Evolving an interval type-2 fuzzy PID controller for the redundant robotic manipulator

Robotic manipulators are a multi-input multi-output, dynamically coupled, highly time-varying, complex and highly nonlinear systems wherein the external disturbances, parameter variations, and random noise adversely affects the performance of the robotic system. Therefore, in order to deal with such complexities, however, an intriguing task for control researchers, these systems require an efficient and robust controller. In this paper, a novel application of genetic algorithms (GA) optimization approach to optimize the scaling factors of interval type-2 fuzzy proportional derivative plus integral (IT2FPD+I) controllers is proposed for 5-DOF redundant robot manipulator for trajectory tracking task. All five controllers' parameters are optimized simultaneously. Further, a procedure for selecting appropriate initial search space is also demonstrated. In order to make a fair comparison between different controllers, the tuning of each of the controllers' parameters is done with GA. This optimization technique uses the time domain optimal tuning while minimizing the fitness function as the sum of integral of multiplication of time with square error (ITSE) for each joint. To ascertain the effectiveness of IT2FPID controller, it is compared against type-1 fuzzy PID (T1FPID) and conventional PID controllers. Furthermore, robustness testing of developed IT2FPID controller for external disturbances, parameter variations, and random noise rejection is also investigated. Finally, the experimental study leads us to claim that our proposed controller can not only assure best trajectory tracking in joint and Cartesian space, but also improves the robustness of the systems for external disturbances, parameter variations, and random noise.     

Efficient control of a 3-link planar rigid manipulator using self-regulated fractional-order fuzzy PID controller

A self-regulated fractional-order fuzzy proportional–integral–derivative (SRFOFPID) controller is proposed to control a highly non-linear, complex and coupled 3-link planar rigid robotic manipulator in a virtual industrial environment. Industrial environment was simulated by introducing different kind of disturbances in the system and sensor noise. Proposed SRFOFPID controller is a direct non-linear adaptive controller having self-regulating feature and has been realized using fractional-order operators i.e. integrator and differentiator in self-regulated integer-order fuzzy PID (SRIOFPID) controller. Gains of SRFOFPID and SRIOFPID controllers are optimized using Backtracking Search Algorithm by minimizing an amalgamation of integral absolute error signal and integral absolute change in control signal as cost function. Performance of SRFOFPID and SRIOFPID controllers are assessed and compared with reference path under virtually simulated industrial environment. Presented intensive simulation studies revealed that both the controllers offered decent reference trajectory tracking performance under nominal operating conditions while SRFOFPID controller offered exceptionally robust performance under industrial scenario and uncertainties. Finally, the stability analysis of overall closed loop system is performed using small gain theorem and necessary and sufficient bounded-input and bounded-output stability conditions are established.     

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.     

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.     

Some investigations on hybrid fuzzy IPD controllers for proportional and derivative kick suppression

Proportional and derivative kick i.e., a large change in control action of a proportional plus integral plus derivative (PID) controller due to a sudden change in reference set-point is generally undesired in process industry. Therefore, the structure of conventional parallel PID controller is modified to integral minus proportional derivative (I-PD) controller. In this paper, three hybrid fuzzy IPD controllers such as a fuzzy I-fuzzy PD (FI-FPD) controller and its hybrid combinations with its conventional counterpart such as fuzzy I-PD (FI-PD) and I-fuzzy PD (I-FPD) are presented in view of above industrial problem. These controllers are based upon the counterpart conventional I-PD controller and contains analytical formulae. Computer simulations are carried out to evaluate the performance of hybrid fuzzy controllers along with conventional I-PD and PID controllers for set-point tracking and disturbance rejection for an induction motor in closed loop using LabVIEW? environment. The gains of conventional and hybrid fuzzy controllers are tuned using genetic algorithm (GA) for minimum overshoot and settling time. It has been observed that hybrid fuzzy controllers along with the conventional I-PD controller significantly remove the kick from the control action in reference set-point tracking. However, in disturbance rejection, I-PD and FI-PD controllers fail to eliminate the kick from the control signal. In contrast, FI-FPD and I-FPD controllers considerably reduced spikes from the control action in disturbance rejection. Among the conventional and hybrid fuzzy IPD controllers, FI-FPD demonstrates much better set-point tracking and disturbance rejection response with spike free control action.     

