Robust Stability Analysis of Smith Predictor Based Interval Fractional-Order Control Systems:A Case Study in Level Control Process

The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.

Precise robust motion control of cell puncture mechanism driven by piezoelectric actuators with fractional-order nonsingular terminal slidingmode control

A novel robust controller is proposed in this study to realize the precise motion control of a cell puncture mechanism(CPM)driven by piezoelectric ceramics(PEAs).The entire dynamic model of CPM is constructed based on the Bouc–Wen model,and the nonlinear part of the dynamic model is optimized locally to facilitate the construction of a robust controller.A model-based,nonlinear robust controller is constructed using time-delay estimation(TDE)and fractional-order nonsingular terminal sliding mode(FONTSM).The proposed controller does not require prior knowledge of unknown disturbances due to its real-time online estimation and compensation of unknown terms by using the TDE technology.The controller also has finite-time convergence and high-precision trajectory tracking capabilities due to FONTSM manifold and fast terminal sliding mode-type reaching law.The stability of the closed-loop system is proved by Lyapunov stability theory.Computer simulation and hardware-in-loop simulation experiments of CPM verify that the proposed controller outperforms traditional terminal sliding mode controllers,such as the integer-order or model-free controller.The proposed controller can also continuously output without chattering and has high control accuracy.Zebrafish embryo is used as a verification target to complete the cell puncture experiment.From the engineering application perspective,the proposed control strategy can be effectively applied in a PEA-driven CPM.

多策略改进粒子群优化AGV模糊PID控制

为解决AGV在复杂环境下控制精度低下、响应速度慢和鲁棒性差等问题,提出一种基于改进粒子群优化模糊PID控制方法。在粒子群算法(PSO)引入Logistic混沌映射对种群进行初始化,其次对惯性权重和学习因子进行非线性控制更新,提升种群寻优能力和避免陷入局部最优;选取9个测试函数验证改进PSO算法效果。仿真结果表明改进PSO在寻优精度和收敛速度都优于其他3种算法,而且不易陷入局部最优。最后对被控系统进行效果验证,结果表明改进PSO优化模糊PID控制器在常规和外部干扰两种环境下控制性能都优于传统PID和模糊PID,具有高可靠性、高控制精度,满足系统要求。

Design and Robust Performance Evaluation of a Fractional Order PID Controller Applied to a DC Motor

This paper proposes a methodology for the quantitative robustness evaluation of PID controllers employed in a DC motor. The robustness analysis is performed employing a 2~3 factorial experimental design for a fractional order proportional integral and derivative controller(FOPID), integer order proportional integral and derivative controller(IOPID)and the Skogestad internal model control controller(SIMC). The factors assumed in experiment are the presence of random noise,external disturbances in the system input and variable load. As output variables, the experimental design employs the system step response and the controller action. Practical implementation of FOPID and IOPID controllers uses the MATLAB stateflow toolbox and a NI data acquisition system. Results of the robustness analysis show that the FOPID controller has a better performance and robust stability against the experiment factors.

Robust Admissibility and Stabilization of Uncertain Singular Fractional-Order Linear Time-Invariant Systems

This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict linear matrix inequalities(LMIs). Then, a static output feedback controller is designed for the uncertain closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods.

Robust Non-fragile PID Controller Design for the Stroke Regulation of Metering Pumps

This job focuses on the stroke regulation of a class of high-precision metering pumps.A parametertuning method of robust non-fragile PID（proportional-integral-derivative）controllers is proposed with the assumption that a PID controller has additive gain perturbations.An H-infinite robust PID controller can be obtained by solving a linear matrix inequality.This approach can guarantee that the closed-loop control systems is asymptotically stable and the H-infinite norm of the transfer function from the disturbance to the output of a controlled system is less than a given constant to attenuate disturbances.The simulation case shows that the control performance of the proposed strategy is significantly better than the traditional PID approach in the situation with perturbations of controller parameters.

