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.     

Auto-tuning of PID controller parameters with supervised receding horizon optimization

In this paper, a novel two-layer online auto-tuning algorithm is presented for a nonlinear time-varying system. The lower layer consists of a conventional proportional-integral-derivative (PID) controller and a plant process, while the upper layer is composed of identification and tuning modules. The purpose of the upper layer is to find a set of optimal PID parameters for the lower layer via an online receding horizon optimization approach, which result in a time-varying PID controller. Through mathematical analysis, the proposed system performance is equivalent to that of a standard generalized predictive control. Simulation and experiment demonstrate that the new method has a better control system performance compared with conventional 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.     

基于改进模型预测控制的加热炉温控系统研究

模型预测控制具有鲁棒性强、跟踪快速性好等特点,能够解决复杂工业过程控制中的大时滞问题。该文提出了一种改进的模型预测控制器,基于事先设定的期望响应,实现参考轨迹在预测时域内最大限度地渐进期望轨迹,使系统响应能够准确地跟踪期望轨迹。该文以硅单晶体加热炉为控制对象,分别采用PID、DMC和改进DMC三种控制方法进行预测控制。仿真结果表明改进的DMC控制方法比传统的预测控制方法具有更好的动态响应性能和跟踪效果。     

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。     

Performance and robustness of optimal fractional fuzzy PID controllers for pitch control of a wind turbine using chaotic optimization algorithms

The most studied controller for pitch control of wind turbines is proportional-integral-derivative (PID) controller. However, due to uncertainties in wind turbine modeling and wind speed profiles, the need for more effective controllers is inevitable. On the other hand, the parameters of PID controller usually are unknown and should be selected by the designer which is neither a straightforward task nor optimal. To cope with these drawbacks, in this paper, two advanced controllers called fuzzy PID (FPID) and fractional-order fuzzy PID (FOFPID) are proposed to improve the pitch control performance. Meanwhile, to find the parameters of the controllers the chaotic evolutionary optimization methods are used. Using evolutionary optimization methods not only gives us the unknown parameters of the controllers but also guarantees the optimality based on the chosen objective function. To improve the performance of the evolutionary algorithms chaotic maps are used. All the optimization procedures are applied to the 2-mass model of 5-MW wind turbine model. The proposed optimal controllers are validated using simulator FAST developed by NREL. Simulation results demonstrate that the FOFPID controller can reach to better performance and robustness while guaranteeing fewer fatigue damages in different wind speeds in comparison to FPID, fractional-order PID (FOPID) and gain-scheduling PID (GSPID) controllers.     

A novel interval type-2 fractional order fuzzy PID controller: Design,performance evaluation,and its optimal time domain tuning

In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases.     

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。     

基于状态反馈线性化的阀控非对称缸系统模型预测控制

针对使用PID方法对阀控非对称液压缸位置控制中出现的超调问题,以及传统非线性模型预测控制优化求解计算时间较长的问题,提出了一种基于状态反馈线性化的阀控非对称缸模型预测控制方案。首先建立了阀控系统状态空间模型,运用微分几何理论讨论系统可反馈线性化的充要条件,并将非线性系统映射为新坐标空间内的线性系统模型;设计了反馈线性化模型预测控制器(Feedback Linearization Model Predictive Controller, FLMPC),讨论了线性系统下的约束问题,其中由于系统仿真预测时域远小于系统响应时间,对模型预测控制的损失函数加以修正。结果证明,在相同输入情况下,反馈线性化系统与原系统的位置误差满足控制需要,且在保证被控对象快速稳定控制的条件下,对比该算法与非线性模型预测控制的单步计算时间,证明该算法能够缩短计算时间。     

Robust friction compensation for submicrometer positioning and tracking for a ball-screw-driven slide system

Ball-screw-driven slide systems are largely used in industry for motion control applications. Their performance using standard proportional-integral-derivative (PID) control algorithm is unsatisfactory in submicrometer motion control because of nonlinear friction effects. In this article, controllers based on a bristle-type nonlinear contact model are developed and implemented for submicrometer motion. For submicrometer positioning, a proportional-derivative (PD) control scheme with a nonlinear friction estimate algorithm is developed, and its performance is compared with that of a PID controller. For tracking, a disturbance observer was added to reject external disturbances and to improve robustness. The experimental results indicate that the proposed controller has consistent performance in positioning with under 1.5% of steady-state error in the submicrometer range. For tracking performance, the proposed controller shows good and robust tracking with respect to parameter variation.     

