Fractional calculus in 13C separation column control

Controller design for an isotope separation column is recognized as a difficult and challenging problem. The dynamics of the isotope separation process is difficult to model precisely using integer order transfer functions; thus, a fractional order approach is preferred. The objective of this work is to design two different PI controllers??a classical one and a fractional order one??and test their closed loop performance under nominal conditions as well as gain uncertainties. Since the process is represented by a fractional order mathematical model, the simplest approach to design both controllers is based on a frequency specification. For the fractional order of the PI controller and its parameters, the authors solve a system of equations that includes a robust performance specification to gain uncertainties. For the classical PI controller, a traditional tuning algorithm based on phase margin specification is implemented. The simulation results show that both controllers meet the design specifications, with the fractional order PI controller behaving more robustly to plant gain variations.     

Identification and tuning fractional order proportional integral controllers for time delayed systems with a fractional pole

First order plus time delay model is widely used to model systems with S-shaped reaction curve. Its generalized form is the model with a single fractional pole replacing the integer order pole, which is believed to better characterize the reaction curve. In this paper, using time delayed system model with a fractional pole as the starting point, fractional order controllers design for this class of fractional order systems is investigated. Integer order PID and fractional order PI and [PI] controllers are designed and compared for these class of systems. The simulation comparison between PID controller and fractional order PI and [PI] controllers show the advantages of the properly designed fractional order controllers. Experimental results on a heat flow platform are presented to validate the proposed design method in this paper.     

Analytical design of fractional order PID controllers based on the fractional set-point weighted structure: Case study in twin rotor helicopter

In this paper, an analytical method for tuning the parameters of the set-point weighted fractional order PID (SWFOPID) controller is proposed. The studied control scheme is the filtered fractional set-point weighted (FFSW) structure. Also to achieve a desired closed-loop performance, a fractional order pre-filter is employed. The proposed method is applicable to stable plants describable by a simple three-parameter fractional order model. Such a model can be considered as the fractional order counterpart of a first order transfer function without time delay. Finally, the proposed method is implemented on a laboratory scale CE 150 helicopter platform and the results are compared with those of applying a filtered fractional order PI (FFOPI) controller in a similar structure. The practical results show the effectiveness of the proposed method.     

New fractional-order LADRC scheme based on a novel filtered-Bode’s ideal transfer function for integer-order systems

In this paper, a new Fractional-Order Linear Active Disturbance Rejection Control scheme (FO-LADRC) is proposed to enhance the robustness against loop gain variations of the standard Active Disturbance Rejection Control (ADRC) in the case of uncertain integer-order systems. A new filtered Bode’s ideal transfer function (F-BITF) is proposed to be used as a reference model in the design approach of the proposed control scheme to ensure the dynamic behavior of the closed-loop BITF to the controlled system. A Fractional-order Extended State Observer (F-ESO) is used in the proposed FO-LADRC structure to approximate the system to be controlled by a filtered fractional-order integrator. The fractional order of the F-ESO is a design parameter to tune to achieve the desired overshoot of the closed-loop step response. For the tuning of FO-LADRC structure, an analytical method is proposed. The performance of the proposed FO-LADRC and the Chen’s et al. FO-ADRC structures are evaluated thorough numerical simulation, and then validated in practice in the case of a Cart-Pendulum. Both the simulation and the experimental results show that the proposed FO-LADRC is able to achieve the desired dynamics of the F-BITF and guarantee the robustness with respect to the controller gain variation and the system parameter uncertainties. The comparative study conducted also reveals that the proposed control scheme is more robust than that of Chen.     

Development and implementation of an FPGA based fractional order controller for a DC motor

Fractional calculus has been gaining more and more popularity in control engineering in numerous fields, including mechatronic applications. One of the most common applications in all mechatronic domains is the control of DC motors. Several control algorithms have been proposed for such motors, ranging from traditional PID algorithms, to the more sophisticated advanced methods, including fractional order controllers. Nevertheless, very little information regarding the implementation problems of such fractional algorithms exists today. The paper proposes a simple approach for designing a fractional order PI controller for controlling the speed of a DC motor. The resulting controller is implemented on an FPGA target and its performance is compared to other possible benchmarks. The experimental results show the efficiency of the designed fractional order PI controller. Beside the initial DC motor, two other different DC motors are also used in the experiments to demonstrate the robustness of the controller.     

