Mathematical models of the simplest fuzzy PI/PD controllers with skewed input and output fuzzy sets

This paper unveils mathematical models for fuzzy PI/PD controllers which employ two skewed fuzzy sets for each of the two-input variables and three skewed fuzzy sets for the output variable. The basic constituents of these models are Gamma-type and L-type membership functions for each input, trapezoidal/triangular membership functions for output, intersection/algebraic product triangular norm, maximum/drastic sum triangular conorm, Mamdani minimum/Larsen product/drastic product inference method, and center of sums defuzzification method. The existing simplest fuzzy PI/PD controller structures derived via symmetrical fuzzy sets become special cases of the mathematical models revealed in this paper. Finally, a numerical example along with its simulation results are included to demonstrate the effectiveness of the simplest fuzzy PI controllers.     

Modeling,stability analysis,and computational aspects of some simplest nonlinear fuzzy two-term controllers derived via center of area/gravity defuzzification

The mathematical models reported in the literature so far have been found using Center of Sums (CoS) defuzzification method only. It appears that no one has found models using Center of Area (CoA) or Center of Gravity (CoG) defuzzification method. Although there have been some works reported to deal with modeling of fuzzy controllers via Centroid method, all of them have in fact used CoS method only. In this paper, for the first time mathematical models of the simplest Mamdani type fuzzy Proportional Integral (PI)/Proportional Derivative (PD) controllers via CoG defuzzification are presented. L-type and Γ-type membership functions over different Universes of Discourse (UoDs) are considered for the input variables. L-type, Π-type and Γ-type membership functions are considered for the output variable. Three linear fuzzy control rules relating all four input fuzzy sets to three output fuzzy sets are chosen. Two triangular norms namely Algebraic Product (AP) and Minimum (Min), Maximum (Max) triangular co-norm, and two inference methods, Larsen Product (LP) and Mamdani Minimum (MM), are used. Properties of the models are studied. Stability analysis of closed-loop systems containing one of these controller models in the loop is done using the Small Gain theorem. Since digital controllers are implemented using digital processors, computational and memory requirements of these fuzzy controllers and conventional (nonfuzzy) controllers are compared. A rough estimate of the computational time taken by the digital computer while implementing any of these discrete-time fuzzy controllers is given. Two nonlinear plants are considered to show the superiority of the simplest fuzzy controller obtained using CoA or CoG defuzzification method over the simplest fuzzy controller obtained using CoS method and reported recently. Real-time implementation of one of the developed controller models is done on coupled tank experimental setup to show the feasibility of the developed model.     

A new self-tuned PID-type fuzzy controller as a combination of two-term controllers

The present paper is a venture into the domain of proportional-integral-derivative (PID) -type adaptive fuzzy logic controllers (FLC's) and proposes a new algorithm which is realized by a self-tuned PI-type FLC (in velocity form) in parallel with a self-tuned PD-type FLC (in position form). Each of these PI/PD controllers implements a supervisory static FLC for adaptive online modification of the output scaling factor (SF) of a static PI/PD FLC. The proposed scheme is developed with a view to having a PID-type FLC with an architecture, simple enough for practical implementation, which at the same time has substantially satisfactory performance for a wide class of processes. Simulation studies on a range of processes reveal that the proposed controller has better performance compared to many of its existing counterparts.     

基于模糊推理原理的多传感器数据融合方法

利用模糊推理方法融合具有不确定性的多传感器数据 ,将传感器的测量值作为模糊系统的输入 ,要计算的结果是模糊系统的输出 ,利用三角形隶属函数表示测量的不确定性 ,在输入变量所确定的区间内 ,不断改变输出变量的位置 ,计算输出与输入的兼容度 ,则兼容度最大的位置 ,就是最后要得到的结果。给出了一个多个传感器数据融合的计算实例 ,验证了本方法的有效性     