真空退火温度的建模与解耦控制

真空退火炉中温度的精确控制是一个多变量控制问题。为实现退火温度的精确控制,以真空退火炉现场实际采集的数据为基础,辨识出真空退火炉温区温度的二阶滞后模型,提出一种二阶滞后系统的多变量预测函数解耦控制算法。将多变量系统的解耦控制问题化简为若干个单变量系统的预测函数控制,采取分散优化策略代替整体优化,利用预测函数控制算法的特点,引入基函数增加了设计的自由度,减少了在线计算量,使参数设计和算法过程求解大为简化,得到一个解析的控制量计算方程,实现退火温度二阶滞后系统的多变量预测函数解耦控制。仿真结果表明,控制方法优于传统或改进的PID控制系统。将该控制方法应用于实际的 2 100×2 100真空退火炉退火温度控制系统中,取得了很好的控制效果。     

一类时滞系统的PID稳定控制器设计

针对工业控制过程中常见的时滞系统,给出了快速计算PI和PID控制器所有稳定参数集的方法。推导了系统开环不稳定情形下稳定控制器存在的必要性条件．通过在该稳定参数区域上进行性能指标寻优,可以得到满足控制器设计性能指标要求的PID控制器参数区域。仿真实例表明了该方法的优越性。     

Smith predictor based-sliding mode controller for integrating processes with elevated deadtime

An approach to control integrating processes with elevated deadtime using a Smith predictor sliding mode controller is presented. A PID sliding surface and an integrating first-order plus deadtime model have been used to synthesize the controller. Since the performance of existing controllers with a Smith predictor decrease in the presence of modeling errors, this paper presents a simple approach to combining the Smith predictor with the sliding mode concept, which is a proven, simple, and robust procedure. The proposed scheme has a set of tuning equations as a function of the characteristic parameters of the model. For implementation of our proposed approach, computer based industrial controllers that execute PID algorithms can be used. The performance and robustness of the proposed controller are compared with the Matausek-Mici? scheme for linear systems using simulations.     

A simple nonlinear PD controller for integrating processes

Many industrial processes are found to be integrating in nature, for which widely used Ziegler–Nichols tuned PID controllers usually fail to provide satisfactory performance due to excessive overshoot with large settling time. Although, IMC (Internal Model Control) based PID controllers are capable to reduce the overshoot, but little improvement is found in the load disturbance response. Here, we propose an auto-tuning proportional-derivative controller (APD) where a nonlinear gain updating factor α continuously adjusts the proportional and derivative gains to achieve an overall improved performance during set point change as well as load disturbance. The value of α is obtained by a simple relation based on the instantaneous values of normalized error (e_N) and change of error (Δe_N) of the controlled variable. Performance of the proposed nonlinear PD controller (APD) is tested and compared with other PD and PID tuning rules for pure integrating plus delay (IPD) and first-order integrating plus delay (FOIPD) processes. Effectiveness of the proposed scheme is verified on a laboratory scale servo position control system.     

基于模糊神经网络PID的复合控制策略

为了结合模糊控制容错力强和神经网络PID在线学习和调整的优点,提出了一种结合模糊控制与神经网络PID控制的复合控制方法,即分别设计模糊控制器和神经网络PID控制器后,再利用权重分配器对这两个控制器进行权重分配来控制被控对象。将该控制策略应用于某火电机组的二级过热器减温水流量系统控制,并在simulink仿真平台进行仿真,仿真实验结果表明:该复合控制策略较传统的模糊控制或神经网络PID控制的上升时间更短,调节时间和超调量更小,稳态性能更好。     

A hybrid intelligent controller for a twin rotor MIMO system and its hardware implementation

