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.     

An adaptive fuzzy strategy for motion control of robot manipulators

This paper makes an attempt to develop a self-tuned proportional-integral-derivative (PID)-type fuzzy controller for the motion control of robot manipulators. In recent past, it has been widely believed that static fuzzy controllers can not be suitably applied for controlling manipulators with satisfaction because the robot manipulator dynamics is too complicated. Hence more complicated and sophisticated neuro-fuzzy controllers and fuzzy versions of nonlinear controllers have been more and more applied in this problem domain. The present paper attempts to look back at this widely accepted idea and tries to develop a self-tuned fuzzy controller with small incremental complexity over conventional fuzzy controllers, which can yet attain satisfactory performance. The proposed controller is successfully applied in simulation to control two-link and three-link robot manipulators.     

Study of Learning Fuzzy Controllers

This paper compares two types of learning fuzzy controllers, the self-organizing fuzzy (SOF) controller and the hybrid self-organizing fuzzy proportional–integral–derivative (SOF-PID) controller. The SOF is an extension of the rule-based fuzzy controller, with additional rule creation and rule modification mechanisms. The hybrid SOF-PID comprises the SOF as a learning supervisory controller readjusting the proportional gain of the PID controller at the actuator section, when the system is on line. The structures of the SOF controller and the hybrid SOF-PID controller are studied. The performances of the SOF controller and the hybrid SOF-PID controller are compared by applying them to a two-link non-linear revolute-joint robot arm. For the path tracking experiments, the hybrid SOF-PID controller followed the required path more closely and smoothly than the SOF controller. The results of the experiments for the SOF controller and the hybrid SOF-PID controller are also compared with those obtained with a conventional PID controller, using the same values supplied at the setpoint.     

Design of a PID optimized neural networks and PD fuzzy logic controllers for a two‐wheeled mobile robot

In this paper, two intelligent techniques for a two‐wheeled differential mobile robot are designed and presented: A smart PID optimized neural networks based controller (SNNPIDC) and a PD fuzzy logic controller (PDFLC). Basically, mobile robots are required to work and navigate under exigent circumstances where the environment is hostile, full of disturbances such as holes and stones. The robot navigation leads to an autonomous decision making to overcome an obstacle and/or to stop the engine to protect it. In fact, the actuators that drive the robot should in no way be damaged and should stop to change direction in case of insurmountable disturbances. In this context, two controllers are implemented and a comparative study is carried out to demonstrate the effectiveness of the proposed approaches. For the first one, neural networks are used to optimize the parameters of a PID controller and for the second a fuzzy inference system type Mamdani based controller is adopted. The goal is to implement control algorithms for safe robot navigation while avoiding damage to the motors. In these two control cases, the smart robot has to quickly perform tasks and adapt to changing environment conditions while ensuring stability and accuracy and must be autonomous with regards to decision making. Simulations results aren't done in real environments, but are obtained with the Matlab/Simulink environment in which holes and stones are modeled by different load torques and are applied as disturbances on the mobile robot environment. These simulation results and the robot performances are satisfactory and are compared to a PID controller in which parameters are tuned by the Ziegler–Nichols tuning method. The applied methods have proven to be highly robust.     

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.     

Polynomial family of PD-type controllers for robot manipulators

This paper addresses the problem of position control for robot manipulators. A new polynomial family of PD-type controllers with gravity compensation for the global position of robots manipulators is presented. The previous results on the linear PD controller are extended to the proposed polynomial family. The classical PD controller can be found among this large class of controllers when its proportional gain is a diagonal matrix. The main contribution of this paper is to prove that the closed-loop system composed by full nonlinear robot dynamics and the proposed family of controllers is globally asymptotically stable in agreement with Lyapunov's direct method and LaSalle's invariance principle. Besides the theoretical results, a real-time experimental comparison is also presented to illustrate the performance of the proposed family with other well-known control algorithms such as PD and PID schemes on a three degrees of freedom direct-drive arm.     

A Markov Game-Adaptive Fuzzy Controller for Robot Manipulators

This paper develops an adaptive fuzzy controller for robot manipulators using a Markov game formulation. The Markov game framework offers a promising platform for robust control of robot manipulators in the presence of bounded external disturbances and unknown parameter variations. We propose fuzzy Markov games as an adaptation of fuzzy Q-learning (FQL) to a continuous-action variation of Markov games, wherein the reinforcement signal is used to tune online the conclusion part of a fuzzy Markov game controller. The proposed Markov game-adaptive fuzzy controller uses a simple fuzzy inference system (FIS), is computationally efficient, generates a swift control, and requires no exact dynamics of the robot system. To illustrate the superiority of Markov game-adaptive fuzzy control, we compare the performance of the controller against a) the Markov game-based robust neural controller, b) the reinforcement learning (RL)-adaptive fuzzy controller, c) the FQL controller, d) the H_infin theory-based robust neural game controller, and e) a standard RL-based robust neural controller, on two highly nonlinear robot arm control problems of i) a standard two-link rigid robot arm and ii) a 2-DOF SCARA robot manipulator. The proposed Markov game-adaptive fuzzy controller outperformed other controllers in terms of tracking errors and control torque requirements, over different desired trajectories. The results also demonstrate the viability of FISs for accelerating learning in Markov games and extending Markov game-based control to continuous state-action space problems.     

