A 2-Dof LQR based PID controller for integrating processes considering robustness/performance tradeoff

This paper focuses on the analytical design of a Proportional Integral and Derivative (PID) controller together with a unique set point filter that makes the overall Two-Degree of-Freedom (2-Dof) control system for integrating processes with time delay. The PID controller tuning is based on the Linear Quadratic Regulator (LQR) using dominant pole placement approach to obtain good regulatory response. The set point filter is designed with the calculated PID parameters and using a single filter time constant (λ) to precisely control the servo response. The effectiveness of the proposed methodology is demonstrated through a series of illustrative examples using real industrial integrated process models. The whole range of PID parameters is obtained for each case in a tradeoff between the robustness of the closed loop system measured in terms of Maximum Sensitivity (M_s) and the load disturbance measured in terms of Integral of Absolute Errors (IAE). Results show improved closed loop response in terms of regulatory and servo responses with less control efforts when compared with the latest PID tuning methods of integrating systems.     

基于遗传算法的PID整定在液位控制中的应用

以IAE为优化目标,将遗传算法优化PID参数,应用于一单容水箱的液位控制系统中,并给出了算法的仿真结果。研究表明,遗传算法得到较好性能指标的搜索结果,对参数整定优化策略具有很强的灵活性、适应性和鲁棒性,具有一定的推广应用价值。     

液压机械手电液比例系统模糊PID控制研究

针对液压机械手的电液比例系统存在较大程度的系统参数变化和负载干扰等特点,一般控制方法难以全部满足性能要求。常规PID控制方法虽然算法简单、可靠性好、鲁棒性高,但由于参数整定繁杂,往往造成参数整定不良、性能欠佳、适用性能差。为了改善这些缺陷,将模糊控制理论与PID控制理论相结合,设计了模糊PID控制器,实现了对PID参数的在线整定。利用MATLAB/Simulink进行仿真,比较常规PID控制与模糊PID控制下电液比例系统的控制效果,发现模糊PID控制器较好地克服了系统的非线性和负载干扰的影响,提高了系统的稳定性和动态性能。     

Classical controller design techniques for fractional order case

This paper presents some classical controller design techniques for the fractional order case. New robust lag, lag-lead, PI controller design methods for control systems with a fractional order interval transfer function (FOITF) are proposed using classical design methods with the Bode envelopes of the FOITF. These controllers satisfy the robust performance specifications of the fractional order interval plant. In order to design a classical PID controller, an optimization technique based on fractional order reference model is used. PID controller parameters are obtained using the least squares optimization method. Different PID controller parameters that satisfy stability have been obtained for the same plant.     

大型卧式仿真转台智能化同步—干扰控制

针对大型卧式液压仿真转台内部双液压马达摩擦力矩干扰、负载干扰和外框双液压马达同步驱动这三个影响转台控制性能的主要问题,分析并总结出转台外框双液压马达在“等同模式”和“主从模式”下的同步驱动模糊控制规则、各种同步控制模式的应用范围和切换规律;根据PID控制经验制定出直接自适应模糊控制规则。依据同步与PID模糊控制规则设计出同步—干扰模糊控制器并进行仿真分析。针对模糊控制器自学习能力较差等缺陷,在模糊控制的基础上,采用模糊神经网络(FNN)模型设计出多输入多输出(MIMO)的转台FNN控制器。软件仿真结果表明,当转台液压马达摩擦力矩发生变化、负载大范围波动或当转台外框两马达转速相差较大时,使用模糊神经网络模型的智能化转台控制系统具有较高的定位精度和动态性能。     

A novel optimized hybrid fuzzy logic intelligent PID controller for an interconnected multi-area power system with physical constraints and boiler dynamics

