一维模糊PID控制器的钝性稳定性分析

本文研究新近提出的模糊PID控制器的稳定性问题．由于该模糊PID控制器的模 糊推理部分具有非线性特性，因此本文采用钝性定理来分析它的稳定性．本文给出分析稳定 性的方法，并针对一阶和二阶对象的一般形式，给出了保证系统稳定的参数范围,用仿真验 证了所得结果．高阶对象也可以使用圆判据求取相应结果．     

一类非线性PID控制系统稳定性分析

针对一类由非线性增益函数与典型PID控制器级联组成的非线性系统，采用波波夫判断对此类闭环控制系统进行稳定性分析，分别确定了确保非线性PID，P，PI，PD闭环控制系统稳定的非线性增益的有效取值范围，为此类此线性控制系统的实际工程应用奠定了基础。     

连续状态模糊控制系统的分区域稳定性分析

给出简化的连续状态下模糊控制系统解的表达形式,并给出简化模糊系统稳定的充分和必要条件,统一了目前有关判定连续状态模糊控制系统的稳定性结论。此外,给出一种寻求稳定模糊控制的方法,即基于梯度的控制器设计方法。     

模糊PID控制器

本文介绍一种新的模糊PID控制的设计和参数整定方法。运行结果表明，在控制非线性和时变对象时，其控制效果优于数字PID控制器。     

一种PID模糊控制器

在传统的PID控制器基础上,本文提出一种基于PID模糊控制的混合型控制算法,旨在能同时兼顾系统的稳态精度和动态响应速度。仿真结果表明,性能更优。     

基地模糊预测的间歇PID控制器

将模糊预测和间歇ＰＩＤ控制器相结合，提出了变控制周期控制器，根据对被调时未来偏差和偏差变化率的模糊预测，合适地造反间歇ＰＩＤ控制器的控制周期，有利于改善具有纯时滞对象控制系统的动态品质，最后由仿真结果说明了该方法的有效性。     

PID控制器的模糊增益调整及在电阻炉温控制系统中的应用

介绍一种带有模糊增益调整的PID控制器，开发了一套软件，并分别将它和传统的PID控制器作用到电阻炉，对二者的控制结果进行了比较。实验结果表明，这种PID控制器能够减小超调，提高控制精度。     

非线性模糊间接和直接自适应控制器的设计和稳定性分析

提出卫种非线性模糊直接和间接自适应控制的统一设计方法,该方法把文献「１,２」中的监督控制器用Ｄ－控制来取代,在闭环系统的渐近稳定性分析中取消了要求逼近误差平方可积的条件,模糊控制器能克服外界干扰对系统误差的影响。仿真结果验证了该控制方案的有效性。     

模糊PID控制算法及其在激光陀螺稳频控制中的应用

在分析环形激光陀螺光强控制系统原理的基础上,针对自行研制的激光陀螺（RLG）计算机稳频控制系统,研究了Fuzzy-PID与常规PID控制算法。介绍了一种应用模糊推理功能实现PID参数知整定的控制器,它是在常规PID调节器的基础上,采用模糊推理思想,根据不同的E和EC,对PID参数KP、KI、KD进行在线自整定的模糊控制器。仿真结果表明：系统的动静态性能都符合指标,该算法是实现激光光强控制进而完成激光频率控制较理想的控制算法。     

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.     

一类模糊P I D 控制器的鲁棒优化设计

研究一类模糊 PID控制器的鲁棒设计。以小增益定理分析得到该模糊 PID控制系统稳定性条件。针对参数摄动系统的“最坏点”,用该稳定性条件作为约束 ,采用遗传算法对标称系统的性能进行优化 ,求得优化鲁棒控制器。以倒立摆为例进行鲁棒模糊 PID控制器的设计 ,实验结果表明了该方法的有效性     

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.     

T-S模糊系统输出反馈控制器的稳定性分析与设计

输出反馈控制是T-S模糊控制系统设计的一种重要方法．本文提出了一类由模糊状态观测器和模糊调节器构成的输出反馈控制器稳定性分析和解析设计的新方法．为了减小稳定性分析的保守性和难度,本文充分利用了模糊规则前件变量模糊隶属度函数的结构信息,对前件变量采用标准模糊分划的T-S模糊系统输出反馈控制器进行了研究,获得了一些新的稳定性条件．然后采用平行分布补偿法(PDC)和线性矩阵不等式方法(LMI),研究了该类输出反馈控制器的解析设计方法．通过一个非线性质量块-弹簧-阻尼器系统输出反馈控制器的设计和计算机仿真,验证了本文方法的有效性．     

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.     

Stability of fuzzy PID controllers

In this paper, the stability of fuzzy PID controllers is studied. Using the passivity theorem, the stability region of the effective PID parameters can be derived and hence some sufficient conditions for a stable fuzzy controller can be obtained. With these conditions satisfied, a stable set of fuzzy rules can be designed easily     

一种PID模糊控制器(fuzzy PI+fuzzy ID型)

提出一种二维PID模糊控制器,其结构形式筒称为fuzzy PI+fuzzy ID型.根据fuzzy PI和fuzzy ID控制器的图解说明,确定该fuzzy PI和fuzzy ID控制器的模糊控制规则的相似性.理论分析表明,该PID模糊控制器除具有常规PID性能外,还具有非线性等特点.仿真结果表明,与常规PID和fuzzy PI控制相比性能更优.     

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.     

The simplest fuzzy controllers using different inference methods are different nonlinear proportional-integral controllers with variable gains

The author analytically proves that the simplest fuzzy controllers using different inference methods are different nonlinear proportional-integral (PI) controllers with proportional-gains and integral-gains changing with inputs of the controllers. The inference methods involved are Mamdani's minimum inference method, Larsen's product inference method, the drastic product inference method and the bounded product inference method. Configuration of the fuzzy controllers is minimal, which includes two input fuzzy sets, three output fuzzy sets, four control rules, Zadeh fuzzy logic AND, Lukasiewicz fuzzy logic OR and a center of gravity defuzzification algorithm. After analytically investigating properties of the nonlinear PI controllers, the author reveals that the bounded product inference method is inappropriate for the control purpose while the other three inference methods are appropriate. Dynamic and static control behaviors of the fuzzy controllers with the appropriate inference methods are analytically compared with each other, and are also compared with those of the linear PI controller. Finally, it is analytically proven that the fuzzy control systems have the same local stability at the equilibrium point as the corresponding linear PI control system does.