Harmony search algorithm-based fuzzy-PID controller for electronic throttle valve

The electronic throttle control (ETC) for a gasoline engine is a typical nonlinear plant because of its nonlinear spring and model-parameter changes caused by external environmental variables. In this paper, a fuzzy proportional-integral-derivative (PID) control strategy is proposed in order to improve the responsiveness of ETC. In the fuzzy-PID scheme, the input variables are the error signal and its derivative, and the output variable is PID gains expressed in terms of fuzzy rules. In this manner, the fuzzy-PID controller has more flexibility and capability than conventional ones. A novel technique to tune the fuzzy rules of fuzzy-PID controller is proposed using a harmony search algorithm, which can search the optimal PID gains for the plant. Simulation and experiment results have shown the effective performance of the proposed controller.     

Sugeno fuzzy PID tuning,by genetic-neutral for AVR in electrical power generation

We report a novel design method for determining the optimal proportional-integral-derivative (PID) controller parameters of an automatic voltage regulator (AVR) system, using a combined genetic algorithm (GA), radial basis function neural network (RBF-NN) and Sugeno fuzzy logic approaches. GA and a RBF-NN with a Sugeno fuzzy logic are proposed to design a PID controller for an AVR system (GNFPID). The problem for obtaining the optimal AVR and PID controller parameters is formulated as an optimization problem and RBF-NN tuned by GA is applied to solve the optimization problem. Whereas, optimal PID gains obtained by the proposed RBF tuning by genetic algorithm for various operating conditions are used to develop the rule base of the Sugeno fuzzy system and design fuzzy PID controller of the AVR system to improve the system's response (∼0.005 s). The proposed approach has superior features, including easy implementation, stable convergence characteristic, good computational efficiency and this algorithm effectively searches for a high-quality solution and improve the transient response of the AVR system (7E−06). Numerical simulation results demonstrate that this is faster and has much less computational cost as compared with the real-code genetic algorithm (RGA) and Sugeno fuzzy logic. The proposed method is indeed more efficient and robust in improving the step response of an AVR system.     

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.     

A PSO method with nonlinear time-varying evolution for optimal design of PID controllers in a pendubot system

A particle swarm optimization method with nonlinear time-varying evolution (PSO-NTVE) is employed in designing an optimal PID controller for asymptotic stabilization of a pendubot system. In the PSO-NTVE method, parameters are determined by using matrix experiments with an orthogonal array, in which a minimal number of experiments would have an effect that approximates the full factorial experiments. The PSO-NTVE method and other PSO methods are then applied to design an optimal PID controller in a pendubot system. Comparing the simulation results, the feasibility and the superiority of the PSO-NTVE method are verified.     

A novel hybrid DEPS optimized fuzzy PI/PID controller for load frequency control of multi-area interconnected power systems

In this paper, a novel hybrid Differential Evolution (DE) and Pattern Search (PS) optimized fuzzy PI/PID controller is proposed for Load Frequency Control (LFC) of multi-area power system. Initially a two-area non-reheat thermal system is considered and the optimum gains of the fuzzy PI/PID controller are optimized employing a hybrid DE and PS (hDEPS) optimization technique. The superiority of the proposed controller is demonstrated by comparing the results with some recently published modern heuristic optimization techniques such as DE, Bacteria Foraging Optimization Algorithm (BFOA), Genetic Algorithm (GA) and conventional Ziegler Nichols (ZN) based PI controllers for the same interconnected power system. Furthermore, robustness analysis is performed by varying the system parameters and operating load conditions from their nominal values. It is observed that the optimum gains of the proposed controller need not be reset even if the system is subjected to wide variation in loading condition and system parameters. Additionally, the proposed approach is further extended to multi-area multi-source power system with/without HVDC link and the gains of fuzzy PID controllers are optimized using hDEPS algorithm. The superiority of the proposed approach is shown by comparing the results with recently published DE optimized PID controller and conventional optimal output feedback controller for the same power systems. Finally, Reheat turbine, Generation Rate Constraint (GRC) and time delay are included in the system model to demonstrate the ability of the proposed approach to handle nonlinearity and physical constraints in the system model.     