Research on fuzzy self-adaptive PI-Smith control in long time-delay system

The long time-delay often exists in industrial process.In order to overcome the big overshoot and long regulating time of the long time-delay system control,a new fuzzy self-adaptive PI-Smith control method is proposed.This method combines the Smith predictive control with fuzzy self-adaptive proportional-integral(PI)control.The traditional proportional-integral-derivative(PID)controller in Smith predictive control is replaced by fuzzy PI controller which utilizes the principle of fuzzy control to tune parameters of PI controller on-line.The results of simulation for electric furnace show that the method has the advantages of shortening regulating time,no overshoot,no steady-state error,excellent control accuracy,and good adaptive ability to the change of system model.     

Gain scheduler middleware: a methodology to enable existing controllers for networked control and teleoperation - part I: networked control

Conventionally, in order to control an application over a data network, a specific networked control or teleoperation algorithm to compensate network delay effects is usually required for controller design. Therefore, an existing controller has to be redesigned or replaced by a new controller system. This replacement process is usually costly, inconvenient, and time consuming. In this paper, a novel methodology to enable existing controllers for networked control and teleoperation by middleware is introduced. The proposed methodology uses middleware to modify the output of an existing controller based on a gain scheduling algorithm with respect to the current network traffic conditions. Since the existing controller can still be utilized, this approach could save much time and investment cost. Two examples of the middleware applied for networked control and teleoperation with IP network delays are given in these two companion papers. Part I of these two companion papers introduces the concept of the proposed middleware approach. Formulation, delay modeling, and optimal gain finding based on a cost function for a case study on DC motor speed control with a proportional-integral (PI) controller are also described. Simulation results of the PI controller shows that, with the existence of IP network delays, the middleware can effectively maintain the networked control system performance and stabilize the system. Part II of this paper will cover the use of the proposed middleware concept for a mobile robot teleoperation.     

一类时变输入时滞不确定系统的鲁棒控制器设计

针对一类具有时变输入时滞的不确定系统,基于Lyapunov-Krasovskii方法,讨论了该类系统鲁棒控制器的设计问题.在不确定性满足范数有界条件下,给出了时滞相关的鲁棒可镇定充分条件及相应的鲁棒控制器设计方法,利用辅助变量和广义状态证明了闭环系统的渐近稳定性.最后,进行了数值仿真,结果证明了该方法的有效性和优越性.     

新型二自由度Smith预估控制在ATP伺服系统中的应用

为了提高空间光通信的捕获、跟踪与瞄准系统的跟踪精度,提出了一种新型二自由度Smith预估控制的实现方法。首先对捕获、跟踪与瞄准伺服系统和新型二自由度Smith预估控制系统进行结构分析,然后通过讨论传递函数建立仿真模型,利用MATLAB仿真软件进行仿真,并与多种传统的比例-积分-微分(PID)控制系统进行比较。结果表明,新型控制方法不但具有Smith预估器对时滞有效控制的优点,更显现出不完全微分先行PID控制和比例-积分控制的良好的匹配效果,能够很好地解决纯时滞造成的不稳定性,而且具有较好的鲁棒性和抗干扰性。     

Hybridized ABC-GA optimized fractional order fuzzy pre-compensated FOPID control design for 2-DOF robot manipulator