Research on Anti-Fluctuation Control of Winding Tension System Based on Feedforward Compensation

In the fiber winding process,strong disturbance,uncertainty,strong coupling,and fiber friction complicate the winding constant tension control.In order to effectively reduce the influence of these problems on the tension output,this paper proposed a tension fluctuation rejection strategy based on feedforward compensation.In addition to the bias harmonic curve of the unknown state,the tension fluctuation also contains the influence of bounded noise.A tension fluctuation observer(TFO)is designed to cancel the uncertain periodic signal,in which the frequency generator is used to estimate the critical parameter information.Then,the fluctuation signal is reconstructed by a third-order auxiliary filter.The estimated signal feedforward compensates for the actual tension fluctuation.Furthermore,a time-varying parameters fractional-order PID controller(TPFOPID)is realized to attenuate the bounded noise in the fluctuation.Finally,TPFOPID is enhanced by TFO and applied to control a tension control system considering multi-source disturbances.The stability of the method is analyzed by using the Lyapunov theorem.Finally,numerical simulations verify that the proposed scheme improves the tracking ability and robustness of the system in response to tension fluctuations.

CONTROL OF ROBOT DRIVEN BY MULTIPLE ULTRASONIC MOTORS BASED ON ROBUST PARAMETER DESIGN

An ultrasonic motor （USM） is difficlt to be mathematically described because of its complex energy conversion and nonlinear parameters from increasing temperature and changing operating conditions. To achieve good performance of a three-joint robot directly driven by USM, according to the operating characteristics of USM, a new position-velocity feedback control strategy is proposed. In the control strategy, there are a total of 18 controller gains to he tuned. Through a series of ＂Design of Experiments＂ by the robust parameter design, an optimal and robust set of proportional integral derivative （PID） controller gains is obtained. Results show that the control strategy can achieve the best performance of the robot and the robust parameter design is effective and convenient to USMs.

油田站库PID控制器参数鲁棒整定及其应用

PID控制器的性能与其参数密切相关,如果油田转油站和联合站的变频器以及游离水脱除器的气动阀等关联的PID控制器参数设置不佳,且油田站库生产过程中存在随机干扰,会导致系统运行波动较大。因此应用数据驱动鲁棒建模构建了多目标融合的PID鲁棒参数整定策略。首先利用最小一乘法建立了对异常值不敏感的鲁棒模型;接着利用内模控制原理并融合PID控制器的动态性能实现PID鲁棒参数整定。实际应用表明该参数整定策略能较好地实现油田站库的PID参数整定,整定后的控制系统不仅运行平稳,且外输能耗大幅降低。

Coordinated Robust PID-based Damping Control of Permanent Magnet Synchronous Generators for Low-frequency Oscillations Considering Power System Operational Uncertainties

In recent years, with the growth of wind energy resources,the capability of wind farms to damp low-frequency oscillations(LFOs) has provided a notable advantage for the stabilityenhancement of the modern power grid. Meanwhile, owingto variations in the power system operating point (OP), thedamping characteristics of LFOs may be affected adversely. Inthis respect, this paper presents a coordinated robust proportional-integral-derivative (PID) based damping control approachfor permanent magnet synchronous generators (PMSGs)to effectively stabilize LFOs, while considering power system operationaluncertainties in the form of a polytopic model constructedby linearizing the power system under a given set ofOPs. The proposed approach works by modulating the DC-linkvoltage control loop of the grid-side converter (GSC) via a supplementaryPID controller, which is synthesized by transformingthe design problem into H-infinity static output feedback(SOF) control methodology. The solution of H-infinity SOF controlproblem involves satisfying linear matrix inequality (LMI)constraints based on the parameter-dependent Lyapunov functionto ensure asymptotic stability such that the minimal H-infinityperformance objective is simultaneously accomplished forthe entire polytope. The coordinated damping controllers forthe multiple wind farms are then designed sequentially by usingthe proposed approach. Eigenvalue analysis confirms the improveddamping characteristics of the closed-loop system forseveral representative OPs. Afterward, the simulation results, includingthe performance comparison with existing approaches,validate the higher robustness of the proposed approach for awide range of operating scenarios.

