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.     

A Novel Robust Pid Controller Design By Fuzzy Neural Network

In this paper, we propose a robust PID controller tuning method for parametric uncertainty systems (or interval plant family) using fuzzy neural networks (FNNs). This robust controller is based on robust gain and phase margin (GM/PM) specifications that satisfy user requirements. Here, the FNN system is used to identify the relation between the PID controller parameters and robust GM/PM. We can use the trained FNN system to determine the parameters of the PID controllers in order to satisfy robust GM/PM specifications that guarantee robustness and performance. Simulation results are shown to illustrate the effectiveness of the robust controller scheme.     

Conical tank level control using fractional order PID controllers: a simulated and experimental study

In this paper, simulated and experimental results on the conical tank level control are presented. PI/PID controllers of integer order (IO) as well as of fractional order (FO) are studied and compared. The tuning parameters are obtained first by using root locus (RL) and Ziegler and Nichols methods, for comparison purposes. Next, particle swarm optimization (PSO) is employed to determine the optimal controllers'' parameters using as fitness function the integral of the absolute value of tracking error (IAE). From the experimental results it is concluded that PI/FOPI are the controllers presenting the lowest IAE indexes, whereas PID/FOPID controllers present the lowest energy consumption by the control signal.     

Statistically optimized FOPID for output force control of SEAs

Fractional order PID (FOPID) controllers have recently found an increasing application in different fields of control. Comparing to traditional PID algorithms, FOPID controllers provide more flexibility and better performances. The simple and non-model-based structure of FOPID controllers has boosted their usage in real-world applications. However, due to having two more control parameters than regular PID controllers and the non-linear structure of FOPID controllers, the tuning procedure of these controllers is still a challenge. The authors of the present paper have recently proposed a Taguchi-based gain tuning algorithm for tuning of control parameters of FOPID controller. The present paper is an experimental evaluation of the proposed method. A custom made SEA, FUM-LSEA, is used as the test bed in this study. Deriving a dynamic model of the FUM-LSEA, feed-forward terms are added to the controller to compensate for disturbances from motions of the output block. Optimal gains and orders of the controller are obtained through a set of experiments suggested by the Taguchi method. The Taguchi optimized controller is also compared to a Ziegler–Nichols tuned controller. The experimental results indicate 45% improvements in force tracking error.     

基于强化迭代学习的四旋翼无人机轨迹控制

为进一步提升在未知环境下四旋翼无人机轨迹的跟踪精度,提出了一种在传统反馈控制架构上增加迭代学习前馈控制器的控制方法。针对迭代学习控制（ILC）中存在的学习参数整定困难的问题,提出了一种利用强化学习（RL）对迭代学习控制器的学习参数进行整定优化的方法。首先,利用RL对迭代学习控制器的学习参数进行优化,筛选出当前环境及任务下最优的学习参数以保证迭代学习控制器的控制效果最优;其次,利用迭代学习控制器的学习能力不断迭代优化前馈输入,直至实现完美跟踪;最后,在有随机噪声存在的仿真环境中把所提出的强化迭代学习控制（RL-ILC）算法与未经参数优化的ILC方法、滑模变结构控制（SMC）方法以及比例-积分-微分（PID）控制方法进行对比实验。实验结果表明,所提算法在经过2次迭代后,总误差缩减为初始误差的0.2%,实现了快速收敛;并且与SMC控制方法及PID控制方法相比,RL-ILC算法在算法收敛后不会受噪声影响产生轨迹波动。由此可见,所提算法能够有效提高无人机轨迹跟踪的准确性和鲁棒性。     

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.     

非线性PID控制器研究——比例分量的非线性方法

研究了基于比例控制分量非线性方法合成的新型非线性PID控制器(简记为:NPID-PCA).该控制器将比例控制分量表示为误差信号的非线性函数,并通过三个独立非线性函数构造合成PID控制器。由于比例控制分量具有最简的非线性特征,因此该类控制器在设计上更为简洁,非线性在控制作用方面的物理意义更为明确.采用样条函数[7]生成非线性作用曲线,用户可以通过图形化交互方式直观地实现非线性设计.通过与文献中的控制实例比较,本文提出的新型非线性PID控制器可以实现更为优良的控制性能指标,包括对带有时延或死区的被控对象.     

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.     

