高速高精度平面并联机器人模糊自调整PID控制方法的研究

针对推力波动、负载变化等非线性因素对高速高精度平面并联机器人系统稳定时间的影响，本文设计了一种新颖的模糊自调整PID控制器：系统的位置偏差较大时，采用PI控制器，保证系统的平滑、稳定；当系统发出停止命令后，引入模糊增益参数自调整机构，加快静差消除．模糊增益参数调整机构采用“一维输入-二维输出”的推理结构，消除了参数调整中的“耦合影响”；为缩短整定时间，减少整定参数的数量，不同增益，误差E的模糊论域划分各不相同．经实验验证：引入该模糊自校正PID控制器后，机器人系统的稳定时间有显著改善．     

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     

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.     

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.     

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.     

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...     

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.     

一种解析的模糊PI自整定方法

针对模糊PID控制器缺乏系统的整定方法的问题,提出了一种解析的基于增益裕度和相位裕度的模糊PI控制器的参数自整定方法。首先推导出模糊PI控制器的解析模型,该解析模型包括线性控制器和非线性补偿控制器2个部分。参数整定时,将非线性补偿控制器看作过程的扰动,由线性控制器和被控对象的一阶纯时滞模型,基于系统的增益裕度和相位裕度,导出模糊PI控制器的参数。仿真结果表明,对于时变高阶系统,和传统的PI控制器相比,模糊PI控制器具有鲁棒性强,超调小,调整时间短等优点。     

Parallel Fuzzy P＋Fuzzy I＋Fuzzy D Controller： Design and Performance Evaluation

In this paper, a parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative (FP+FI+FD) controller is proposed. It is derived from the conventional parallel proportional-integral-derivative (PID) controller. It preserves the linear structure of a conventional parallel PID controller, with analytical formulas. The final shape of the controller is a discrete-time fuzzy version of a conventional parallel PID controller. Computer simulations are performed to evaluate the performance of the FP+FI+FD controller for setpoint tracking and load-disturbance rejection for some complex processes, such as first- and second-order processes with delay, inverse response process with and without delay and higher order processes. Also, the performance of the proposed fuzzy controller is evaluated experimentally on highly nonlinear liquid-flow process with a hysteresis characteristic due to a pneumatic control valve. The simulation and real time control is done using National Instrument hardware and software (LabVIEW). The response of the FP+FI+FD controller is compared with the conventional parallel PID controller, tuned with the Ziegler-Nichols (Z-H) and Astrom-Hagglund (A-H) tuning technique. It is observed that the FP+FI+FD controller performed much better than the conventional PI/PID controller. Simulation and experimental results demonstrate the effectiveness of the proposed parallel FP+FI+FD controller.     

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.