In the fast developing world nowadays, load frequency control (LFC) is considered to be a most significant role for providing the power supply with good quality in the power system. To deliver a reliable power, LFC system requires highly competent and intelligent control technique. Hence, in this article, a novel hybrid fuzzy logic intelligent proportional-integral-derivative (FLiPID) controller has been proposed for LFC of interconnected multi-area power systems. A four-area interconnected thermal power system incorporated with physical constraints and boiler dynamics is considered and the adjustable parameters of the FLiPID controller are optimized using particle swarm optimization (PSO) scheme employing an integral square error (ISE) criterion. The proposed method has been established to enhance the power system performances as well as to reduce the oscillations of uncertainties due to variations in the system parameters and load perturbations. The supremacy of the suggested method is demonstrated by comparing the simulation results with some recently reported heuristic methods such as fuzzy logic proportional-integral (FLPI) and intelligent proportional-integral-derivative (PID) controllers for the same electrical power system. the investigations showed that the FLiPID controller provides a better dynamic performance and outperform compared to the other approaches in terms of the settling time, and minimum undershoots of the frequency as well as tie-line power flow deviations following a perturbation, in addition to perform appropriate settlement of integral absolute error (IAE). Finally, the sensitivity analysis of the plant is inspected by varying the system parameters and operating load conditions from their nominal values. It is observed that the suggested controller based optimization algorithm is robust and perform satisfactorily with the variations in operating load condition, system parameters and load pattern.     

基于粒子群算法液压伺服系统PID参数的优化

PID控制器在液压伺服系统中得到广泛的应用。为了有效地寻找液压伺服系统的最佳PID控制器参数,提出一种基于粒子群算法的PID参数优化策略。通过建立PSO-PID控制器参数模型,对PID控制器的参数进行实时优化;利用MATLAB对系统进行仿真,结果显示在液压伺服系统的工况相同时．新型控制器能取得满意的控制效果。     

电液伺服扭振试验机模糊PID控制仿真研究

为提高电液伺服扭振试验机控制系统抗参数变化和干扰的能力,保证控制精度,提出了应用于本试验机控制系统的模糊PID控制。首先根据控制系统结构原理建立了控制对象的数学模型。然后设计了模糊PID控制器,使用正交试验法对PID控制参数进行整定,以获得较优的PID控制参数,同时使用模糊控制器对PID的控制效果加以修正。最后利用MATLAB／Simulink对控制系统进行了仿真。仿真结果表明：模糊PID控制对于参数的变化和干扰,能实现控制参数的自调整．具有较好的控制效果。     

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.     

阀控非对称伺服缸基于粒子群优化的模糊PID控制器研究

针对阀控非对称伺服缸非线性、参数时变的特点,考虑到油液压缩特性的影响,建立了包含变体积弹性模量的系统数学模型。提出一种基于粒子群算法优化(PSO)的模糊自适应PID控制方法(简称PSO_FPID)。模糊逻辑推理在线调整PID控制器的比例、积分和微分系数,以粒子群算法实现对模糊控制比例因子和量化因子的参数寻优,两种方法的组合保证了系统最佳参数匹配下的自适应控制。同时,利用AMESim与Simulink联合仿真研究不同含气量的阀控缸模型在传统PID与PSO_FPID两种控制方法下的动态响应特性。结果表明:PSO_FPID综合了PID控制器高精度的优点和模糊控制器快速、适应性强的特点,能够有效抑制油液动态压缩特性的非线性影响,使系统具有良好的动、稳态特性。     

Indirect predictive type-2 fuzzy neural network controller for a class of nonlinear input - delay systems

In this paper a new indirect type-2 fuzzy neural network predictive (T2FNNP) controller has been proposed for a class of nonlinear systems with input-delay in presence of unknown disturbance and uncertainties. In this method, the predictor has been utilized to estimate the future state variables of the controlled system to compensate for the time-varying delay. The T2FNN is used to estimate some unknown nonlinear functions to construct the controller. By introducing a new adaptive compensator for the predictor and controller, the effects of the external disturbance, estimation errors of the unknown nonlinear functions, and future sate estimation errors have been eliminated. In the proposed method, using an appropriate Lyapunov function, the stability analysis as well as the adaptation laws is carried out for the T2FNN parameters in a way that all the signals in the closed-loop system remain bounded and the tracking error converges to zero asymptotically. Moreover, compared to the related existence predictive controllers, as the number of T2FNN estimators are reduced, the computation time in the online applications decreases. In the proposed method, T2FNN is used due to its ability to effectively model uncertainties, which may exist in the rules and data measured by the sensors. The proposed T2FNNP controller is applied to a nonlinear inverted pendulum and single link robot manipulator systems with input time-varying delay and compared with a type-1 fuzzy sliding predictive (T1FSP) controller. Simulation results indicate the efficiency of the proposed T2FNNP controller.     

