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.     

Nominal and robust stability regions of optimization-based PID controllers

In recent decades, several optimization-based methods have been developed for the proportional-integral-derivative (PID) controller design, and the common feature of these methods is that the controller has only one adjustable parameter. To keep the closed-loop systems stable is an essential requirement for the optimization-based PID controllers. In almost all these methods, however, no exact stability region for the single adjustable parameter was sketched. In this paper, using the proposed analytical procedure based on the dual-locus diagram technique, explicit stability regions of the optimization-based PID controllers are derived for stable, integrating, and unstable processes with time delay in the nominal and perturbed cases, respectively. It is revealed that the proposed analytical procedure is effective for the determination of the nominal and robust stability regions and it offers simplicity and ease of mathematical calculations over other available stability analysis methods. The results in this paper provide some insight into the tuning of the optimization-based PID controllers.     

PD plus error-dependent integral nonlinear controllers for robot manipulators with an uncertain Jacobian matrix

In framework of traditional PID controllers, there are only three parameters available to tune, as a result, performance of the resulting system is always limited. As for Cartesian regulation of robot manipulators with uncertain Jacobian matrix, a scheme of PID controllers with error-dependent integral action is proposed. Compare with traditional PID controllers, the error-dependent integration is employed in the proposed PID controller, in which more parameters are available to be tuned. It provides additional flexibility for controller characteristics and tuning as well, and hence makes better transient performance. In addition, asymptotic stability of the resulting closed-loop system is guaranteed. All signals in the system are bounded when exogenous disturbances and measurement noises are bounded. Numerical example demonstrates the superior transient performance of the proposed controller over the traditional one via Cartesian space set-point manipulation of two-link robotic manipulator.     

PID controller auto-tuning based on process step response and damping optimum criterion

This paper presents a novel method of PID controller tuning suitable for higher-order aperiodic processes and aimed at step response-based auto-tuning applications. The PID controller tuning is based on the identification of so-called n-th order lag (PTn) process model and application of damping optimum criterion, thus facilitating straightforward algebraic rules for the adjustment of both the closed-loop response speed and damping. The PTn model identification is based on the process step response, wherein the PTn model parameters are evaluated in a novel manner from the process step response equivalent dead-time and lag time constant. The effectiveness of the proposed PTn model parameter estimation procedure and the related damping optimum-based PID controller auto-tuning have been verified by means of extensive computer simulations.     

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.     

Stabilization and PID tuning algorithms for second-order unstable processes with time-delays

Open-loop unstable systems with time-delays are often encountered in process industry, which are often more difficult to control than stable processes. In this paper, the stabilization by PID controller of second-order unstable processes, which can be represented as second-order deadtime with an unstable pole (SODUP) and second-order deadtime with two unstable poles (SODTUP), is performed via the necessary and sufficient criteria of Routh-Hurwitz stability analysis. The stability analysis provides improved understanding on the existence of a stabilizing range of each PID parameter. Three simple PID tuning algorithms are proposed to provide desired closed-loop performance-robustness within the stable regions of controller parameters obtained via the stability analysis. The proposed PID controllers show improved performance over those derived via some existing methods.     

An effective frequency domain approach to tuning non-PID controllers for high performance

In this paper, a new tuning method is proposed for the design of non-PID controllers for complex processes to achieve high performance. Compared with the existing PID tuning methods, the proposed non-PID controller design method can yield better performance for a wide range of complex processes. A suitable objective transfer function for the closed-loop system is chosen according to process characteristics. The corresponding ideal controller is derived. Model reduction is applied to fit the ideal controller into a much simpler and realizable form. Stability analysis is given and simulation examples are provided to demonstrate the effectiveness of the proposed method.     

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.     

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.     

Performance-based parameter tuning method of model-driven PID control systems

In this paper, performance-based parameter tuning method of model-driven Two-Degree-of-Freedom PID (MD TDOF PID) control system has been proposed to enhance the control performances of a process. Known for its ability of stabilizing the unstable processes, fast tracking to the change of set points and rejecting disturbance, the MD TDOF PID has gained research interest recently. The tuning methods for the reported MD TDOF PID are based on internal model control (IMC) method instead of optimizing the performance indices. In this paper, an Integral of Time Absolute Error (ITAE) zero-position-error optimal tuning and noise effect minimizing method is proposed for tuning two parameters in MD TDOF PID control system to achieve the desired regulating and disturbance rejection performance. The comparison with Two-Degree-of-Freedom control scheme by modified smith predictor (TDOF CS MSP) and the designed MD TDOF PID tuned by the IMC tuning method demonstrates the effectiveness of the proposed tuning method.     