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.     

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.     

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.     

Neural Networks Based PID Control of Bidirectional Inductive Power Transfer System

Inductive power transfer (IPT) systems facilitate contactless power transfer between two sides and across an air-gap, through weak magnetic coupling. However, IPT systems constitute a high order resonant circuit and, as such, are difficult to design and control. Aiming at the control problems for bidirectional IPT system, a neural networks based proportional-integral-derivative (PID) control strategy is proposed in this paper. In the proposed neural PID method, the PID gains, \(K_{P}\), \(K_{I}\) and \(K_{D}\) are treated as Gaussian potential function networks (GPFN) weights and they are adjusted using online learning algorithm. In this manner, the neural PID controller has more flexibility and capability than conventional PID controller with fixed gains. The convergence of the GPFN weights learning is guaranteed using Lyapunov method. Simulations are used to test the effective performance of the proposed controller.     

模糊控制器的实时精确算法与优化设计

将T-S型模糊控制器与PID控制器相结合,提出了TS-PID模糊控制器模型。推导出了输入采用正规模糊集、三角形全交迭隶属度函数的典型TS-PID模糊控制器的插值解析表达式,揭示了TS-PID模糊控制器本质上是一种非线性PID控制器,为实际应用提供了一种快速精确的控制算法。基于该插值表达式,进一步探讨了利用遗传算法对TS-PID模糊控制器进行优化设计的方法。     

Nonlinear CSTR control system design using an artificial bee colony algorithm

This paper proposes a novel controller design method based on using artificial bee colony (ABC) algorithms for an unstable nonlinear continuously stirred tank reactor (CSTR) chemical system. Such CSTR process is highly nonlinear and its dynamic is significantly dominated by system parameters. It is a good challenge to access the controller design performance when the controller is applied in the CSTR control system. The commonly used proportional–integral-derivative (PID) controller is taken into account in this study, and tuning three PID control gains is carried out by the artificial bee colony algorithm. With the use of the optimal ABC algorithm, PID controller gains can be derived suitably by means of minimizing the cost function given in advance. Finally, several control operations are provided to confirm the feasibility and effectiveness of the proposed method. We also discuss the influence of algorithm initial conditions on the control performance with many different tests.     

深度确定性策略梯度与模糊PID的协同温度控制

针对现有温度控制系统控温时间长、误差大的问题, 本文提出了一种基于深度确定性策略梯度(DDPG)和模糊自整定PID的协同温度控制. 首先, 模糊PID在控制大滞后系统时, 控制器不能立刻对产生的干扰起抑制作用, 且无法保证大滞后系统的稳定性等问题, 本文建立了模糊PID和DDPG算法相结合的温度控制模型, 该模型将模糊PID作为主控制器, DDPG算法作为辅助控制, 利用双控制器模型实现温度协同控制. 接着, 利用遗传算法对模糊PID的隶属函数和模糊规则进行寻优, 获得模型参数最优解. 最后, 在仿真实验中验证所提方法的有效性. 仿真实验结果表明, 本文提出的算法可有效减少噪声干扰, 减小控制系统的响应时间、误差和超调量.     

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.     

基于X-Y定位平台的力/位置混合控制

在确定了X-Y定位平台系统数学模型的基础上,提出了一种力/位置混合控制方法。在位置控制部分,采用了基于重复控制补偿的PID控制方法。用重复控制作为误差补偿与传统简单的PID控制器相结合作为位置控制部分所采用的控制算法。在力控制回路中采用一种自适应模糊控制方法。通过引入一个切换函数来确定控制律形式,根据所设计的模糊规则对变量进行模糊化,通过解模糊得到控制律结果,自适应律是通过调制饱和度得到的。仿真结果表明,该控制方法能使系统的自适应能力和鲁棒性均有显著改善。     

