Performance analysis of two-degree of freedom fractional order PID controllers for robotic manipulator with payload

The robotic manipulators are multi-input multi-output (MIMO), coupled and highly nonlinear systems. The presence of external disturbances and time-varying parameters adversely affects the performance of these systems. Therefore, the controller designed for these systems should effectively deal with such complexities, and it is an intriguing task for control engineers. This paper presents two-degree of freedom fractional order proportional-integral-derivative (2-DOF FOPID) controller scheme for a two-link planar rigid robotic manipulator with payload for trajectory tracking task. The tuning of all controller parameters is done using cuckoo search algorithm (CSA). The performance of proposed 2-DOF FOPID controllers is compared with those of their integer order designs, i.e., 2-DOF PID controllers, and with the traditional PID controllers. In order to show effectiveness of proposed scheme, the robustness testing is carried out for model uncertainties, payload variations with time, external disturbance and random noise. Numerical simulation results indicate that the 2-DOF FOPID controllers are superior to their integer order counterparts and the traditional PID controllers.     

FEEDBACK LINEARIZATION CONTROL FOR ELECTRONICALLY CONTROLLABLE CLUTCH OF VEHICLE

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基于模糊神经网络的不确定机器人实时轨迹跟踪控制的研究

针对机器人建模的不精确性以及扰动的存在给机器人控制增加难度的问题,提出了一种基于模糊神经网络的不确定机器人实时轨迹跟踪控制方法。该控制方法的控制器由模糊神经网络(FNN)控制器和CMAC控制器组成,FNN控制器代替传统的计算力矩法,CMAC控制器在线补偿控制误差,有效补偿机器人存在的各种不确定性。对二自由度机器人的仿真结果表明了所提出的控制方法的可行性。     

A novel auto-tuning method for fractional order PI/PD controllers

Fractional order PID controllers benefit from an increasing amount of interest from the research community due to their proven advantages. The classical tuning approach for these controllers is based on specifying a certain gain crossover frequency, a phase margin and a robustness to gain variations. To tune the fractional order controllers, the modulus, phase and phase slope of the process at the imposed gain crossover frequency are required. Usually these values are obtained from a mathematical model of the process, e.g. a transfer function. In the absence of such model, an auto-tuning method that is able to estimate these values is a valuable alternative. Auto-tuning methods are among the least discussed design methods for fractional order PID controllers. This paper proposes a novel approach for the auto-tuning of fractional order controllers. The method is based on a simple experiment that is able to determine the modulus, phase and phase slope of the process required in the computation of the controller parameters. The proposed design technique is simple and efficient in ensuring the robustness of the closed loop system. Several simulation examples are presented, including the control of processes exhibiting integer and fractional order dynamics.     

快速刀具伺服分数阶PID控制仿真的研究

利用分数阶PID控制,提出了一种新的快速刀具伺服(FTS)跟踪控制方法,以改善FTS的控制性能。根据差分进化算法,讨论了分数阶PID控制器的参数整定;通过数值仿真,考察了该方法的可行性和有效性。针对FTS的轨迹跟踪,根据响应时间、跟踪精度等指标,详细比较了分数阶PID控制与传统PID控制的性能。仿真结果表明,分数阶PID控制器的阶跃响应时间约为5×10-7s,是PID控制响应时间的42%,对频率为1 kHz,幅值为1μm的正弦信号的跟踪误差约为6 nm,是PID跟踪误差的50%,验证了基于分数阶PID控制器实现FTS轨迹跟踪控制的可行性和优越性。     

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。     

多关节机器人反馈线性化双模糊滑模控制

为了提高多关节机器人轨迹跟踪控制性能,提出了一种反馈线性化双模糊滑模控制方法。该方法在对机器人非线性动力学模型反馈线性化的基础上,设计了一种双模糊滑模控制器。通过设计一个模糊控制器,根据跟踪误差和误差变化率自适应地调整滑模面的斜率,从而加快响应速度。通过设计另一个模糊控制器,根据滑模面自适应地调整滑模控制的切换控制部分,从而减弱抖振。利用李亚普诺夫定理证明了控制系统的稳定性。针对空间三关节机器人进行了仿真实验,结果表明了所提方法的有效性。     

An integer order approximation method based on stability boundary locus for fractional order derivative/integrator operators

This paper introduces an integer order approximation method for numerical implementation of fractional order derivative/integrator operators in control systems. The proposed method is based on fitting the stability boundary locus (SBL) of fractional order derivative/integrator operators and SBL of integer order transfer functions. SBL defines a boundary in the parametric design plane of controller, which separates stable and unstable regions of a feedback control system and SBL analysis is mainly employed to graphically indicate the choice of controller parameters which result in stable operation of the feedback systems. This study reveals that the SBL curves of fractional order operators can be matched with integer order models in a limited frequency range. SBL fitting method provides straightforward solutions to obtain an integer order model approximation of fractional order operators and systems according to matching points from SBL of fractional order systems in desired frequency ranges. Thus, the proposed method can effectively deal with stability preservation problems of approximate models. Illustrative examples are given to show performance of the proposed method and results are compared with the well-known approximation methods developed for fractional order systems. The integer-order approximate modeling of fractional order PID controllers is also illustrated for control applications.     