Tuning of fuzzy PID controller for Smith predictor

An analytical tuning method was proposed for fuzzy PID controller used in Smith predictor in order to extend its application and improve its robustness. The fuzzy PID controller was expressed as a sliding mode control. Based on Lyapunov theory, Smith predictor was analyzed in time domain. The parameters of the fuzzy PID controller can be obtained using traditional linear control theory and sliding mode control theory. The simulation experiments were implemented. The simulation results show that the control performance, robustness and stability of the fuzzy PID controller are better than those of the PID controller in Smith predictor.

Generalized Internal Model Robust Control for Active Front Steering Intervention

Because of the tire nonlinearity and vehicle＇s parameters＇uncertainties,robust control methods based on the worst cases,such as H_∞,μsynthesis,have been widely used in active front steering control,however,in order to guarantee the stability of active front steering system（AFS）controller,the robust control is at the cost of performance so that the robust controller is a little conservative and has low performance for AFS control.In this paper,a generalized internal model robust control（GIMC）that can overcome the contradiction between performance and stability is used in the AFS control.In GIMC,the Youla parameterization is used in an improved way.And GIMC controller includes two sections：a high performance controller designed for the nominal vehicle model and a robust controller compensating the vehicle parameters＇uncertainties and some external disturbances.Simulations of double lane change（DLC）maneuver and that of braking on split-μroad are conducted to compare the performance and stability of the GIMC control,the nominal performance PID controller and the H_∞controller.Simulation results show that the high nominal performance PID controller will be unstable under some extreme situations because of large vehicle＇s parameters variations,H_∞controller is conservative so that the performance is a little low,and only the GIMC controller overcomes the contradiction between performance and robustness,which can both ensure the stability of the AFS controller and guarantee the high performance of the AFS controller.Therefore,the GIMC method proposed for AFS can overcome some disadvantages of control methods used by current AFS system,that is,can solve the instability of PID or LQP control methods and the low performance of the standard H_∞controller.

堆芯功率的自耦PID控制策略研究

针对堆芯功率的非线性控制问题,提出了一种自耦PID(SCPID)功率控制方法。该方法将系统内部所有已知或未知复杂因素及外部扰动定义为一个总扰动,建立了以总扰动为激励的受控误差系统,进而设计了基于SCPID控制理论的堆芯功率控制系统,并在复频域对闭环控制系统的稳定性进行严格的数学分析和证明。结果表明:与其他方法相比,SCPID控制方法简单高效,在堆芯功率系统控制领域具有实际应用价值。

相变材料充装换热装置双自由度内模PID控制器设计

针对相变材料充装过程中换热装置出口温度控制非线性、时滞性特点,提出了一种基于粒子群优化(PSO)算法整定的双自由度内模控制PID(PSO-TDF-IMC-PID)控制策略。基于内模原理设计了IMC-PID控制器,并利用PSO算法对控制器参数进行整定。借助仿真工具,进行阶跃响应仿真、抗干扰性仿真研究、模型失配情况仿真研究。结果表明:所提控制方法克服了IMC-PID的缺点,参数整定效率高,鲁棒性强,改善了相变材料出口温度控制效果,并且具有很好的抗干扰能力。

On the Comparisons of PID and GI-PD Control

In conjunction with a second order uncertain nonlinear system, this paper makes some comparisons between PID control and general-integral-proportional-derivative (GI-PD) control;that is, by Routh’s stability criterion, we demonstrate that the system matrix under GI-PD control can be stabilized more easily;by linear system theory and Lyapunov method, we demonstrate that GI-PD control can deal with the uncertain nonlinearity more effectively;by analyzing and comparing the integral control action, we demonstrate that GI-PD control has the better control performance. Design example and simulation results verify the justification of our conclusions again. All these mean that GI-PD control has the stronger robustness and higher control performance than PID control. Consequently, GI-PD control has broader application prospects than PID control.