烧结混合料加水的模糊自适应分数阶PI~λD~u控制

烧结混合料加水系统具有大滞后、模型复杂的特性,且客观环境中存在干扰因素,传统的控制方法很难取得理想的控制效果。分数阶PIλDu控制器比常规PID控制器多了两个可调参数,具有更好的控制效果。在分析分数阶微积分的基础上,给出了分数阶微积分的数字实现,用分数阶PIλDu控制代替常规PID控制,结合模糊控制,首次提出了一种针对烧结混合料加水系统的模糊自适应分数阶PIλDu控制方法,利用模糊逻辑实现分数阶PIλDu控制参数的在线调整。并用MATLAB/simulink进行建模仿真。仿真结果验证该控制算法的有效性,能取得较好的控制效果。     

模糊自适应PID控制的仿真研究

首先介绍了PID控制系统的工作原理,因PID控制器结构简单、实现简单,控制效果良好,所以已得到广泛应用。但当控制对象变化时,控制器的参数难以自动调整。为了使控制器具有较好的自适应性,可以采用模糊控制理论的方法来实现控制器参数的自动调整。模糊PID控制系统就是模糊理论与传统的PID控制器的结合。最后以一控制对象为例,对该两种方式的控制进行了仿真和比较,并得出了相应的结论。     

模糊可靠度计算模型

将模糊集合论应用于可靠性设计,建立了戒上型、戒下型及对称型隶属函数与不同概率密度函数相遇时的模糊可靠度计算模型,为模糊可靠性的设计计算提供了理论依据和便利。最后,对公式作了简要的说明,并给出了使用示例。     

模糊规则调整微分作用的PID控制方法

PID控制器广泛应用于工业过程控制中 ,但对于非线性、时变不确定性的系统 ,常规 PID控制器难以获得满意效果。随着模糊控制理论的不断发展 ,利用其非线性特征 ,将其与 PID控制相结合 ,能有效改善 PID控制效果。设定值权系数的模糊逻辑整定 PID控制器 (FSW)方法在固定设定值权系数的基础上 ,用模糊推理方式计算“动态”的权系数 ,取得了一定的效果 ,但是仍存在一些问题。针对阶跃响应的上升及调整时间长、第一次超调后的反向振幅较大的缺点 ,采用模糊逻辑规则调整微分作用的改进方法 ,可以弥补上述不足。对一些典型对象进行仿真 ,结果表明该方法明显优于 Z- N方法 ,固定设定值权系数 b方法和 FSW方法     

PID参数的模糊整定器研究

提出了一种基于模式识别的PID参数模糊自整定方法。其中,PID参数模糊整定规则知识库是由专家经验和整定知识构成的。文中整定知识来自于对典型过程的参数整定经验。仿真结果证明了该方法的有效性。     

An analytical method for PID controller tuning with specified gain and phase margins for integral plus time delay processes

In this paper, an analytical method is proposed for proportional-integral/proportional-derivative/proportional-integral-derivative (PI/PD/PID) controller tuning with specified gain and phase margins (GPMs) for integral plus time delay (IPTD) processes. Explicit formulas are also obtained for estimating the GPMs resulting from given PI/PD/PID controllers. The proposed method indicates a general form of the PID parameters and unifies a large number of existing rules as PI/PD/PID controller tuning with various GPM specifications. The GPMs realized by existing PID tuning rules are computed and documented as a reference for control engineers to tune the PID controllers.     

Design of a fractional order PID controller using GBMO algorithm for load–frequency control with governor saturation consideration

Load–frequency control is one of the most important issues in power system operation. In this paper, a Fractional Order PID (FOPID) controller based on Gases Brownian Motion Optimization (GBMO) is used in order to mitigate frequency and exchanged power deviation in two-area power system with considering governor saturation limit. In a FOPID controller derivative and integrator parts have non-integer orders which should be determined by designer. FOPID controller has more flexibility than PID controller. The GBMO algorithm is a recently introduced search method that has suitable accuracy and convergence rate. Thus, this paper uses the advantages of FOPID controller as well as GBMO algorithm to solve load–frequency control. However, computational load will higher than conventional controllers due to more complexity of design procedure. Also, a GBMO based fuzzy controller is designed and analyzed in detail. The performance of the proposed controller in time domain and its robustness are verified according to comparison with other controllers like GBMO based fuzzy controller and PI controller that used for load–frequency control system in confronting with model parameters variations.     