Adaptive intelligent cascade control of a ball-riding robot for optimal balancing and station-keeping

This paper presents an adaptive intelligent cascade control strategy to maintain the dynamic stability of a ball-riding robot (BRR). The four-wheeled mechanism beneath the robot body balances it on a spherical wheel. The BRR is modeled as a combination of two decoupled inverted pendulums. Therefore, two independent controllers are used to control its pitch and roll rotations. An incremental proportional–integral–derivative (PID) is implemented in the inner loop of the cascade to maintain the vertical balance. A generic PD controller is used in the outer loop to keep the station by controlling its spatial position. The controller parameters are automatically tuned via a fuzzy adaptation mechanism. The centers of fuzzy output membership functions are dynamically updated via an extended Kalman filter (EKF). The proposed controller quickly responds to changes in system’s state and effectively rejects the exogenous disturbances. The results of real-time experiments are presented to validate the effectiveness of the proposed hybrid controller over the conventional classical controllers.     

重介选煤工艺多参数模糊控制方法研究

针对重介选煤工艺过程中悬浮液密度、磁性物含量以及液位三个参数相互耦合,采用人工或PID调节方式效果不理想的问题,通过分析重介选煤工艺过程,提出了一种重介选煤工艺多参数模糊控制方法。该方法采用两个模糊控制器分别控制液位和悬浮液密度,对两个模糊控制器的输出去模糊化后结合煤泥含量计算出分流量与补水量,进而控制分流箱阀门和清水阀的开度。工业试验结果表明,与传统PID控制方法相比,该控制方法的稳定性更高,响应速度更快,超调量更小。     

模糊PID控制下移动机器人定位方法研究

机器人定位研究一直是机器人学研究的重点,但目前机器人定位方法都存在缺点,抗干扰能力差,不能做到准确定位,主要是由于环境等多方面因素的干扰,定位误差会逐渐加大;由于上述原因,提出了一种基于设定值加权模糊PID控制的移动机器人自定位方法;给出了定位过程的参数,为机器人移动建立模型,设计一种模糊 PID 控制器,根据误差及变化率大小,选择模糊定位或PID定位,实现移动机器人的智能定位,提高机器人定位准确的准确性;通过仿真实验结果证明:模糊PID控制的机器人自定位方法对移动机器人的定位过程有较好的改善作用,实用效果较好。     

Fuzzy control-based real-time robust balance for a humanoid robot

This paper studies and implements a real-time robust balance control for a humanoid robot under three environment disturbances which are an external thrust, an inclinable platform, and a see-saw. More precisely to say, the robot with robust control can resist an external thrust, stand on a two-axis inclinable platform, or walk on a see-saw successfully. The main feature of the robot is that it has a waist joint which has three degrees of freedom. With the aids of the proposed fuzzy controllers, the robot can change the posture of the body nimbly by adjusting the waist joint and two ankle joints to strengthen the stabilization capacity. The sensory system of the robot includes eight force sensors and one inertial measurement unit sensor in order to measure the center of pressure and the slant angle of the robot’s body. According to the measured data from the sensors and by imitating human reflex actions, the proposed fuzzy controllers perform real-time balance control for the robot under three environment disturbances. According to the experiment results, the stability of the robot is increased at least 32.2 and 61.7% under the first two environment disturbances, respectively. In addition, the robot walking on a see-saw has a success rate of about 95%.     

自平衡两轮机器人的分层模糊控制

为解决具有非线性、强耦合和绝对不稳定特点的自平衡两轮机器人的运动控制问题,提出一种分层模糊控制方法.该方法对机器人体的倾斜角度和轮子转动速度分别设计相应的模糊控制器,其输出同时进入决策器,由决策器进行智能判断与协调,输出控制量.两控制器交替工作,实现机器人体倾角控制和轮子转速控制的有机统一.该方法具有模糊规则少,控制逻辑简单的特点.对机器人的速度跟踪、运动停止及转弯等多种运动方式进行了控制仿真实验,验证了控制方法的正确性和有效性.     

The simplest fuzzy PID controllers: mathematical models and stability analysis

This paper reveals mathematical models for the simplest fuzzy PID controllers which employ two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. Mathematical models are derived via left and right trapezoidal membership functions for each input, singleton or triangular membership functions for output, algebraic product triangular norm, different combinations of triangular co-norms and inference methods, and center of sums (COS) defuzzification method. Properties of these structures are studied to examine their suitability for control application. For the structure which is suitable for control, bounded-input bounded-output (BIBO) stability proof is presented. An approach to design fuzzy PID controllers is given. Finally, some numerical examples along with their simulation results are included to demonstrate the effectiveness of the simplest fuzzy PID controllers.     