Evolutionary optimization of sliding mode controller for level control system

This paper accords the level control of single-input-single-output (SISO) level control system based on the fusion of sliding mode control (SMC) and evolutionary techniques or bio-inspired techniques. The non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective particle swarm optimization (MOPSO) are considered as two evolutionary techniques. Here, a comparative analysis of performances of an optimal proportional–integral (PI) controller, proportional–integral–derivative (PID) controller, conventional SMC, NSGA-II based tuned SMC and SMC parameter tuning using MOPSO algorithm has been carried out through MATLAB/SIMULINK. The objective functions, integral absolute error (IAE), integral squared error (ISE) and an integration of weighted objective function aggregated approach of the error performance indices, IAE and ISE are considered. Realistic conditions are used in a plant for testing the robustness of controller. The stability of the controller is successfully obtained which satisfies the Lyapunov stability criteria. Reduction in long settling time with tiny magnitude variations about an equilibrium point is achieved using bio-inspired techniques. The simulation as well as experimental results reveal that SMC parameter tuning based on NSGA-II algorithm gives a better performance as compared to the other design strategies.     

Simple PID parameter tuning method based on outputs of the closed loop system

Most of the existing PID parameters tuning methods are only effective with pre-known accurate system models, which often require some strict identification experiments and thus infeasible for many complicated systems. Actually, in most practical engineering applications, it is desirable for the PID tuning scheme to be directly based on the input-output response of the closed-loop system. Thus, a new parameter tuning scheme for PID controllers without explicit mathematical model is developed in this paper. The paper begins with a new frequency domain properties analysis of the PID controller. After that, the definition of characteristic frequency for the PID controller is given in order to study the mathematical relationship between the PID parameters and the open-loop frequency properties of the controlled system. Then, the concepts of M-field and θ-field are introduced, which are then used to explain how the PID control parameters influence the closed-loop frequency-magnitude property and its time responses. Subsequently, the new PID parameter tuning scheme, i.e., a group of tuning rules, is proposed based on the preceding analysis. Finally, both simulations and experiments are conducted, and the results verify the feasibility and validity of the proposed methods. This research proposes a PID parameter tuning method based on outputs of the closed loop system.     

New tuning method for PID controller

In this paper, a tuning method for proportional-integral-derivative (PID) controller and the performance assessment formulas for this method are proposed. This tuning method is based on a genetic algorithm based PID controller design method. For deriving the tuning formula, the genetic algorithm based design method is applied to design PID controllers for a variety of processes. The relationship between the controller parameters and the parameters that characterize the process dynamics are determined and the tuning formula is then derived. Using simulation studies, the rules for assessing the performance of a PID controller tuned by the proposed method are also given. This makes it possible to incorporate the capability to determine if the PID controller is well tuned or not into an autotuner. An autotuner based on this new tuning method and the corresponding performance assessment rules is also established. Simulations and real-time experimental results are given to demonstrate the effectiveness and usefulness of these formulas.     

FUZZY NEURAL NETWORK CONTROL FOR VIBRATION WAVEFORM SYSTEM OF MOLD

Combining with the characteristic of the fuzzy control and the neural network control(NNC), a new kind of the fuzzy neural network controller is proposed, and the synthesis design method of the control law and fast speed learning algorithm of the parameters of networks are put forward. The output of the controller is composed of two parts, part one is derived on basis of the principle of sliding control, the lower order model and the estimated parameters of the plant are only required, part two is derived on basis FNN, it is used to compensate the uncertainties of the systems. Because new type of FNN controller extracts from the advantages of the intelligent control and model based sliding mode control, the numbers of adjusting parameters and the structure of FNN are simplified at large, and the practical significance and variation range are attached to each layer of the network and its connected weights, the control performance and learning speed are increased at large. The lightness of the conclusions     

A novel auto-tuning PID control mechanism for nonlinear systems

In this paper, a novel Runge–Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence.     

