Fractional robust control of main irrigation canals with variable dynamic parameters

A new method is proposed for controlling main irrigation canals with variable dynamical parameters based on robust fractional order controllers. A methodology for designing PID controllers robust to changes in the time delay and the gain is presented first. Then this method is generalized to design fractional controllers that exhibit the same robustness as the previous PID to time delay and gain changes, but are noticeably more robust to variations in the dominant time constant of the process. This method is applied to control main irrigation canals. Extensive numerical simulations using the dynamic model of a real canal were carried out. Then experimental results were obtained in a prototype canal that proved the effectiveness of the proposed control method in terms of performance and robustness.     

Graphical computation of gain and phase margin specifications-oriented robust PID controllers for uncertain systems with time-varying delay

This paper proposes a novel graphical method to compute all feasible gain and phase margin specifications-oriented robust PID controllers to stabilize uncertain control systems with time-varying delay. A virtual gain-phase margin tester compensator is incorporated to guarantee the concerned system with certain robust safety margins. The complex Kharitonov theorem is used to characterize the parametric uncertainties of the considered system and is exploited as a stability criterion for the Hurwitz property of a family of polynomials with complex coefficients varying within given intervals. The coefficients of the characteristic equation are overbounded and eight vertex Kharitonov polynomials are derived to perform stability analysis. The stability equation method and the parameter plane method are exploited to portray constant gain margin and phase margin boundaries. The feasible controllers stabilizing every one of the eight vertex polynomials are identified in the parameter plane by taking the overlapped region of the plotted boundaries. The overlapped region of the useful region of each vertex polynomial is the Kharitonov region, which represents all the feasible specifications-oriented robust PID controller gain sets. Variations of the Kharitonov region with respect to variations of the derivative gain are extensively studied. The way to select representative points from the Kharitonov region for designing robust controllers is suggested. Finally, three illustrative examples with computer simulations are provided to demonstrate the effectiveness and confirm the validity of the proposed methodology. Based on the pre-specified gain and phase margin specifications, a non-conservative Kharitonov region can be graphically identified directly in the parameter plane for designing robust PID controllers.     

参数不确定时滞系统的鲁棒P ID 控制

提出一种简单而有效的参数不确定时滞系统鲁棒PID控制器设计方法．通过在kp-ki平面上绘制稳定边界线,确定稳定的PID控制器参数区域;推导了一阶不稳定时滞系统PI控制器和PID控制器的存在性条件;基于推广到时滞系统的棱边定理,确定所有鲁棒PID控制器参数集．仿真实例表明了该方法的优越性．     

Smith predictor based robust fractional order control: Application to water distribution in a main irrigation canal pool

This paper proposes a new methodology to design fractional integral controllers combined with Smith predictors, which are robust to high frequency model changes. In particular, special attention is paid to time delay changes. These controllers show also less sensitivity to high frequency measurement noise and disturbances than PI or PID controllers. This methodology is applied to design controllers for water distribution in a main irrigation canal pool. Simulated results of standard PI and PID controllers plus a Smith predictor, and the controller developed in this paper are compared when applied to the dynamical model of a real main irrigation canal pool showing that our controller exhibits better and more robust features than these. Moreover our controller is compared with other more complex control techniques as predictive control and robust H_∞ controllers, exhibiting better or similar performances than these.     

一类模糊P I D 控制器的鲁棒优化设计

研究一类模糊 PID控制器的鲁棒设计。以小增益定理分析得到该模糊 PID控制系统稳定性条件。针对参数摄动系统的“最坏点”,用该稳定性条件作为约束 ,采用遗传算法对标称系统的性能进行优化 ,求得优化鲁棒控制器。以倒立摆为例进行鲁棒模糊 PID控制器的设计 ,实验结果表明了该方法的有效性     

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.     