Decomposed fuzzy proportional–integral–derivative controllers

In this paper, several types of decomposed proportional–integral–derivative fuzzy logic controllers (PID FLCs) are tested and compared. An important feature of decomposed PID FLCs are their simple structures. In its simplest version, the decomposed PID FLC uses three one-input one-output inferences with three separate rule bases. Behaviours of proportional, integral and derivative PID FLC parts are defined with simple rules in proportional rule base, integral rule base and derivative rule base. The proposed decomposed PID FLC has been compared with several PID FLCs structures. All PID FLCs have been realised by the same hardware and software tools and have been applied as a real-time controller to a simple magnetic suspension system.     

关于模糊PID控制器推理机维数的研究

对一维(1D)至三维(3D)模糊PID控制器进行了系统的分析研究,提出了四项系 统功能特性指标来评价不同结构的控制器;这包括控制分量合成,耦合影响,增益相关和规则 增长.通过对最常见的二维Mamdani模糊控制器进行分析研究,发现该控制器存在功能缺 陷.为此,提出了最优结构的一维模糊PID控制器.该控制器采用了"1D-3D"映射关系的模糊 推理机,从而实现了三个控制分量可以独立不相关的调整功能.通过与二维和三维控制器比 较结果表明,一维控制器具有最佳系统功能特性.     

Multi‐objective robust fuzzy fractional order proportional–integral–derivative controller design for nonlinear hydraulic turbine governing system using evolutionary computation techniques

The present paper proposes a novel multi‐objective robust fuzzy fractional order proportional–integral–derivative (PID) controller design for nonlinear hydraulic turbine governing system (HTGS) by using evolutionary computation techniques. The fuzzy fractional order PID (FOPID) controller takes closed loop error and its fractional derivative as inputs and performs fuzzy logic operations. Then, it produces the output through the fractional order integrator. The predominant advantages of the proposed controller are its capability to handle complex nonlinear processes like HTGS in heuristic manner, due to fuzzy incorporation and extending an additional flexibility in tuning the order of fractional derivative/integral terms to enhance the closed loop performance. The present work formulates the optimal tuning problem of fuzzy FOPID controller for HTGS as a multi‐objective one instead of a traditional single‐objective one towards satisfying the conflicting criteria such as less settling time and minimum damped oscillations simultaneously to ensure the improved dynamic performance of HTGS. The multi‐objective evolutionary computation techniques such as non‐dominated sorting genetic algorithm‐II (NSGA‐II) and modified NSGA‐II have been utilized to find the optimal input/output scaling factors of the proposed controller along with the order of fractional derivative/integral terms for HTGS system under no load and load turbulence conditions. The performance of the proposed fuzzy FOPID controller is compared with PID and FOPID controllers. The simulations have been conducted to test the tracking capability and robust performance of HTGS during dynamic set point changes for a wide range of operating conditions and model parameter variations, respectively. The proposed robust fuzzy FOPID controller has ensured better fitness value and better time domain specifications than the PID and FOPID controllers, during optimization towards satisfying the conflicting objectives such as less settling time and minimum damped oscillations simultaneously, due to its special inheritance of fuzzy and FOPID properties.     

不确定性操作臂的混合模糊P+ID控制的实验研究

提出了一种机械臂的混合模糊控制策略,它由一企增量模糊逻辑控制器和传统的积分－微分管制器构成,简称ＰｕｚｚｙＰ＋ＩＤ控制器,与传统的ＰＩＤ控制器相比,设计ＦｕｚｚｙＰ＋ＩＤ控制器时,只需多调节一个附加参数,我们应用ＦｕｚｚｙＰ＋ＩＤ控制器控制几何参数变化的两连杆机构臂ＥＤＤＡ,ＥＤＤＡ的阶跃和跟踪控制的实验结果表明：ＦｕｚｚｙＰ＋ＩＤ控制器更有效和更鲁棒。     

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 Highly Accurate Model-Free Motion Control System with a Mamdani Fuzzy Feedback Controller combined with a TSK Fuzzy Feed-forward Controller