Model Based Tuning of Controller for Non‐Linear Hemispherical Tank Processes

Abstract

A non linear liquid level process represented by a 5 liter hemispherical tank was subjected to dynamic analysis using a step response technique. The data fitted a first order plus dead time model with an error of less than 3 percent. The level was measured using an on‐line Honeywell capacitance sensor. From the model parameters, PI and fuzzy tuned PI controllers were designed using MATLAB. The closed loop performance was studied for both the servo and regulator problems. Based on the overshoot, rise time, settling time, and ISE, it is found that the Fuzzy tuned PI controller is better suited for this process.     

Adaptive PI controller to voltage regulation in power systems: STATCOM as a case study

Static synchronous compensator (STATCOM) provides the means to improve quality and reliability of a power system as it has the functional capability to handle dynamic disturbances, such as transient stability and power oscillation damping as well as to providing voltage regulation. In this paper, a robust adaptive PI-based optimal fuzzy control strategy is proposed to control a STATCOM used in distribution systems. The proposed intelligent strategy is based on a combination of a new General Type-II Fuzzy Logic (GT2FL) with a simple heuristic algorithm named Teaching Learning Based Optimization (TLBO) Algorithm. The proposed framework optimally tunes parameters of a Proportional-Integral (PI) controller which, similar to most of other researchers regarding control of STATCOM, are in charge of controlling the device. The proposed controller guaranties robustness and stability against uncertainties caused by external disturbances or ever-changing nature of the power systems. The TLBO optimizes the parameters of the controller as well as the input and output membership functions. To validate the efficiency of the proposed controller, the obtained simulation results are compared with those of the two most recent researches applied in this field, namely, conventional Proportional Integral (PI) controller and Optimal Fuzzy PI (OFPI) controller. Results demonstrate the successfulness and effectiveness of the proposed online-TLBO General Type-2 Fuzzy PI (OGT2FPI) controller and its superiority over conventional approaches.     

随机应力模糊强度时模糊可靠性的计算理论

由于常规可靠性理论基本假设的局限性,对于具有模糊性的各种系统和问题,用常规可靠性理论和方法对其进行描述是非常困难的,甚至是不可能的,在一些问题上由于不恰当地使用常规可靠性理论,而使计算结果和实际完全不一致的情况时有发生,要解决这些问题,必须借助新的工具,建立新的可靠性概念和方法,以摆脱目前物困难,为此,模糊数学不可避免地进入可靠性领域,而可靠性理论研究不中避免地发展到一个新阶段-模糊可靠性理论的创立,本文研究了以模糊强度表示模糊安全状态时模糊可靠度的计算问题,模糊安全事件的隶属函数由模糊强度的隶属函数直接构造,克服了现有文献中模糊安全事件的隶属函数为不连续函数这一缺陷。     

数字PID控制方程的参数在线Fuzzy自校正方法研究

运用Ｆｕｚｚｙ集合理论，对ＰＩＤ调节器的３个参数进行在线自动校正，以实现对一类不确定系统的控制。本文试图建立ＰＩＤ参数Ｆｕｚｚｙ规则模型并对Ｆｕｚｚｙ校正方法进行研究探讨。     

PID参数模糊自适应控制器的设计

本文提出一种基于FUZZY推理的PID控制器，经利用FUZZY推理，对系统所处的不同状态实现POID参数的在线自适应控制，使系统在任何状态下，都能得到比传统PID更好的控制效果和更强的鲁棒性，住、仿真结果也证明了这一点。     