模糊自整定PID温度控制系统的建模与仿真

针对炒茶机的加热控制系统跟踪设定的温度值滞后、自动调节加热装置实时性差的问题,设计一种模糊自整定比例积分微分(PID)参数控制器。采用PID控制和模糊控制算法相结合的方法,实现模糊控制对PID参数的调整。利用Matlab在Simulink中建立模型,并对该控制器进行仿真分析。结果表明,模糊PID自整定控制器的超调量 ≈1%,稳态误差es=0。该方法可提高温度控制系统的性能。     

On rule self-generating for fuzzy control

It has been proved that fuzzy control is a powerful tool to control a complicated system. But, sometimes it has still suffered from collecting fuzzy control rules which is its critical part. In this article, inspired by the control strategy of the conventional PID control, we propose a rule self-generating method for fuzzy control. With the help of the proposed self-generating algorithm, we can obtain the fuzzy rules for a fuzzy controller easily. the numerical results confirm the effectivity of the designed algorithm compared with PID controller and a common Fuzzy Controller whose rules are derived from the experts' experience and knowledge by use of a practical temperature process. © 1994 John Wiley & Sons, Inc.     

自适应模糊PID控制器在跟踪器瞄准线稳定系统中的应用

针对陀螺惯性平台上的跟踪器瞄准线稳定系统中非线性不确定因素对稳定精度的影响, 设计了一种自适应模糊PID复合控制策略. 提出了改进的自适应调整因子和学习算法进行控制参数和规则的在线修正; 采用PID控制克服模糊控制固有的精度盲区. 实验结果表明该方法在一定测量噪声和速度敏感范围内, 能有效地隔离载体扰动,保证跟踪器对目标的准确瞄准, 具有动态响应快、稳定精度高、自适应抗干扰鲁棒性强等特点.     

Optimum Design of Fractional Order Pid Controller Using Chaotic Firefly Algorithms for a Control CSTR System

A fractional‐order PID controller is a generalization of a standard PID controller using fractional calculus. Compared with the standard PID controller, two adjustable variables, “differential order” and “integral order”, are added to the PID controller. Fractional‐order PID is more flexible, has better responses, and the precise adjustment closed‐loop system stability region is larger than that of a classic PID controller. But the design and stability analysis is more complicated than for the PID controller. Therefore, the optimal setting of parameters is very important. A firefly algorithm in standard mode has only local optimization and accuracy is low. In order to fix this flaw an improved chaotic algorithm firefly is proposed for a design controller FOPID. To evaluate the performance of the proposed controller, it has been used in the control of a CSTR system with a variety of fitness functions. Simulations confirm the optimal performance of the proposed controller.     

Swing-Up Control of the Pendubot: An Impulse–Momentum Approach

The standard control problem of the pendubot refers to the task of stabilizing its equilibrium configuration with the highest potential energy. Linearization of the dynamics of the pendubot about this equilibrium results in a completely controllable system and allows a linear controller to be designed for local asymptotic stability. For the underactuated pendubot, the important task is, therefore, to design a controller that will swing up both links and bring the configuration variables of the system within the region of attraction of the desired equilibrium. This paper provides a new method for swing-up control based on a series of rest-to-rest maneuvers of the first link about its vertically upright configuration. The rest-to-rest maneuvers are designed such that each maneuver results in a net gain in energy of the second link. This results in swing-up of the second link and the pendubot configuration reaching the region of attraction of the desired equilibrium. A four-step algorithm is provided for swing-up control followed by stabilization. Simulation results are presented to demonstrate the efficacy of the approach.      

一种新型自适应复合控制器在锂电池充电系统中的应用

为了解决锂电池充电系统的不确定性和参数整定困难的问题,本文提出了一种基于蚁群算法优化的模糊＋变论域模糊PID复合控制器的新方法。该控制器在系统波动频繁时,采用模糊控制使其具有最优的动态性能;当系统进入稳定阶段,采用PID参数自适应的变论域模糊控制以提高准确度。而用蚁群算法对PID参数值进行离线优化,并将优化后的值作为在线调节的初值,使系统更加稳定。将提出的复合控制策略应用于锂电池充电控制系统中。仿真结果表明,该系统具有良好的抗干扰性和鲁棒性。