In this paper, a new intelligent robot motion control architecture – a highly accurate model-free fuzzy motion control- is proposed in order to achieve improved robot motion accuracy and dynamic performance. Its architecture combines a Mamdani fuzzy proportional (P) and a conventional integral (I) plus derivative (D) controller for the feedback part of the system, and a Takagi-Sugeno-Kang fuzzy controller for the feed-forward, nonlinear part. The fuzzy P + ID controller improves the performance of the nonlinear system, and the TSK fuzzy controller uses a TSK fuzzy inference system based on extended subtractive- clustering method which integrates information on joint angular displacement, velocity and acceleration for torque identification. The advantage of this kind of model-free control is that it uses the information directly from the input/output of the nonlinear system, without any complex robot model computation, in order to decrease the control system’s sensitivity to any dynamical uncertainty. Furthermore, parametric search for clustering parameters in extended subtractive clustering secures the high accuracy of the system identification. Consequently, this proposed model-free fuzzy motion control benefits from the advantages of two kinds of fuzzy system. It not only incorporates flexible design, good performance and simple conception but also ensures precise motion control and great robustness. Comparisons with other intelligent models and results from numerical studies on a 4-bar planar parallel mechanism show the effectiveness and competitiveness of the proposed control.     

Direct digital design of computed torque controllers

Direct digital design of computed torque controllers for a robot manipulator is discussed in this article. A simple discrete-time model of the robot manipulator obtained by Euler's method is used for the design. Taking account of computation delay in the digital processor, we propose predictor-based designs of the PD and PID type controllers. The PID-type controller is designed based on a modified version of the discrete-time integral controller proposed by Mita. For both controllers, the feedback gains can be determined easily by using simple formulas. A simulation example is presented to illustrate the relevance of the proposed designs and the robustness of PID-type controller against physical parameter variations. © 1994 John Wiley & Sons, Inc.     

Design of fractional-order PIλDμ controllers with an improved differential evolution

Differential evolution (DE) has recently emerged as a simple yet very powerful technique for real parameter optimization. This article describes an application of DE to the design of fractional-order proportional–integral–derivative (FOPID) controllers involving fractional-order integrator and fractional-order differentiator. FOPID controllers’ parameters are composed of the proportionality constant, integral constant, derivative constant, derivative order and integral order, and its design is more complex than that of conventional integer-order proportional–integral–derivative (PID) controller. Here the controller synthesis is based on user-specified peak overshoot and rise time and has been formulated as a single objective optimization problem. In order to digitally realize the fractional-order closed-loop transfer function of the designed plant, Tustin operator-based continuous fraction expansion (CFE) scheme was used in this work. Several simulation examples as well as comparisons of DE with two other state-of-the-art optimization techniques (Particle Swarm Optimization and binary Genetic Algorithm) over the same problems demonstrate the superiority of the proposed approach especially for actuating fractional-order plants. The proposed technique may serve as an efficient alternative for the design of next-generation fractional-order controllers.     

Stability Analysis of Parallel Fuzzy P ＋ Fuzzy I ＋ Fuzzy D Control Systems

The study presented in this paper is in continuation with the paper published by the authors on parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative (FP + FI + FD) controller. It addresses the stability analysis of parallel FP + FI + FD controller. The famous"small gain theorem" is used to study the bounded-input and bounded-output (BIBO) stability of the fuzzy controller. Sufficient BIBO-stability conditions are developed for parallel FP + FI + FD controller. FP + FI + FD controller is derived from the conventional parallel proportional plus integral plus derivative (PID) controller. The parallel FP + FI + FD controller is actually a nonlinear controller with variable gains. It shows much better set-point tracking, disturbance rejection and noise suppression for nonlinear processes as compared to conventional PID controller.     

变频多联机空调模糊逻辑控制及仿真研究 *

变频多联机空调由于各蒸发器之间参数相互影响 ,使其运行特性非常复杂。以各室内温度和吸气压力为被控变量分别调节电子膨胀阀开度和压缩机转速 ,提出了一种鲁棒自适应两级模糊比例 —积分 —微分控制器并进行了仿真。该控制器通过一个模糊切换开关将模糊比例 —微分控制器与模糊积分控制器结合起来 ,模糊比例—微分控制器用来在系统动态响应期间减少上升时间和超调 ;模糊积分控制器用来抗干扰和消除稳态误差。仿真结果表明 ,该控制方法和控制器用于温度控制时不仅鲁棒性好 ,而且能够获得优良的动静态控制性能。     