一种新型的二维PID模糊控制器

通过对常规PID控制器的结构分析,设计出一种新型的二维PID模糊控制器,其结构形式简称为fuzzy PD+ fuzzy ID型.根据模糊规则的图解分析,提出fuzzy ID控制嚣的输入变量(偏差和偏差变化加速率)与输出变量之间的控制结构,并确定两控制器的模糊控制规则的相似性.通过对该PID模糊控制器的结构分析,给出与常...     

PD and PID model-based control stability analysis of the PUMA-560 robot manipulator under model mismatch

The stability of the PUMA-560 robot manipulator is investigated under model mismatch using PD and PID controllers. Craig's quadratic half-plane constraint analysis is applied, and conditions are found in terms of calculated position and velocity error upper bounds to guarantee the stability of the robot arm under PD control. The theory is extended to guarantee stability under PID control using the modified positive quadratic space constraint analysis. Dynamic model mismatch is assumed to result from incomplete knowledge of the link masses, centers of mass and radii of gyration. The results indicate stability regions under different percentages of individual and combined parameter mismatch in the model.     

T-S 模糊模型变结构的机器臂轨迹跟踪控制

针对不确定性的机械臂轨迹跟踪问题,结合滑模变结构和T-S模糊模型的优点,给出一种基于T-S模糊模型的变结构轨迹跟踪的方法。首先采用T-S模型建模,得到机械臂的模糊模型;然后设计出保证机械臂全局渐近稳定的滑模控制器。仿真结果表明,所设计的模糊变结构控制器与普通变结构控制器相比,可使机械臂无论在计算时间、误差上都具有更大的优势和更强的鲁棒性。     

基于Fuzzy-PID的移动机器人运动控制

移动机器人涉及到许多研究方向,运动控制是其中的基础。通过对移动机器人运动学模型进行分析,以足球机器人系统为实验平台,论证了Fuzzy-PID技术应用于移动机器人运动控制的可行性。将传统的PID控制与模糊控制相结合,通过PID控制实现控制的准确性,利用模糊控制提高控制的快速性。针对移动机器人运动控制中的实际问题,着重提出了基于误差分区的PID控制器和模糊控制器的设计方法。实验证明该方法不仅增强了控制器的调节能力,还在一定程度上简化了控制器的设计。     

基于变增益模糊PID控制的移动机器人轨迹跟踪

该文对轮式移动机器人提出了一种基于变增益的模糊PID轨迹跟踪控制方法。首先将常规PID分为PI和PD的组合,再把PID的输出转化为误差和误差变化率之和,然后设计增益随误差变化的自适应调节律,使得移动机器人跟踪期望的运动轨迹。最后通过实验验证了所提方法的有效性。     

基于视觉伺服控制的光伏板清洗系统设计

光伏板上的鸟粪、枯叶等污渍若不及时清理会导致光伏板热斑现象的发生,严重影响光伏板的使用寿命和安全。现有光伏板清理方法存在清洗效果不好、浪费水资源、清洗效率低等问题,为此,及时清理维护光伏板成为光伏发电企业亟待解决的首要问题。基于以上问题,该文提出光伏板清洗视觉伺服控制系统和一种改进型模糊PID控制算法,利用从实时视频图像中提取的反馈信息控制机械臂对准污渍点,实现定点喷射清洗污渍点,达到节水高效的目的。实验结果表明,基于改进型模糊PID控制算法的光伏板清洗视觉伺服控制系统能够准确地定位到光伏板污渍位置并精准喷射清洗污渍,最大限度地节约水资源。     

Adaptive hierarchical tuning of fuzzy controllers

Fuzzy controller design includes both linear and non-linear dynamic analysis. The knowledge base parameters associated within the fuzzy rule base influence the non-linear control dynamics while the linear parameters associated within the fuzzy output signal influence the overall control dynamics. For distinct identification of tuning levels, an equivalent linear controller output and a normalized non-linear controller output are defined. A linear proportional-integral-derivative (PID) controller analogy is used for determining the linear tuning parameters. Non-linear tuning is derived from the locally defined control properties in the non-linear fuzzy output. The non-linearity in the fuzzy output is then represented in a graphical form for achieving the necessary non-linear tuning. Three different tuning strategies are evaluated. The first strategy uses a genetic algorithm to simultaneously tune both linear and non-linear parameters. In the second strategy the non-linear parameters are initially selected on the basis of some desired non-linear control characteristics and the linear tuning is then performed using a trial and error approach. In the third method the linear tuning is initially performed off-line using an existing linear PID law and an adaptive non-linear tuning is then performed online in a hierarchical fashion. The control performance of each design is compared against its corresponding linear PID system. The controllers based on the first two design methods show superior performance when they are implemented on the estimated process system. However, in the presence of process uncertainties and external disturbances these controllers fail to perform any better than linear controllers. In the hierarchical control architecture, the non-linear fuzzy control method adapts to process uncertainties and disturbances to produce superior performance.