The robotic manipulator is an extremely nonlinear, multi-input multi-output (MIMO), highly coupled, and complex system wherein the parameter uncertainties and external disturbances adversely affect the performance of this system. From this, it necessitates that the controllers designed for such system must overcome these complexities. In this paper, we develop a novel fractional order fuzzy pre-compensated fractional order PID (FOFP-FOPID) controller for 2-degree of freedom (2-DOF) manipulator dealing with trajectory tracking problem. In order to optimize the controller’s parameters while minimizing integral of time absolute error (ITAE), a metaheuristic optimization technique, viz., artificial bee colony-genetic algorithm (ABC-GA) is presented. The efficacy of our proposed controller is demonstrated by comparing it with some existing controllers, such as integer order fuzzy pre-compensated PID (IOFP-PID), fuzzy PID (FPID), and conventional PID controllers. Furthermore, the robustness analysis for proposed controllers is also investigated for parameter variations and external disturbances. The simulation results indicate that FOFP-FOPID controller can not only guarantee the best trajectory tracking but also ameliorate the system robustness for parameter variations as well as external disturbances.     

基于最小CIM准则的Farrow结构分数时延估计

提出了一种基于最小相关熵诱导距离（CIM）和Farrow结构的分数时延估计算法。该算法具有较强的抗脉冲噪声的能力,且所需观测数据较少,时延估计结果精度较高。理论分析和仿真实验表明,所提算法的估计精度和抗脉冲噪声性能均优于基于分数低阶统计量的LETDE算法。     

Neural-network-based self-tuning PI controller for precise motioncontrol of PMAC motors

In general, proportional plus integral (PI) controllers used in computer numerically controlled machines possess fixed gain. They may perform well under some operating conditions, but not all. To increase the robustness of fixed-gain PI controllers, we propose a new neural-network-based self-tuning PI control system. In this new approach, a well-trained neural network supplies the PI controller with suitable gain according to each operating condition pair (torque, angular velocity, and position error) detected. To demonstrate the advantages of our proposed neural-network-based self-tuning PI control technique, both computer simulations and experiments were executed in this research. During the computer simulation, the direct experiment method was adopted to better model the problem of hysteresis in the AC servo motor. In real experiments, a PC-based controller was used to carry out the control tasks. Results of both computer simulations and experiments show that the newly developed dynamic PI approach outperforms the fixed PI scheme in rise time, precise positioning, and robustness     

Time-delay based output feedback control of fourth-order oscillatory systems

We consider stabilization of the fourth-order oscillatory systems with non-collocated output sensing. Worth recalling is that the fourth-order systems are relatively common in mechatronics as soon as there are two-mass or more generally two-inertia dynamics with significant elasticities in between. A novel yet simple control method is introduced based on the time-delayed output feedback. The delayed output feedback requires only the oscillation frequency to be known and allows for a robust control design that leads to cancelation of the resonance peak. We use the stability margins to justify the transfer characteristics and robustness of the time-delay control in frequency domain. The main advantage of the proposed method over the other possible lead-based loop-shaping strategies is that neither time derivatives of the noisy output nor the implementation of transfer functions with a numerator degree greater than zero are required to deploy the controller. This comes in favor of practical applications. An otherwise inherently instable proportional-integral (PI) feedback of the non-collocated output is shown to be stabilized by the proposed method. The control developed and associated analysis are also confirmed by the experimental results shown for the low damped two-mass oscillator system with uncertainties.     

控制增益符号已知的MIMO非线性时滞系统自适应控制

针对一类具有死区模型并且控制增益符号已知的不确定多输入多输出非线性时滞系统,基于滑模控制原理提出了一种稳定的自适应神经网络控制方案。该方案通过使用Lyapunov-Krasovskii泛函抵消了因未知时变时滞带来的系统不确定性。通过利用积分型李亚普诺夫函数,并且构造逼近连续函数,闭环系统证明是半全局一致终结有界。仿真结果表明了该方法的有效性。     