Research on Airborne Electro-Optical Tracking and Sighting System Based on Fuzzy PID and H_∞ Control

Airborne electro-optical tracking and sighting system is a three-degree-of-freedom angular position servo system which is influenced by multi-disturbance,and its control system consists of stabilizing and tracking components.Stabilizing control is applied to track angular velocity order and control multi-disturbance under airborne condition,and its robustness should be very good;tracking control is applied to compensate tracking error of angular position.A mathematical model is established by taking the control of yaw loop as example.H∞ stabilizing controller is designed by taking the advantage of H∞ control robustness and combining with Kalman filter.A fuzzy control is introduced in general PID control to design a decoupled fuzzy Smith estimating PID controller for tracking control.Simulation research shows that the control effect of airborne electro-optical tracking and sighting system based on fuzzy PID and H∞ control is good,especially when the model parameters change and the multi-disturbance exists,the system capability has little fall,but this system still can effectively track a target.

食品协作机器人动态目标抓取控制方法研究

目的:解决目前协作机器人在食品动态目标抓取中存在的准确性较低问题。方法:基于协作机器人体系结构,提出将模糊自整定PID控制和鲁棒自适应补偿器相结合用于协作机器人食品动态目标抓取。PID结合模糊控制完成参数自整定,鲁棒算法与自适应算法相结合用于系统不确定性补偿。通过试验分析了所提方法的性能,验证了该方法的可行性。结果:所提方法在协作机器人动态目标抓取中具有较好的效果,提高了协作机器人动态抓取的准确性,在传送带速度100 mm/s时,动态抓取成功率达到99.50%,对食品动态目标抓取具有一定的应用价值。结论:通过优化现有目标抓取控制方法,可有效提高协作机器人的抓持精度。

永磁直线同步电机进给系统模糊PID控制

针对永磁直线同步电机(PMLSM)永磁体磁链为常数的特点,对其d-q轴模型进行分析,提出了永磁直线同步电机进给系统的动力学方程。结合传统PID控制和模糊控制的优点,根据永磁直线同步电机直接进给系统的非线性和可能的不确定性因素,建立PID参数自调整的推理规则,设计了永磁直线同步电机进给系统的模糊PID控制器。仿真和实验结果表明,模糊PID控制器与传统PID控制器相比具有更好的动态稳定性和跟踪性能,对外界干扰具有较强的鲁棒性。

基于多级鲁棒PID控制的汽车稳定性控制策略

利用AMESim软件搭建了整车和液压制动系统模型。将基于H∞控制理论的PID控制算法应用于汽车稳定性控制的研究。根据车辆行驶状态的变化调整鲁棒PID控制器的参数,构建以横摆角速度和质心侧偏角为控制目标的汽车稳定性控制算法。进而利用PID控制算法得出制动轮缸压力,实现了整车的稳定性控制。利用Matlab/Simulink和AMESim建立联合仿真平台,对控制算法进行验证。结果表明,该控制算法具有很好的实时性和控制效果,能够满足车辆稳定性控制的要求。

基于遗传算法的协调控制系统鲁棒PID参数寻优

针对火电机组的机炉协调模型,提出一种基于遗传算法的协调控制系统多变量鲁棒PID参数寻优方法.该方法以控制器的设定点跟踪性能为寻优目标,鲁棒性能为约束惩罚条件,采用遗传算法对控制器参数进行寻优.仿真结果表明:与鲁棒H∞控制器降阶后所得到的PID控制器相比,利用本文方法得到的控制器具有更好的负荷设定值跟踪性能,并且具有良好的鲁棒性.