基于LQR指标的直线伺服系统最优PID控制器设计

由音圈电动机驱动的直线伺服系统是实现非圆截面类零件数控车削加工的关键。基于二次型性能指标（LQR）设计了直线伺服系统的最优PID控制器。首先给出了直线伺服系统的双闭环PID控制结构，其次研究了基于二次型性能指标的数字PID参数最优整定方法。最后通过仿真实验验证了该控制方法的有效性。     

0.6MN自由锻造液压机力闭环控制系统性能分析

为提高锻件性能和材料利用率,研究了锻造液压机的工作原理,并建立其数学模型,采用频域分析方法,研究负载刚度对力控系统特性的影响。利用AMESim与MATLAB/Simulink建立协同仿真平台,分析系统动态性能,同时分别引入PID控制器、积分分离控制器以及模糊PID控制器分析研究其对于0.6MN自由锻造液压机力闭环控制性能的影响,并通过实验验证仿真结果的正确性。     

Robust control for a biaxial servo with time delay system based on adaptive tuning technique

A robust control method for synchronizing a biaxial servo system motion is proposed in this paper. A new network based cross-coupled control and adaptive tuning techniques are used together to cancel out the skew error. The conventional fixed gain PID cross-coupled controller (CCC) is replaced with the adaptive cross-coupled controller (ACCC) in the proposed control scheme to maintain biaxial servo system synchronization motion. Adaptive-tuning PID (APID) position and velocity controllers provide the necessary control actions to maintain synchronization while following a variable command trajectory. A delay-time compensator (DTC) with an adaptive controller was augmented to set the time delay element, effectively moving it outside the closed loop, enhancing the stability of the robust controlled system. This scheme provides strong robustness with respect to uncertain dynamics and disturbances. The simulation and experimental results reveal that the proposed control structure adapts to a wide range of operating conditions and provides promising results under parameter variations and load changes.     

基于改进遗传算法的气体混合控制系统的设计与仿真

针对传统气体混合存在精度低、混合时间长等问题,研究了以质量流量控制器为主的气体混合系统,设计了改进遗传算法整定PID参数的控制系统。利用模式识别建立了系统数学模型,针对标准遗传算法的缺陷,设计了一种改进比例选择算子并提出自适应法调整交叉、变异概率。进行仿真实验验证改进遗传算法优化PID控制系统的控制性能。实验结果表明,相比标准遗传算法和Z-N法优化PID,基于改进遗传算法优化PID控制系统具有更高的控制精度以及更快的混合时间。     

变频泵控预应力张拉设备的自适应模糊PID张拉力控制

为提高预应力张拉设备对工程现场的适应性与可靠性,设计了一种基于变频电机驱动定量泵的张拉力控制系统。基于该液压系统建立其数学模型,针对该变频液压控制系统的非线性与参数时变性,提出了应用自适应模糊PID控制算法解决常规PID控制的适应性问题,并基于专家经验给出了模糊集及模糊整定规则,选取了合理的PID参数论域取值。利用MATLAB/Simulink对该控制系统进行了仿真研究,通过实验对该算法的控制效果进行了验证。由仿真与实验结果可知,自适应模糊PID控制能够减小超调量,缩短调整时间,能够有效提高张拉力变频泵控系统的动态响应与稳态性能。     

基于遗传算法的PID控制器参数优化研究

本文提出了一种基于遗传算法的PID控制器参数优化设计。在参数整定与优化过程中。考虑了过程控制系统的参数整定特点和寻优精度。通过仿真研究表明：该方法比一般PID参数整定方法具有更好的控制性能指标。     

Robust fast controller design via nonlinear fractional differential equations

A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods.     

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。     

金属板材加工张力控制的模糊PID方法

针对金属板材加工张力PID控制参数频繁调整的问题,采用现代模糊理论与PID控制算法相结合,给出一种基于板材加工的模糊PID张力控制方法。文章在简要介绍张力控制系统基本框架的基础上,着重描述PID参数调整原则及模糊PID控制器的整个设计过程。经过仿真分析与实际试运行表明,所设计的模糊PID张力控制算法有效可行,系统不仅实现了在线自整定PID参数的目的,而且具有较好的自适应能力,控制效果比较理想。     

H(infinity) PID controller design for runaway processes with time delay

This paper presents an efficient method for designing proportional-integra-derivative (PID) controllers for runaway processes with time delay. The method is developed based on the H(infinity) control theory in frequency domain. The constraints imposed by the internal stability and asymptotic properties of the closed-loop system are first investigated, a new procedure is then developed for analytically designing the controller, and simple design formulas are obtained. It is shown that the new controller can be designed to meet specified time domain performances. Typical design examples are provided to illustrate the proposed method.