A frequency response model matching method for PID controller design for processes with dead-time

In this paper, a PID controller design method for the integrating processes based on frequency response matching is presented. Two approaches are proposed for the controller design. In the first approach, a double feedback loop configuration is considered where the inner loop is designed with a stabilizing gain. In the outer loop, the parameters of the PID controller are obtained by frequency response matching between the closed-loop system with the PID controller and a reference model with desired specifications. In the second approach, the design is directly carried out considering a desired load-disturbance rejection model of the system. In both the approaches, two low frequency points are considered for matching the frequency response, which yield linear algebraic equations, solution of which gives the controller parameters. Several examples are taken from the literature to demonstrate the effectiveness and to compare with some well known design methods.     

Modeling and control of the magnetic suspension system

A fuzzy logic based controller applied to a simple magnetic suspension is presented in this paper. The simple electromagnet-ball system and the contactless optical position measurement system are developed as a physical model of the magnetic suspension. A nonlinear mathematical model is presented and linearized. This model has been used to design a discrete linear PID controller with optimal parameters. The physical real-time model was constructed in order to compare the performance of the linear discrete PID controller and the proposed fuzzy logic based PID controller. The decomposed fuzzy PID controller has proportional, integral, and derivative separate parts which are tuned independently. When testing it becomes clear that the decomposed fuzzy PID controller gives better performance over a typical operational range than a traditional linear PID controller.     

基于MATLAB的高速公路隧道通风控制系统仿真研究

高速公路长大隧道的通风控制具有非线性及大滞后等问题,运用传统控制方法已不能满足系统的精度要求;因此,提出采取RBF-PID控制方法,通过RBF神经网络整定PID控制器的参数,以达到要求的控制指标。运用MATLAB仿真软件,分别建立基于传统PID控制器和RBF-PID控制器的系统模型,并进行仿真对比。结果表明,RBF-PID控制器比传统的PID控制器对系统输入的响应更加精确,具有最大绝对误差值较小和无负误差的优点,能更有效地解决高速公路长大隧道的通风控制非线性及大滞后的问题。     

Determination of all feasible robust PID controllers for open-loop unstable plus time delay processes with gain margin and phase margin specifications

This paper proposes a novel alternative method to graphically compute all feasible gain and phase margin specifications-oriented robust PID controllers for open-loop unstable plus time delay (OLUPTD) processes. This method is applicable to general OLUPTD processes without constraint on system order. To retain robustness for OLUPTD processes subject to positive or negative gain variations, the downward gain margin (GM_down), upward gain margin (GM_up), and phase margin (PM) are considered. A virtual gain-phase margin tester compensator is incorporated to guarantee the concerned system satisfies certain robust safety margins. In addition, the stability equation method and the parameter plane method are exploited to portray the stability boundary and the constant gain margin (GM) boundary as well as the constant PM boundary. The overlapping region of these boundaries is graphically determined and denotes the GM and PM specifications-oriented region (GPMSOR). Alternatively, the GPMSOR characterizes all feasible robust PID controllers which achieve the pre-specified safety margins. In particular, to achieve optimal gain tuning, the controller gains are searched within the GPMSOR to minimize the integral of the absolute error (IAE) or the integral of the squared error (ISE) performance criterion. Thus, an optimal PID controller gain set is successfully found within the GPMSOR and guarantees the OLUPTD processes with a pre-specified GM and PM as well as a minimum IAE or ISE. Consequently, both robustness and performance can be simultaneously assured. Further, the design procedures are summarized as an algorithm to help rapidly locate the GPMSOR and search an optimal PID gain set. Finally, three highly cited examples are provided to illustrate the design process and to demonstrate the effectiveness of the proposed method.