Multi-objective robust PID controller tuning using two lbests multi-objective particle swarm optimization

In this paper, two lbests multi-objective particle swarm optimization (2LB-MOPSO) is applied to design multi-objective robust Proportional-integral-derivative (PID) controllers for two MIMO systems, namely, distillation column plant and longitudinal control system of the super maneuverable F18/HARV fighter aircraft. Multi-objective robust PID controller design problem is formulated by minimizing integral squared error (ISE) and balanced robust performance criteria. During the search, 2LB-MOPSO can focus on small regions in the parameter space in the vicinity of the best existing fronts. As the lbests are chosen from the top fronts in a non-domination sorted external archive of reasonably large size, the offspring obtained can be more diverse with good fitness. The performance of various optimal PID controllers is compared in terms of the sum of ISE and balanced robust performance criteria. For the purpose of comparison, 2LB-MOPSO, NSGA-II as well as earlier reported Riccati, IGA and OSA methods are considered. The performance of PID controllers obtained using 2LB-MOPSO is better than that of others. In addition, Hypervolume-based comparisons are carried out to show the superior performance of 2LB-MOPSO over NSGA-II. The results reveal that 2LB-MOPSO yields better robustness and consistency in terms of the sum of ISE and balanced robust performance criteria than various optimal PID controllers.     

On the synthesis of robust PID controllers for plants with structured and unstructured uncertainty

In this paper, we consider the problems of synthesizing PID controllers for robust stability and performance for a given linear time‐invariant plant subject to both parametric and H_∞‐norm‐bounded perturbations. Using results from the area of parametric robust control, synthesis problems are converted into simultaneous stabilization of a family of complex segment polynomials. The results on H_∞ PID synthesis are then used to devise a design procedure for determining the admissible PID gain values. One of the important features of the proposed method is that it constructively characterizes the approximated set of all admissible PID controllers. This characterization can facilitate the optimal design of any additional design requirements. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust ℋ︁∞ PID control for multivariable networked control systems with disturbance/noise attenuation

In this paper, we study the design problem of PID controllers for networked control systems (NCSs) with polyhedral uncertainties. The load disturbance and measurement noise are both taken into account in the modeling to better reflect the practical scenario. By using a novel technique, the design problem of PID controllers is converted into a design problem of output feedback controllers. Our goal of this paper is two‐fold: (1) To design the robust PID tracking controllers for practical models; (2) To develop the robust ??_∞ PID control such that load and reference disturbances can be attenuated with a prescribed level. Sufficient conditions are derived by employing advanced techniques for achieving delay dependence. The proposed controller can be readily designed based on iterative suboptimal algorithms. Finally, four examples are presented to show the effectiveness of the proposed methods. Copyright © 2011 John Wiley & Sons, Ltd.     

基于H∞回路成形的鲁棒PID参数整定

积分过程在工业过程控制中经常遇到,采用常规的PID参数整定方法很难得到理想的控制效果。本文采用基于H∞回路成形的鲁棒PID参数整定方法,实现对积分过程的有效控制。通过Simulink软件的仿真结果表明该方法的有效性。     

Model-based robust control design and experimental validation of collaborative industrial robot system with uncertainty

Based on the traditional PID control and robust control algorithm, a novel practical robust control method is designed for the 6-DOF collaborative industrial robot with uncertainty. The proposed algorithm consists of a robust term and a model-based PD control term, which we call MPDP controller. It is demonstrated by Lyapunov theoretical analysis that the algorithm is able to guarantee uniform boundedness and uniform ultimate boundedness of the system. Simulations and experiments show the good performance of MPDP control in a robot with smaller steady-state tracking errors and better robustness compared to PID controllers.     

Online tuning fuzzy PID controller using robust extended Kalman filter

Fuzzy PID controllers have been developed and applied to many fields for over a period of 30 years. However, there is no systematic method to design membership functions (MFs) for inputs and outputs of a fuzzy system. Then optimizing the MFs is considered as a system identification problem for a nonlinear dynamic system which makes control challenges. This paper presents a novel online method using a robust extended Kalman filter to optimize a Mamdani fuzzy PID controller. The robust extended Kalman filter (REKF) is used to adjust the controller parameters automatically during the operation process of any system applying the controller to minimize the control error. The fuzzy PID controller is tuned about the shape of MFs and rules to adapt with the working conditions and the control performance is improved significantly. The proposed method in this research is verified by its application to the force control problem of an electro-hydraulic actuator. Simulations and experimental results show that proposed method is effective for the online optimization of the fuzzy PID controller.     