An improved auto-tuning scheme for PI controllers

Ziegler-Nichols tuned PI and PID controllers are usually found to provide poor performances for high-order and nonlinear systems. In this study, an improved auto-tuning scheme is presented for Ziegler-Nichols tuned PI controllers (ZNPICs). With a view to improving the transient response, the proportional and integral gains of the proposed controller are continuously modified based on the current process trend. The proposed controller is tested for a number of high-order linear and nonlinear dead-time processes under both set-point change and load disturbance. It exhibits significantly improved performance compared to ZNPIC, and Refined Ziegler-Nichols tuned PI controller (RZNPIC). Robustness of the proposed scheme is established by varying the controller parameters as well as the dead-time of the process under control.     

基于模糊综合评判的部件失效区域的确定

应用模糊方法评估部件振动可靠性时,需构建部件振动的模糊共振区域及相应的隶属函数和模糊强度失效区域及相应的隶属函数。针对航空发动机关键部件振动可靠性评估中影响部件模糊共振失效区域及其隶属函数、模糊强度失效区域及其隶属函数确定的众多复杂的、非确定的、时变的因素,将二级模糊综合评判方法应用于航空发动机关键部件模糊共振失效区域及其隶属函数、模糊强度失效区域及其隶属函数的确定,采用层次分析法(AHP法)确定评价指标权重,建立确定模糊共振失效区域及其隶属函数、模糊强度失效区域及其隶属函数的数学模型和流程。结果表明,该方法能够解决航空发动机关键部件模糊共振失效区域及其隶属函数、模糊强度失效区域及其隶属函数确定中一些复杂因素的处理问题。     

Design and implementation of a new fuzzy PID controller for networked control systems

This paper presents a practical network platform to design and implement a networked-based cascade control system linking a Smar Foundation Fieldbus (FF) controller (DFI-302) and a Siemens programmable logic controller (PLC-S7-315-2DP) through Industrial Ethernet to a laboratory pilot plant. In the presented network configuration, the Smar OPC tag browser and Siemens WinCC OPC Channel provide the communicating interface between the two controllers. The paper investigates the performance of a PID controller implemented in two different possible configurations of FF function block (FB) and networked control system (NCS) via a remote Siemens PLC. In the FB control system implementation, the desired set-point is provided by the Siemens Human-Machine Interface (HMI) software (i.e, WinCC) via an Ethernet Modbus link. While, in the NCS implementation, the cascade loop is realized in remote Siemens PLC station and the final element set-point is sent to the Smar FF station via Ethernet bus. A new fuzzy PID control strategy is then proposed to improve the control performances of the networked-based control systems due to an induced transmission delay degradation effect. The proposed strategy utilizes an innovative idea based on sectionalizing the error signal of the step response into three different functional zones. The supporting philosophy behind these three functional zones is to decompose the desired control objectives in terms of rising time, settling time and steady-state error measures maintained by an appropriate PID-type controller in each zone. Then, fuzzy membership factors are defined to configure the control signal on the basis of the fuzzy weighted PID outputs of all three zones. The obtained results illustrate the effectiveness of the proposed fuzzy PID control scheme in improving the performances of the implemented NCS for different transportation delays.     

Analysis,control and design of a non-inverting buck-boost converter: A bump-less two-level T–S fuzzy PI control

In this paper, a new modified fuzzy Two-Level Control Scheme (TLCS) is proposed to control a non-inverting buck-boost converter. Each level of fuzzy TLCS consists of a tuned fuzzy PI controller. In addition, a Takagi–Sugeno–Kang (TSK) fuzzy switch proposed to transfer the fuzzy PI controllers to each other in the control system. The major difficulty in designing fuzzy TLCS which degrades its performance is emerging unwanted drastic oscillations in the converter output voltage during replacing the controllers. Thereby, the fuzzy PI controllers in each level of TLCS structure are modified to eliminate these oscillations and improve the system performance. Some simulations and digital signal processor based experiments are conducted on a non-inverting buck-boost converter to support the effectiveness of the proposed TLCS in controlling the converter output voltage.