New modifying self-organizing fuzzy controller for robotic motion control

The precise motion control of robotic manipulators is important in improving productivity and quality. However, robotic manipulators are multivariable nonlinear dynamic systems. Designing a model-based controller for robotic system control is difficult because its mathematical model is hard to accurately establish. This study proposed a self-organizing fuzzy controller (SOFC) to control a robotic system and evaluate its control performance. The SOFC continually updates the learning strategy in the form of fuzzy rules during the control process. The learning rate and the weighting distribution value of the controller are hard to regulate, so its fuzzy control rules may be modified to such an extent that the system response generally causes oscillatory phenomena. Two fuzzy logic controllers were designed according to the system output error and the error change, and introduced to the SOFC to determine the appropriate parameters of the learning rate and the weighting distribution, in order to eliminate this oscillation. This new modifying self-organizing fuzzy controller (NMSOFC) can effectively improve the control performance of the system, reduce the time consumed to establish a suitable fuzzy rule table, and support practical and convenient fuzzy controller applications. To confirm the applicability of the proposed intelligent controllers, this work retrofitted an old robot for a control system to evaluate the feasibility of motion control. Experiment results indicate the NMSOFC has better control performance in reducing the tracking errors of the joint-space trajectories and the positions, and requires less computational time than does the traditional fuzzy controller.     

机器人焊缝跟踪神经网络控制的研究

研究神经网络技术在弧焊机器人焊缝跟踪过程中的应用,通过神经网络在笛卡尔空间轨迹的补偿作用,确定出基于笛卡尔空间参考轨迹控制的机器人焊缝跟踪神经网络控制器。与传统的关节计算力矩法相比,所设计的神经网络控制器具有良好的控制特性及较强的鲁棒性,焊缝跟踪精度得到了显著的提高。     

IMC-PID-fractional-order-filter controllers design for integer order systems

One of the reasons of the great success of standard PID controllers is the presence of simple tuning rules, of the automatic tuning feature and of tables that simplify significantly their design. For the fractional order case, some tuning rules have been proposed in the literature. However, they are not general because they are valid only for some model cases. In this paper, a new approach is investigated. The fractional property is not especially imposed by the controller structure but by the closed loop reference model. The resulting controller is fractional but it has a very interesting structure for its implementation. Indeed, the controller can be decomposed into two transfer functions: an integer transfer function which is generally an integer PID controller and a simple fractional filter.     

Neural network controller for robotic motion control

Since a robotic manipulator has a complicated mathematical model, it is difficult to design a control system based on the complicated multi-variable nonlinear coupling dynamic model. Intelligent controllers using fuzzy and neural network approaches do not need a real mathematical model to design the control structure and have attracted the attention of robotic control researchers recently. A traditional fuzzy logic controller does not have learning capability and it needs a lot of effort to search for the optimal control rules and the shapes of membership functions. Owing to the time-varying behaviour of the system, the required fine tracking accuracy is difficult to achieve by adjusting the fuzzy rules only. The implementation problems of neural network control are the initial training and initial transient stability. In order to improve the position control accuracy and system robustness for industrial applications, a neural controller is first trained off-line by using the input and output (I/O) data of a traditional fuzzy controller. Then the neural controller is implemented on a five-degrees-of-freedom robot with a back propagation algorithm for online adjustment. The experimental results show that this neural network controller achieved the required trajectory tracking accuracy after 15 on-line operations.     

Load transportation by dual arm robot using sliding mode control

In this study, a sliding mode controlled dual arm robotic system was designed. Such multi-arm, collaborative and synchronous robots typically are employed in hazardous situations such as radioactive materials transport explosives disposal and industrial applications. In the present study, a high performance, robust, non-chattering sliding mode controller (SMC) was developed for the purpose of safe load handling, transportation and trajectory realization. First, dynamic equations of robot/load interaction were derived. Then, the robust SMC was designed for the dual arm robotic system. In order to test the robustness of the proposed SMC, parameter variations and external disturbances were introduced to the system. Furthermore, for comparative purposes, the conventional and widely used, PID controller was also applied to the dual arm robot. Significantly, it was found that the SMC made smaller trajectory tracking errors than the PID controller. An overall analysis of the numerical results confirmed that the dual-arm robotic systems with the proposed SMC can safely and effectively be used in hazardous applications.     

