A numerical optimization approach for tuning fuzzy logiccontrollers

This paper develops a method to tune fuzzy controllers using numerical optimization. The main attribute of this approach is that it allows fuzzy logic controllers to be tuned to achieve global performance requirements. Furthermore, this approach allows design constraints to be implemented during the tuning process. The method tunes the controller by parameterizing the membership functions for error, change-in-error, and control output. The resulting parameters form a design vector which is iteratively changed to minimize an objective function. The minimal objective function results in an optimal performance of the system. A spacecraft mounted science payload line-of-sight pointing control is used to demonstrate results.     

调整系统控制量的模糊PID控制器的计算机设计与仿真

该文提出调整系统控制量的模糊PID控制器的计算机设计与仿真。以碱回收炉的水位控制为例具体论述调整系统控制量的模糊PID控制器的设计、2-D控制表的建立、以及控制器计算机设计与仿真的实现。借助MATLAB模糊控制工具箱和SIMULINK仿真工具进行的仿真实验表明．该控制器既吸收了模糊控制器良好的动态性能．又克服了模糊控制器静态性能较差的缺点。并且为碱回收炉上汽包水位控制提出了一种新的尝试。该控制器结构简单、参数调整方便、快捷。     

Tuning of a neuro-fuzzy controller by genetic algorithm

Due to their powerful optimization property, genetic algorithms (GAs) are currently being investigated for the development of adaptive or self-tuning fuzzy logic control systems. This paper presents a neuro-fuzzy logic controller (NFLC) where all of its parameters can be tuned simultaneously by GA. The structure of the controller is based on the radial basis function neural network (RBF) with Gaussian membership functions. The NFLC tuned by GA can somewhat eliminate laborious design steps such as manual tuning of the membership functions and selection of the fuzzy rules. The GA implementation incorporates dynamic crossover and mutation probabilistic rates for faster convergence. A flexible position coding strategy of the NFLC parameters is also implemented to obtain near optimal solutions. The performance of the proposed controller is compared with a conventional fuzzy controller and a PID controller tuned by GA. Simulation results show that the proposed controller offers encouraging advantages and has better performance.     

Fuzzy Constrained Min-Max Model Predictive Control Based on Piecewise Lyapunov Functions

This paper proposes two novel stable fuzzy model predictive controllers based on piecewise Lyapunov functions and the min-max optimization of a quasi-worst case infinite horizon objective function. The main idea is to design state feedback control laws that minimize the worst case objective function based on fuzzy model prediction, and thus to obtain the optimal transient control performance, which is of great importance in industrial process control. Moreover, in both of these predictive controllers, piecewise Lyapunov functions have been used in order to reduce the conservatism of those existent predictive controllers based on common Lyapunov functions. It is shown that the asymptotic stability of the resulting closed-loop discrete-time fuzzy predictive control systems can be established by solving a set of linear matrix inequalities. Moreover, the controller designs of the closed-loop control systems with desired decay rate and input constraints are also considered. Simulations on a numerical example and a highly nonlinear benchmark system are presented to demonstrate the performance of the proposed fuzzy predictive controllers.     

A new adjusting technique for PID type fuzzy logic controller using PSOSCALF optimization algorithm

The main aim of this work consists of proposing a new three-step adjusting approach for an improved version of PID-type fuzzy structure in order to determine its design parameters based on a novel hybrid PSO search technique called PSOSCALF, combining Sine Cosine Algorithm (SCA) and Levy Flight (LF) distribution. In addition, conventional and self-tuning controllers are designed to get a better understanding of the performance and robustness of the proposed PID-type FLC approach. At first, the proposed PID-type FLC structure is defined as an optimization problem and then the PSOSCALF algorithm is applied to resolve it systematically. Evaluation of the performance quality of the proposed fuzzy structure is accomplished based on the stabilization and tracking control of a nonlinear Inverted Pendulum (IP) system. To make a complete comparison, the performance of three other optimization techniques namely simple PSO, Differential Evolution (DE) and Cuckoo Search (CS) are examined against the hybrid PSOSCALF algorithm. The simulation results demonstrate that the proposed PSOSCALF-tuned PID-type FLC structure is able to decrease the overshoot and integral square error amounts by about 25% and 10%, respectively compared to the self-tuning controllers. Finally, for more validation, all the controllers are tested under four different disturbance scenarios. Obtained results show that the proposed PID-type FLC can better stabilize the pendulum angle under all the scenarios compared to the PID and self-tuning controllers.     