A fuzzy sliding controller for nonlinear systems

It is well known that sliding-mode control can give good transient performance and system robustness. However, the presence of chattering may introduce problems to the actuators. Many chattering elimination methods use a finite DC gain controller which leads to a finite steady-state error. One method to ensure zero steady-state error is using a proportional plus integral (PI) controller. This paper proposes a fuzzy logic controller which combines a sliding-mode controller (SMC) and a PI controller. The advantages of the SMC and the PI controller can be combined and their disadvantages can be removed. The system stability is proved, although there is one more state variable to be considered in the PI subsystem. An illustrative example shows that good transient and steady-state responses can be obtained by applying the proposed controller     

On the distributed order PID controller

This paper proposes a generalized fractional controller that covers the complete range of differintegrators of order −1 to order 1. This controller is named distributed order PID controller (DOPID) due to the fact that it broadens the structure of the conventional PID controller. Furthermore, a new method for implementation of distributed order PID controller (DOPID), as well as analysis of its properties in both time and frequency domain are proposed. As DOPID controller represents generalized classical PID controller, it is approximated by a compound fractional controller with multiple fractional differintegrators, with multiple gains, connected in parallel. Orders of these differintegrators have been equally spaced, with the first one being the first order classical integrator, and the last one being the first order classical differentiator. Noise cancellation filter is considered explicitly in the controller’s structure.     

A compensated PID active queue management controller using an improved queue dynamic model

Beside the major objective of providing congestion control, achieving predictable queuing delay, maximizing link utilization, and robustness are the main objectives of an active queue management (AQM) controller. This paper proposes an improved queue dynamic model while incorporating the packet drop probability as well. By applying the improved model, a new compensated PID AQM controller is developed for Transmission Control Protocol/Internet Protocol (TCP/IP) networks. The non‐minimum phase characteristic caused by Padé approximation of the network delay restricts the direct application of control methods because of the unstable internal dynamics. In this paper, a parameter‐varying dynamic compensator, which operates on tracking error and internal dynamics, is proposed to not only capture the unstable internal dynamics but also reduce the effect of uncertainties by unresponsive flows. The proposed dynamic compensator is then used to design a PID AQM controller whose gains are obtained directly from the state‐space representation of the system with no further gain tuning requirements. The packet‐level simulations using network simulator (ns2) show the outperformance of the developed controller for both queuing delay stability and resource utilization. The improved underlying model leads also to the faster response of the controller. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust Non-Fragile Guaranteed Cost Control for Nonlinear Time Delay Discrete-Time Systems Based on T-S Model

This paper concerns the robust non-fragile guaranteed cost control for nonlinear time delay discrete-time systems based on Takagi-Sugeno （T-S） model. The problem is to design a guaranteed cost state feedback controller which can tolerate uncertainties from both models and gain variation. Sufficient conditions for the existence of such controller are given based on the linear matrix inequality （LMI） approach combined with Lyapunov method and inequality technique. A numerical example is given to illustrate the feasibility and effectiveness of our result.     

基于分数低阶矩的非整数时间延迟估计方法

依据信号的噪声特性和分数低阶矩理论,提出一种基于最小平均p范数的非整数时间延迟估计方法(称为LMPFTDE算法)。该算法是对直接估计非整数采样间隔的时间延迟估计算法(ETDGE)的广义化,运用最小分散系数准则,通过使误差的p阶矩最小得到非整数时间延迟估计值。理论分析和计算机仿真结果都表明该方法不仅可以在高斯噪声环境下工作,而且在脉冲噪声下也具有良好的健壮性。     

Multiple-Model Adaptive Control of Blood Pressure Using Sodium Nitroprusside

This paper presents a multiple-model adaptive control procedure for sodium nitroprusside regulation of arterial pressure. Pole-placement, via state-variable feedback, is included in the controller to achieve desired performance characteristics. A Smith predictor in the controller effectively removes the infusion delay time, thus simplifying the control analysis and design. Proportional-plus-integral control is used to achieve zero steady-state error. Computer simulations on linear transfer function models with varying gains, time constants, and infusion delays demonstrate the robustness of this multiple-model controller. Additional simulations on nonlinear, pulsatile-flow cardiovascular models lend further support to the ultimate use of this controller for blood-pressure regulation.