Feedback QoS control scheme for wireless network applications

Wireless LAN networking is an indispensable technology in an All-IP network architecture to satisfy the “anytime and anywhere” communication requirement of end users. This investigation proposes feedback controllers designing based on dynamic quality-of-service requirement for wireless LAN multimedia services. During the controllers design process, the time-domain is replaced by the s-domain, simplifying the calculation. This work presents three controllers namely proportional integral (PI), proportional derivative (PD) and proportional integral derivative (PID). Experimental results show that systems that employ the proposed controllers can quickly achieve the required system performance. Additionally, the PID controller has the best performance, and can improve delay performance by a rate 11.44% that without the feedback controller. The PI controller is superior to the PD controller. The delay when using the PD is 6.2% less than that achieved without the feedback controller.     

Sliding Mode and PI Controllers for Uncertain Flexible Joint Manipulator

This paper is dealing with the problem of tracking control for uncertain flexible joint manipulator robots driven by brushless direct current motor(BDCM). Flexibility of joint in the manipulator constitutes one of the most important sources of uncertainties. In order to achieve high performance, all parts of the manipulator including actuator have been modeled. To cancel the tracking error, a hysteresis current controller and speed controllers have been developed. To evaluate the effectiveness of speed controllers, a comparative study between proportional integral(PI) and sliding mode controllers has been performed. Finally, simulation results carried out in the Matlab simulink environment demonstrate the high precision of sliding mode controller compared with PI controller in the presence of uncertainties of joint flexibility.     

Indirect disturbance compensation control of a planar parallel (2-PRP and 1-PPR) robotic manipulator

This study addresses the dynamic modelling and indirect disturbance compensation control of planar parallel robotic motion platform with three degrees of freedom (3-DOF) in the presence of parameter uncertainties and external disturbances. The proposed planar parallel motion platform is a singularity free manipulator and has three manipulator legs located on the same plane linked with a moving platform. Of the three aforementioned manipulator legs, two legs have a prismatic–revolute–prismatic (PRP) joint configuration each with only one prismatic joint deliberated to be active, and the other leg consists of prismatic–revolute–prismatic (PPR) joint configuration with one active prismatic joint. The closed form kinematic solution (both forward and reverse kinematics) for the platform has been obtained in completion. In addition, the dynamic model for the platform has been communicated using the energy based Euler–Lagrangian formulation method. The proposed controller is based on a computer torque control with disturbance compensation integrated with it. Disturbance vectors comprising disturbances due to parameter variations, payload variations, frictional effects and other additional effects have been estimated using an extended Kalman filter (EKF). The EKF proposed for this specific platform uses only position and orientation measurements for estimation and noise mitigation. Simulations with a characteristic trajectory are presented and the results have been paralleled with traditional controllers such as the proportional integral derivative (PID) controller and computed torque controller (CTC). The results demonstrate satisfactory tracking performance for the proposed controller in the presence of parameter uncertainties and external disturbances.     

THE GENETIC DESIGN OF HYBRID FUZZY CONTROLLERS

In this study, we introduce a comprehensive design methodology of hybrid fuzzy controllers (HFCs). The hybrid facet of the proposed architecture of the controller manifests in the form of a convex combination of a standard proportional integral derivative (PID) controller and a fuzzy controller. The design procedure dwells on the use of evolutionary computing (genetic algorithms) and an autotuning algorithm based on estimation modes. The tuning of the scaling factors of the HFC is an essential component of the entire optimization process. Numerical studies are presented and a detailed comparative analysis is included as well.     

A precise robust fuzzy control of robots using voltage control strategy

Fuzzy control of robot manipulators with a decentralized structure is facing a serious challenge. The state-space model of a robotic system including the robot manipulator and motors is in non-companion form, multivariable, highly nonlinear, and heavily coupled with a variable input gain matrix. Considering the problem, causes and solutions, we use voltage control strategy and convergence analysis to design a novel precise robust fuzzy control (PRFC) approach for electrically driven robot manipulators. The proposed fuzzy controller is Mamdani type and has a decentralized structure with guaranteed stability. In order to obtain a precise response, we regulate a fuzzy rule which governs the origin of the tracking space. The proposed design is verified by stability analysis. Simulations illustrate the superiority of the PRFC over a proprotional derivative like (PD-like) fuzzy controller applied on a selective compliant assembly robot arm (SCARA) driven by permanent magnet DC motors.