Backstepping approach for design of PID controller with guaranteed performance for micro-air UAV

Flight controllers for micro-air UAVs are generally designed using proportional-integral-derivative (PID) methods, where the tuning of gains is difficult and time-consuming, and performance is not guaranteed. In this paper, we develop a rigorous method based on the sliding mode analysis and nonlinear backstepping to design a PID controller with guaranteed performance. This technique provides the structure and gains for the PID controller, such that a robust and fast response of the UAV (unmanned aerial vehicle) for trajectory tracking is achieved. First, the second-order sliding variable errors are used in a rigorous nonlinear backstepping design to obtain guaranteed performance for the nonlinear UAV dynamics. Then, using a small angle approximation and rigorous geometric manipulations, this nonlinear design is converted into a PID controller whose structure is naturally determined through the backstepping procedure. PID gains that guarantee robust UAV performance are finally computed from the sliding mode gains and from stabilizing gains for tracking error dynamics. We prove that the desired Euler angles of the inner attitude controller loop are related to the dynamics of the outer backstepping tracker loop by inverse kinematics, which provides a seamless connection with existing built-in UAV attitude controllers. We implement the proposed method on actual UAV, and experimental flight tests prove the validity of these algorithms. It is seen that our PID design procedure yields tighter UAV performance than an existing popular PID control technique.     

Robust PID controller tuning based on the constrained particle swarm optimization

This paper proposes a novel tuning strategy for robust proportional-integral-derivative (PID) controllers based on the augmented Lagrangian particle swarm optimization (ALPSO). First, the problem of PID controller tuning satisfying multiple H_∞ performance criteria is considered, which is known to suffer from computational intractability and conservatism when any existing method is adopted. In order to give some remedy to such a design problem without using any complicated manipulations, the ALPSO based robust gain tuning scheme for PID controllers is introduced. It does not need any conservative assumption unlike the conventional methods, and often enables us to find the desired PID gains just by solving the constrained optimization problem in a straightforward way. However, it is difficult to guarantee its effectiveness in a theoretical way, because PSO is essentially a stochastic approach. Therefore, it is evaluated by several simulation examples, which demonstrate that the proposed approach works well to obtain PID controller parameters satisfying the multiple H_∞ performance criteria.     

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。     

PID controller design for robust performance

This note is devoted to the problem of synthesizing proportional-integral-derivative (PID) controllers for robust performance for a given single-input-single-output plant in the presence of uncertainty. First, the problem of robust performance design is converted into simultaneous stabilization of a complex polynomial family. An extension of the results on PID stabilization is then used to devise a linear programming design procedure for determining all admissible PID gain settings. The most important feature of the proposed approach is that it computationally characterizes the entire set of the admissible PID gain values for an arbitrary plant.     

Multivariable PID control with set-point weighting via BMI optimisation

The paper focuses on the design of multivariable PID controllers with set-point weighting. The advantage of this PID structure is that the responses of the system to disturbances and to changes in the set-point can be adjusted separately. The proposed design methods rely on the transformation of the tuning of the controller gains into a static output feedback (SOF) problem. Hence, multivariable PID controllers can be designed by solving an optimisation problem with bilinear matrix inequalities (BMIs). The paper addresses the design of both time-invariant and gain-scheduled robust controllers. All of the tuning methods discussed through the paper are based on a PID structure with filtered derivative term, thus guaranteeing the well-posedness of the closed loop system.     

Design of a memory‐based prefilter supplementing a robust PID control system

For systems with uncertainties, lots of PID parameter tuning methods have been proposed from the view point of the robust stability theory. However, the control performance becomes conservative using robust PID controllers. In this paper, a new two‐degree‐of‐freedom (2DOF) controller, which can improve the tracking properties, is proposed for nonlinear systems. According to the proposed method, the prefilter is designed as the PD compensator whose control parameters are tuned by the idea of a memory‐based modeling (MBM) method. Since the MBM method is a type of local modeling methods for nonlinear systems, PD parameters can be tuned adequately in an online manner corresponding to nonlinear properties. Finally, the effectiveness of the newly proposed control scheme is numerically evaluated on a simulation example. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于改进Smith预估控制结构的二自由度PID控制

针对工业过程中的二阶不稳定时滞过程, 基于改进史密斯预估控制结构提出了一种简单的两自由度控制方案.设定值跟踪控制器和扰动抑制控制器采用同一设计程序, 并基于内模控制原理提出了控制器解析设计方案.设定值跟踪控制器和抗扰动控制器可分别通过单性能参数独立调节和优化, 每个控制器都具有PID形式, 给出了控制器调整参数的选择范围和扰动抑制闭环保证鲁棒稳定性的条件.仿真实例验证了提出方法对于近期其他方法的优越性.