Handling packet dropouts and random delays for unstable delayed processes in NCS by optimal tuning of PIλDμ controllers with evolutionary algorithms

The issues of stochastically varying network delays and packet dropouts in Networked Control System (NCS) applications have been simultaneously addressed by time domain optimal tuning of fractional order (FO) PID controllers. Different variants of evolutionary algorithms are used for the tuning process and their performances are compared. Also the effectiveness of the fractional order PI(λ)D(μ) controllers over their integer order counterparts is looked into. Two standard test bench plants with time delay and unstable poles which are encountered in process control applications are tuned with the proposed method to establish the validity of the tuning methodology. The proposed tuning methodology is independent of the specific choice of plant and is also applicable for less complicated systems. Thus it is useful in a wide variety of scenarios. The paper also shows the superiority of FOPID controllers over their conventional PID counterparts for NCS applications.     

Fractional order model reduction approach based on retention of the dominant dynamics: application in IMC based tuning of FOPI and FOPID controllers

Fractional order PI and PID controllers are the most common fractional order controllers used in practice. In this paper, a simple analytical method is proposed for tuning the parameters of these controllers. The proposed method is useful in designing fractional order PI and PID controllers for control of complicated fractional order systems. To achieve the goal, at first a reduction technique is presented for approximating complicated fractional order models. Then, based on the obtained reduced models some analytical rules are suggested to determine the parameters of fractional order PI and PID controllers. Finally, numerical results are given to show the efficiency of the proposed tuning algorithm.     

新型雕刻机器人控制策略的研究

建立了新型雕刻机器人的雕刻并联头的运动学模型,计算出了运动学的正解和反解;研究了新型雕刻并联工作头的控制策略,建立了PD算法、PD加重力补偿算法和计算力矩法3种控制策略的模型;采用Matlab/Simulink软件,仿真了3种算法搭建的数学模型,比较得出了不同控制算法的优劣。结果表明,在3种控制策略中,计算力矩法的位置控制效果最好,能够保证系统有较强的抗干扰性。所以,新型雕刻机器人选用计算力矩法作为自身的控制策略。     

基于分数阶微积分的机械臂迭代滑模控制策略研究

为提高工业机械臂的控制性能,将分数阶微积分理论与迭代学习控制及滑模控制相结合,提出一种有效的分数阶迭代滑模控制策略.在控制器的设计过程中,分别采用分数阶趋近律与分数阶滑模控制律两种方法将分数阶微积分引入到迭代滑模控制中,提出分数阶迭代滑模控制策略.并使用李雅普诺夫理论分析系统的稳定性.然后以一个两关节机械臂为例,通过MATLAB仿真对所提出的控制策略进行了验证.实验表明:分数阶迭代滑模控制策略可以有效提高关节的跟踪速度和跟踪精度,减小跟踪误差,具有较强的鲁棒性,并有效地抑制了滑模控制的抖振现象.     

基于分数阶微积分的机械臂迭代滑模控制策略研究

为提高工业机械臂的控制性能,将分数阶微积分理论与迭代学习控制及滑模控制相结合,提出一种有效的分数阶迭代滑模控制策略.在控制器的设计过程中,分别采用分数阶趋近律与分数阶滑模控制律两种方法将分数阶微积分引入到迭代滑模控制中,提出分数阶迭代滑模控制策略.并使用李雅普诺夫理论分析系统的稳定性.然后以一个两关节机械臂为例,通过MATLAB仿真对所提出的控制策略进行了验证.实验表明:分数阶迭代滑模控制策略可以有效提高关节的跟踪速度和跟踪精度,减小跟踪误差,具有较强的鲁棒性,并有效地抑制了滑模控制的抖振现象.     

直接驱动型机械手的变结构控制

针对直接驱动型机械手的随动控制问题,提出了一种基于滑动模态扰动观测器的变结构控制器.通过观测由系统的非线性、模型的不确定性和外来干扰所造成的广义扰动,将非线性、强耦合的机械手动力学系统线性化,并解耦为多个单输入、单输出线性系统.控制器的设计不再依赖于机械手的精确模型.在二连杆机械手上做的仿真研究表明,在负载大范围变化的条件下,采用滑动模态扰动观测器的控制系统,比全状态反馈的控制系统具有更好的鲁棒性.     

机械手鲁棒自适应PD控制

针对工业机械手的轨迹跟踪问题,设计了一种鲁棒自适应PD控制策略,避免了初始输出力矩过大的弊端.考虑将控制器分为非线性补偿控制和PD反馈控制两部分,机械手的不确定动力学部分由回归矩阵构成的自适应控制器进行补偿,实现了对机械手的运动控制.通过计算机仿真结果验证了所提出控制策略的有效性,能够很好地跟踪期望轨迹.