Stable and optimal fuzzy control of linear systems

A number of stable and optimal fuzzy controllers are developed for linear systems. Based on some classical results in control theory, we design the structure and parameters of fuzzy controllers such that the closed-loop fuzzy control systems are stable, provided that the process under control is linear and satisfies certain conditions. It turns out that if stability is the only requirement, there is much freedom in choosing the fuzzy controller parameters. Therefore, a performance criterion is set to optimalize the parameters. Using the Pontryagin minimum principle, we design an optimal fuzzy controller for linear systems with quadratic cost function. Finally, the optimal fuzzy controller is applied to a ball-and-beam system     

Incremental Evolutionary Design of TSK Fuzzy Controllers

This paper proposes a novel method for the incremental design and optimization of first order Tagaki-Sugeno-Kang (TSK) fuzzy controllers by means of an evolutionary algorithm. Starting with a single linear control law, the controller structure is gradually refined during the evolution. Structural augmentation is intertwined with evolutionary adaptation of the additional parameters with the objective not only to improve the control performance but also to maximize the stability region of the nonlinear system. From the viewpoint of optimization the proposed method follows a divide-and-conquer approach. Additional rules and their parameters are introduced into the controller structure in a neutral fashion, such that the adaptations of the less complex controller in the previous stage are initially preserved. The proposed scheme is evaluated at the task of TSK fuzzy controller design for the upswing and stabilization of a rotational inverted pendulum. In the first case, the objective is a time optimal controller that upswings the pendulum in to the upper equilibrium point in shortest time. The stabilizing controller is designed as a state optimal controller. In a second application the optimization method is applied to the design of a fuzzy controller for vision-based mobile robot navigation. The results demonstrate that the incremental scheme generates solutions that are similar in control performance to pure parameter optimization of only the gains of a TSK system. Even more important, whereas direct optimization of control systems with more than 35 rules fails to identify a stabilizing control law, the incremental scheme optimizes fuzzy state-space partitions and gains for hundreds of rules.     

Reliability-based robust Pareto design of linear state feedback controllers using a multi-objective uniform-diversity genetic algorithm (MUGA)

In this paper, fuzzy threshold values, instead of crisp threshold values, have been used for optimal reliability-based multi-objective Pareto design of robust state feedback controllers for a single inverted pendulum having parameters with probabilistic uncertainties. The objective functions that have been considered are, namely, the normalized summation of rising time and overshoot of cart (S_RO–C) and the normalized summation of rising time and overshoot of pendulum (S_RO–P) in the deterministic approach. Accordingly, the probabilities of failure of those objective functions are also considered in the reliability-based design optimization (RBDO) approach. A new multi-objective uniform-diversity genetic algorithm (MUGA) is presented and used for Pareto optimum design of linear state feedback controllers for single inverted pendulum problem. In this way, Pareto front of optimum controllers is first obtained for the nominal deterministic single inverted pendulum using the conflicting objective functions in time domain. Such Pareto front is then obtained for single inverted pendulum having probabilistic uncertainties in its parameters using the statistical moments of those objective functions through a Monte Carlo simulation (MCS) approach. It is shown that multi-objective reliability-based Pareto optimization of the robust state feedback controllers using MUGA with fuzzy threshold values includes those that may be obtained by various crisp threshold values of probability of failures and, thus, remove the difficulty of selecting suitable crisp values. Besides, the multi-objective Pareto optimization of such robust feedback controllers using MUGA unveils some very important and informative trade-offs among those objective functions. Consequently, some optimum robust state feedback controllers can be compromisingly chosen from the Pareto frontiers.     