模糊自适应PID控制的研究及应用仿真

传统PID控制器参数的整定是在获取对象数学模型的基础上,根据某一整定规则来确定的,难以适应复杂多变的控制系统。针对其参数整定不良、性能欠佳,对被控过程的适应性差等缺点采用模糊控制与自适应PID控制结合起来,设计了模糊自适应PID控制器。利用模糊推理方法实现对PID参数的在线自整定,进一步完善PID控制器的性能,提高系统的控制精度。仿真结果表明该模糊自适应PID控制器既具有PID控制器高精度的优点,又具有模糊控制器快速、适应性强的特点,使被控对象具有良好的动、稳态特性,有较好的工程应用前景。     

Robust tuning of Two-Degree-of-Freedom (2-DoF) PI/PID based cascade control systems

A design approach for Two-Degree-of-Freedom (2-DoF) PID controllers within a cascade control configuration that guarantees robust and smooth control is presented in this paper. The use of a cascade control configuration comes into place when the use of an additional (intermediate) sensor provides the possibility for a compensation of a load-disturbance before it affects the output variable. The rationale of operation associated to both the inner and outer controllers determines the need of good performance for disturbance attenuation (regulation) as well as set-point following (tracking). Therefore, the use of 2-DoF controllers is introduced. However, the use of 2-DoF controllers, introduces additional parameters that need to be tuned appropriately. Specially for the case of PI/PID controllers there are not known clear auto-tuning guidelines for such situation. The approach undertaken in this paper provides the complete set of tuning parameters for the inner (2-DoF PI) controller and the outer (2-DoF PID) controller. The trade-off among control system performance (measured in terms of closed-loop response speed) and robustness allows to derive a recommendation for the design-parameter lower limit. The design equations are formulated in such a way that a non-oscillatory response is specified for both the inner and outer loop. A side advantage of providing the complete set of parameters is that it avoids the need for the usual identification experiment for the tuning of the outer controller.     

基于Adaptive Interaction理论的PID控制器的设计及应用

本文在Adaptive Interaction理论的基础上,提出了一种新的自调整 PID 控制器。这种新的控制器根据输入及其误差信号进行在线训练,通过误差评价函数的最小化,在模型未知的情况下能很好地调整比例、积分、微分三个参数。对于被控对象的变化具有鲁棒性,很大程度上解决了传统的 PID 控制器对于非线性、不稳定系统控制效果不佳及在线调整困难的问题。通过仿真实例,验证了应用 Adaptive Interaction 理论的 PID 控制器的有效性和实用性。     

Simultaneous automatic tuning of cascade control systems from closed-loop step response data

This study presents a novel automatic tuning method for cascade control systems in which both primary and secondary controllers are tuned simultaneously using a single closed-loop step test. The proposed technique identifies the required process information with the help of B-spline series representation for the step responses. The two proportional–integral–derivative (PID) controllers are then tuned using an internal model control (IMC) approach. Considering the rationale of cascade control, the secondary controller is designed for faster disturbance attenuation. Without requiring an additional experiment, the primary controller is designed based on an identified process model that accurately accounts for inner loop dynamics. Finally, this study includes robustness considerations in the controller tuning process, and develops explicit guidelines for the selection of the IMC tuning parameters, completing the automatic tuning procedure for cascade control systems. The proposed method is robust to measurement noise because of the filtering property of the B-splines, and can provide superior control performance for both set-point tracking and disturbance rejection. Simulation examples demonstrate the effectiveness of the proposed automatic tuning method.     

Adaptive control of a CSTR with a neural network model

An adaptive control algorithm with a neural network model, previously proposed in the literature for the control of mechanical manipulators, is applied to a CSTR (Continuous Stirred Tank Reactor). The neural network model uses either radial Gaussian or “Mexican hat” wavelets as basis functions. This work shows that the addition of linear functions to the networks significantly improves the error convergence when the CSTR is operated for long periods of time in a neighborhood of one operating point, a common scenario in chemical process control. Then, a quantitative comparative study based on output errors and control efforts is conducted where adaptive controllers using wavelets or Gaussian basis functions and PID controllers (IMC tuning with fixed parameters and self tuning PID) are compared. From this comparative study, the practicality and advantages of the adaptive controllers over fixed or adaptive PID control is assessed.     