This paper presents a fuzzy PID control scheme with a real-valued genetic algorithm (RGA) to a setpoint control problem. The objective of this paper is to control a twin rotor MIMO system (TRMS) to move quickly and accurately to the desired attitudes, both the pitch angle and the azimuth angle in a cross-coupled condition. A fuzzy compensator is applied to the PID controller. The proposed control structure includes four PID controllers with independent inputs in 2-DOF. In order to reduce total error and control energy, all parameters of the controller are obtained by a RGA with the system performance index as a fitness function. The system performance index utilized the integral of time multiplied by the square error criterion (ITSE) to build a suitable fitness function in the RGA. A new method for RGA to solve more than 10 parameters in the control scheme is investigated. For real-time control, Xilinx Spartan II SP200 FPGA (Field Programmable Gate Array) is employed to construct a hardware-in-the-loop system through writing VHDL on this FPGA.     

Improved linear quadratic and proportional control system for improved liquid level system regulation in a coke fractionation tower

A new linear quadratic regulation (LQ) control plus a proportional (P) control system is proposed for the level regulation in an industrial coke fractionation tower. The process is first stabilized using a P controller and then a subsequent LQ controller is designed for the P control system. The P control system is modeled as a generalized first order plus dead time (FOPDT) process using step-response test and the LQ-P controller is designed through a new state space structure. Performance in terms of regulatory and servo issues were investigated. Simulation results showed that the proposed method is more robust and improves performance than traditional model predictive control.     

Experimental evaluation of adaptive three-tank level control

Liquid level control through regulation of mass flow rates is an important application in various areas of the power industry. Very often a PID controller is used for these applications. This paper compares a nonconventional PID controller and three different types of adaptive controller, a direct model reference adaptive controller (MRAC), an indirect MRAC with Lyapunov estimation, and an indirect MRAC with recursive least-squares (RLS) updating estimation, for liquid level control. By implementing all four controllers on a three-tank system, the performances of each are compared. All controllers track a sinusoidal input very well and overall exhibit somewhat varying performance. The direct MRAC and the indirect MRAC with RLS estimation give the best performance. With Lyapunov estimation and RLS estimation, all the system parameter estimates converge to the reference model values. However, RLS estimation has a much faster convergence. It is concluded that adaptive liquid level control is an improvement over traditional liquid level control when precise level control in three coupled tanks is desired.     

基于模糊神经网络的精密角度定位PID控制

针对精密角度定位系统存在非线性、时变性,传统PID控制难以获得理想控制效果的问题,提出一种基于模糊神经网络的PID控制方法,将模糊控制、神经网络与PID控制相结合,采用3层前向网络、动态BP算法,利用神经网络的自学习和自适应能力,实时调整网络的权值,改变PID控制器的控制参数,整定出一组适用于控制对象的kp、ki、kd参数,实现精密角度定位PID控制的自适应和智能化。实验结果表明,采用BP神经网络整定的PID控制较传统的PID控制,控制性能有较大的提高,能有效提高定位精度,缩短定位时间。     

Disturbance-rejection-based tuning of proportional–integral–derivative controllers by exploiting closed-loop plant data

A systematic data-based design method for tuning proportional–integral–derivative (PID) controllers for disturbance attenuation is proposed. In this method, a set of closed-loop plant data are directly exploited without using a process model. PID controller parameters for a control system that behaves as closely as possible to the reference model for disturbance rejection are derived. Two algorithms are developed to calculate the PID parameters. One algorithm determines the optimal time delay in the reference model by solving an optimization problem, whereas the other algorithm avoids the nonlinear optimization by using a simple approximation for the time delay term, enabling derivation of analytical PID tuning formulas. Because plant data integrals are used in the regression equations for calculating PID parameters, the two proposed algorithms are robust against measurement noises. Moreover, the controller tuning involves an adjustable design parameter that enables the user to achieve a trade-off between performance and robustness. Because of its closed-loop tuning capability, the proposed method can be applied online to improve (retune) existing underperforming controllers for stable, integrating, and unstable plants. Simulation examples covering a wide variety of process dynamics, including two examples related to reactor systems, are presented to demonstrate the effectiveness of the proposed tuning method.