PID plus fuzzy controller structures as a design base for industrial applications

This paper investigates the practical ways of designing effective combinations of classical PID controllers and emerging intelligent technologies for real-life industrial projects. It analyses the evolution of fuzzy controller (FC) design methodology. Based on the analysis, structures and methods that combine both approaches are proposed and considered. The paper is not intended to develop a mathematical theory, but to give some practical recommendations on replacing control by a human operator control with fuzzy control, and an on-line parameter tuning of FC parameters. These two main points are illustrated with two application projects, which are studied in greater detail. The first one includes the design of a FC supervising a PID control system in an automatic aircraft guidance system. The second project describes the tuning of the scaling factors of a fuzzy PID-type controller with other fuzzy systems, used in the excitation control of a synchronous power generator connected to an infinite bus through a transmission line.     

基于粒子群优化的一类模糊控制器设计

针对一般模糊控制器存在稳态性能与动态性能之间的矛盾,提出一种参数自整定模糊控制器.该控制器结构简单,算法简便,具有良好的动态特性,能有效消除静态偏差,且有一定的鲁棒性.为避免模糊控制器设计中参数调试的复杂性,获得最佳的控制性能,应用改进的自适应粒子群优化算法对模糊控制器参数进行优化设计.通过典型的被控对象的仿真研究,验证了所提出算法的有效性和适应性以及所设计控制器的优越性.     

一种基于遗传算法优化的模糊控制器研究

模糊控制中的模糊推理规则和隶属函数的选取往往依据相关专家或技术人员的实际经验,具有较大的人为主观性,尤其在面对具有较强的非线性系统和未知动态环境条件下,其控制性能达不到客观要求。本文采用改进的遗传算法优化模糊控制中的比例因子,从而对控制规则和隶属函数进行优化。仿真结果表明,经过优化后的模糊控制器和传统的Fuzzy-PID控制器相比,其控制规则和隶属函数更加客观合理,控制系统的动、静态性能都有较大提高。     

模糊免疫PID控制器的设计与仿真

针对模糊控制系统设计复杂，实验数据调整繁琐的现象，设计了一种模糊自调整免疫PID控制器，该控制器结构简单，参数调整方便，快捷，并成功应用于冷轧带钢的厚度自动控制系统中。借助MATLAB的模糊控制工具箱和SMULINK仿真工具对其进行的仿真实验表明，该控制器的控制性能远优于常规的PID控制器，为冷轧带钢厚度精度的提高提供了一种新的尝试。     

智能集成控制在大功率电弧炉系统中的应用研究

针对冶金行业大功率电弧炉的控制，提出了一种基于模糊控制、神经网络和多目标 优化决策相结合的智能集成控制方案．首先采用变结构模糊神经网络控制来设计温度外环控制器，给三相电极电流平衡内环提供电流指令信号，然后在内环控制中综合各种优化目标，构造优化目标函数，运用多目标模糊优化决策来实现整个系统的平衡．现场数据表明运用该控制方案的系统目前已在广东韶关冶炼厂成功运行．     

PID数字控制器多指标优化模拟设计方法研究

建立PID数字控制器多指标统一优化模拟设计方法;用SIMULINK仿真研究数字PID控制对模拟PID控制的复现能力和PID计算机控制系统的阶跃响应,用MATLAB仿真筛选PID参数的优化组合值;提出并建立了一种新的PID数字控制器多指标优化模拟设计方法,包括:PID初值确定方法、模拟PID优化参数MATLAB筛选方案和软件流程图、模拟PID参数转换数字PID参数的方法、SIMULINK仿真验证设计结果的有效性的方法等;研究表明,该方法可用于1～5ms采样周期的PID数字控制器多指标优化模拟设计,且能独立使用、无需PID经验数据和其它设计/整定方法;提供了4个代表性的实例设计,验证了该方法的有效性。     

A Hybrid Approach for Design of Stable Adaptive Fuzzy Controllers Employing Lyapunov Theory and Particle Swarm Optimization

This paper proposes a new approach for designing stable adaptive fuzzy controllers, which employs a hybridization of a conventional Lyapunov-theory-based approach and a particle swarm optimization (PSO) based stochastic optimization approach. The objective is to design a self-adaptive fuzzy controller, optimizing both its structures and free parameters, such that the designed controller can guarantee desired stability and can simultaneously provide satisfactory performance. The design methodology for the controller simultaneously utilizes the good features of PSO (capable of providing good global search capability, required to provide a high degree of automation) and Lyapunov-based tuning (providing fast adaptation utilizing a local search method). Three different variants of the hybrid controller are proposed in this paper. These variants are implemented for benchmark simulation case studies and real-life experimentation, and their results demonstrate the usefulness of the proposed approach.     