双闭环直流调速系统模糊PID控制研究*

针对电压和负载扰动导致传统PID控制双闭环直流调速系统性能下降的问题,本文提出一种模糊PID控制方法。本文的控制方法根据调速系统的转速偏差e和偏差变化率ec,经过模糊逻辑推理,动态自适应调整PID控制器的三个参数,能够有效提高系统抗扰动能力。为了对两种控制方法的性能进行比较分析,文中对系统在理想空载状态、负载扰动和电压波动三种情况下进行仿真试验。结果表明两种控制方法在理想空载状态下的稳态性能基本相同。在负载扰动和电压波动的情况下,本文的方法能使系统更快恢复到平衡状态,且具有更小的转速降。因此,本文的控制方法能够保证系统具有较好的动态性能和抗扰性能。     

A numerical optimization approach for tuning fuzzy logiccontrollers

This paper develops a method to tune fuzzy controllers using numerical optimization. The main attribute of this approach is that it allows fuzzy logic controllers to be tuned to achieve global performance requirements. Furthermore, this approach allows design constraints to be implemented during the tuning process. The method tunes the controller by parameterizing the membership functions for error, change-in-error, and control output. The resulting parameters form a design vector which is iteratively changed to minimize an objective function. The minimal objective function results in an optimal performance of the system. A spacecraft mounted science payload line-of-sight pointing control is used to demonstrate results.     

Robust adaptive control of a bio-inspired robot manipulator using bat algorithm

This paper proposes a novel adaptive fractional order PID sliding mode controller (AFOPIDSMC) using a Bat algorithm to control of a Caterpillar robot manipulator. A fractional order PID (FOPID) control is applied to improve both trajectory tracking and robustness. Sliding mode controller (SMC) is one of the control methods which provides high robustness and low tracking error. Using hybridization, a new combined control law is proposed for chattering reduction by means of FOPID controller and high trajectory tracking through using SMC. Then, an adaptive controller design motivated from the SMC is applied for updating FOPID parameters. A metaheuristic approach, the Bat search algorithm based on the echolocation behavior of bats is applied for optimal design of the Caterpillar robot in order to tune the parameter AFOPIDSMC controllers (BA-AFOPIDSMC). To study the effectiveness of Bat algorithm, its performance is compared with five other controllers such as PID, FOPID, SMC, AFOPIDSMC and PSO-AFOPIDSMC. The stability of the AFOPIDSMC controller is proved by Lyapunov theory. Numerical simulation results completely indicate the advantage of BA-AFOPIDSMC for trajectory tracking and chattering reduction.     

Fuzzy PID Control of a Five DOF Robot Arm

This paper studies the application of fuzzy logic control on a five degrees of freedom (DOF) robot arm, the Maker 100 of U.S. Robots. The elaboration of the fuzzy control laws is based on two structures of coupled rules fuzzy PID controllers. The fuzzy PID controllers are numerically simulated and the simulation results confirm the success of the fuzzy PID control in trajectory tracking problems. Seeking a performance optimization, a systematic study of the choice of tuning parameters of the controllers is done. The success of the proposed fuzzy control law is again affirmed by a comparative evaluation with respect to the computed torque control method and the direct adaptive control method, the last two controls being also numerically implemented using the same dynamic model of the robot arm.     

PID control of MIMO process based on rank niching genetic algorithm

Non-linear multiple-input multiple-output (MIMO) processes which are common in industrial plants are characterized by significant interactions and non- linearities among their variables. Thus, tuning several controllers in complex industrial plants is a challenge for process engineers and operators. An approach for adjusting the parameters of n proportional–integral–derivative (PID) controllers based on multiobjective optimization and genetic algorithms (GA) is presented in this paper. A modified genetic algorithm with elitist model and niching method is developed to guarantee a set of solutions (set of PID parameters) with different tradeoffs regarding the multiple requirements of the control performance. Experiments considering a fluid catalytic cracking (FCC) unit, under PI and dynamic matrix control (DMC) are carried out in order to evaluate the proposed method. The results show that the proposed approach is an alternative to classical techniques as Ziegler–Nichols rules and others.     

基于执行器–评价器学习的自适应PID控制

针对传统PID控制器无法在线自整定参数的不足,提出了一种基于执行器一评估器（Actor-Critic,AC）学习的自适应PID控制器结构与学习算法．该控制器利用AC学习实现PID参数的自适应整定,采用一个径向基函数网络同时对Actor的策略函数和Critic的值函数进行逼近．径向基函数网络的输入为系统误差、误差的一次差分和二次差分,Actor实现系统状态到PID参数的映射,Critic则对Actor的输出进行评判并且生成时序差分（temporaldifference,TD）误差信号．基于AC学习的体系结构和TD误差性能指标,给出了控制器设计的步骤流程图．两个仿真实验表明：与传统的PID控制器相比,基于AC学习的PID控制器在响应速度和自适应能力方面要优于传统PID控制器．