory-scale water-gas shift reactor. The experimental results were compared with those obtained by PID with standard fuzzy gain scheduling, PID with conventional gain scheduling, simple PID and a nonlinear model predictive control (NMPC) strategy. The MFGS technique performed comparably to the NMPC method. It exhibited excellent control behaviour over the desired operating space, which spanned a wide temperature range. The other three PID-based techniques were adequate only within a limited range of the same operating space. Due to the simple algorithm involved, the MFGS technique provides a low cost alternative to other computationally intensive control algorithms such as NMPC.     

Fuzzy Sliding‐mode Strategy for Air–fuel Ratio Control of Lean‐burn Spark Ignition Engines

Minimization of emissions of carbon dioxide and harmful pollutants and maximization of fuel economy for lean‐burn spark ignition (SI) engines relies to a large extent on precise air–fuel ratio (AFR) control. However, the main challenge of AFR control is the large time‐varying delay in lean‐burn engines. Since the system is usually subject to external disturbances and uncertainties, a high level of robustness in AFR control design must be considered. We propose a fuzzy sliding‐mode control (FSMC) to track the desired AFR in the presence of periodic disturbances. The proposed method is model free and does not need any system characteristics. Based on the fuzzy system input–output data, two scaling factors are first employed to normalize the sliding surface and its derivative. According to the concept of the if‐then rule, an appropriate rule table for the logic system is designed. Then, based on Lyapunov stability criteria, the output scaling factor is determined such that the closed‐loop stability of the internal dynamics with uniformly ultimately bounded (UUB) performance is guaranteed. Finally, the feasibility and effectiveness of the proposed control scheme are evaluated under various operating conditions. The baseline controllers, namely, a PI controller with Smith predictor and sliding‐mode controller, are also used to compare with the proposed FSMC. It is shown that the proposed FSMC has superior regulation performance compared to the baseline controllers.     

Two-level tuning of fuzzy PID controllers

Fuzzy PID tuning requires two stages of tuning; low level tuning followed by high level tuning. At the higher level, a nonlinear tuning is performed to determine the nonlinear characteristics of the fuzzy output. At the lower level, a linear tuning is performed to determine the linear characteristics of the fuzzy output for achieving overall performance of fuzzy control. First, different fuzzy systems are defined and then simplified for two-point control. Non-linearity tuning diagrams are constructed for fuzzy systems in order to perform high level tuning. The linear tuning parameters are deduced from the conventional PID tuning knowledge. Using the tuning diagrams, high level tuning heuristics are developed. Finally, different applications are demonstrated to show the validity of the proposed tuning method.     

Simultaneous automatic tuning of cascade control systems from closed-loop step response data

This study presents a novel automatic tuning method for cascade control systems in which both primary and secondary controllers are tuned simultaneously using a single closed-loop step test. The proposed technique identifies the required process information with the help of B-spline series representation for the step responses. The two proportional–integral–derivative (PID) controllers are then tuned using an internal model control (IMC) approach. Considering the rationale of cascade control, the secondary controller is designed for faster disturbance attenuation. Without requiring an additional experiment, the primary controller is designed based on an identified process model that accurately accounts for inner loop dynamics. Finally, this study includes robustness considerations in the controller tuning process, and develops explicit guidelines for the selection of the IMC tuning parameters, completing the automatic tuning procedure for cascade control systems. The proposed method is robust to measurement noise because of the filtering property of the B-splines, and can provide superior control performance for both set-point tracking and disturbance rejection. Simulation examples demonstrate the effectiveness of the proposed automatic tuning method.