Fractional-order load-frequency control of interconnected power systems using chaotic multi-objective optimization

Fractional-order proportional-integral-derivative (FOPID) controllers are designed for load-frequency control (LFC) of two interconnected power systems. Conflicting time-domain design objectives are considered in a multi-objective optimization (MOO)-based design framework to design the gains and the fractional differ-integral orders of the FOPID controllers in the two areas. Here, we explore the effect of augmenting two different chaotic maps along with the uniform random number generator (RNG) in the popular MOO algorithm—the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Different measures of quality for MOO, e.g. hypervolume indicator, moment of inertia-based diversity metric, total Pareto spread, spacing metric, are adopted to select the best set of controller parameters from multiple runs of all the NSGA-II variants (i.e. nominal and chaotic versions). The chaotic versions of the NSGA-II algorithm are compared with the standard NSGA-II in terms of solution quality and computational time. In addition, the Pareto optimal fronts showing the trade-off between the two conflicting time domain design objectives are compared to show the advantage of using the FOPID controller over that with simple PID controller. The nature of fast/slow and high/low noise amplification effects of the FOPID structure or the four quadrant operation in the two inter-connected areas of the power system is also explored. A fuzzy logic-based method has been adopted next to select the best compromise solution from the best Pareto fronts corresponding to each MOO comparison criteria. The time-domain system responses are shown for the fuzzy best compromise solutions under nominal operating conditions. Comparative analysis on the merits and de-merits of each controller structure is reported then. A robustness analysis is also done for the PID and the FOPID controllers.     

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     

Stability and control of fuzzy dynamic systems via cell-statetransitions in fuzzy hypercubes

The objective of this paper is to provide fuzzy control designers with a generalized design tool for stable fuzzy logic controllers in an optimal sense. Given multiple sets of data disturbed by vagueness uncertainty, we generate the implicative rules that guarantee stability and robustness of closed-loop fuzzy dynamic systems. First, the mathematical basis of fuzzy hypercubes and fuzzy dynamic systems is rigorously studied by considering the membership conditions for perfect recall and the evidential combination for reliable reasoning. Second, the author suggests the cell-state transition method, which utilizes Hsu's cell-to-cell mapping concept. As a result, a generic and implementable design methodology for obtaining a fuzzy feedback gain K, a fuzzy hypercube, is provided and illustrated with simple examples. The designed rules or membership functions in K form the cell-state transitions that lead an initial state to the goal state globally. The cell-state transition approach provides flexibility in choosing different controller rule bases depending on optimal strategies     

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.     

Voltage and frequency regulation in autonomous microgrids using Hybrid Big Bang-Big Crunch algorithm

This paper proposes an optimal power control strategy for inverter-based Distributed Generation (DG) units in autonomous microgrids. It consists of power, voltage, and current controllers with Proportional-Integral (PI) regulators. The droop concept is used for the power control strategy. Static parameters in PI regulators may not ensure the most optimal solution due to inevitable changes happening in microgrid configuration and loads. In the proposed method, after occurring a load change in a standalone microgrid, parameters of the PI controller are dynamically adjusted to get the most optimal operating point that satisfies objective functions. The optimization problem is formulated as a multi-objective programming with objective functions of minimizing overshoot/undershoot, settling time, rise time, and Integral Time Absolute Error (ITAE) in the output voltage. These objective functions are combined using fuzzy memberships. The Hybrid Big Bang-Big Crunch algorithm (HBB-BC) is used to solve the optimization problem. The proposed methodology is simulated on a case study and according to obtained results, the suggested tuning of PI parameters leads to a better voltage response than previous methods. The case study is also solved using the Particle Swarm Optimization (PSO) and Big Bang-Big Crunch (BB-BC) algorithms and it is found that the HBB-BC gives a better solution than the PSO and BB-BC.