PID tuning rules for SOPDT systems: review and some new results

PID controllers are widely used in industries and so many tuning rules have been proposed over the past 50 years that users are often lost in the jungle of tuning formulas. Moreover, unlike PI control, different control laws and structures of implementation further complicate the use of the PID controller. In this work, five different tuning rules are taken for study to control second-order plus dead time systems with wide ranges of damping coefficients and dead time to time constant ratios (D/tau). Four of them are based on IMC design with different types of approximations on dead time and the other on desired closed-loop specifications (i.e., specified forward transfer function). The method of handling dead time in the IMC type of design is important especially for systems with large D/tau ratios. A systematic approach was followed to evaluate the performance of controllers. The regions of applicability of suitable tuning rules are highlighted and recommendations are also given. It turns out that IMC designed with the Maclaurin series expansion type PID is a better choice for both set point and load changes for systems with D/tau greater than 1. For systems with D/tau less than 1, the desired closed-loop specification approach is favored.     

Enhanced IMC design of load disturbance rejection for integrating and unstable processes with slow dynamics

In view of the deficiencies in existing internal model control (IMC)-based methods for load disturbance rejection for integrating and unstable processes with slow dynamics, a modified IMC-based controller design is proposed to deal with step- or ramp-type load disturbance that is often encountered in engineering practices. By classifying the ways through which such load disturbance enters into the process, analytical controller formulae are correspondingly developed, based on a two-degree-of-freedom (2DOF) control structure that allows for separate optimization of load disturbance rejection from setpoint tracking. An obvious merit is that there is only a single adjustable parameter in the proposed controller, which in essence corresponds to the time constant of the closed-loop transfer function for load disturbance rejection, and can be monotonically tuned to meet a good trade-off between disturbance rejection performance and closed-loop robust stability. At the same time, robust tuning constraints are given to accommodate process uncertainties in practice. Illustrative examples from the recent literature are used to show effectiveness and merits of the proposed method for different cases of load disturbance.     

CONVEX CONTROLLER DESIGN APPLIED TO AC INDUCTION MOTOR TO SATISFY MULTIPLE SIMULTANEOUS SPECIFICATIONS

The application of a closed-loop specification oriented feedback control design method, which addresses the design of controllers to satisfy multiple simultaneous conflicting closed-loop performance specifications is presented. The proposed approach is well suited to the design of controllers which must meet a set of conflicting performance specifications. Gain tuning is central to the design process, however, the tuning process is greatly simplified over that presented by the problem of tuning a PID controller for example. The proposed control method is applied to an AC induction motor, with an inner-loop flux vector controller applied to design a position control system. Experimental results verify the effectiveness of this method.     

基于深度代理模型的叉车臂架液压系统设计优化

为了提升利用微调构造的深度神经网络代理模型(又名深度代理模型)的性能,提出了一种主动闭环蒙特卡罗试验设计方法,通过费雪尔信息矩阵将设计点与模型梯度关联,并利用乘法算法求解,然后引入随机离散蒙特卡罗算法进行闭环采样,使得设计点具有覆盖整个设计空间的统计学特性.基于该方法,利用多层感知器建立了某伸缩臂叉车臂架动作特性深度代...     

One-step receding horizon H(∞) control for networked control systems with random delay and packet disordering

The receding horizon H(∞) control (RHHC) problem is investigated in this paper for a class of networked control systems (NCSs) with random delay and packet disordering. A new model is proposed to describe the NCS with random delay which may be larger than one sampling period. The random delay is modeled as a Markov chain while the closed-loop system is described as a Markovian jump system. Sufficient conditions for the closed-loop NCS to be stochastically stable and the performance index to be upper bounded are derived by using the receding optimization principle. Furthermore, by solving a semi-definite programming (SDP) with linear matrix inequalities (LMIs) constraint, a piecewise-constant receding horizon H(∞) controller is obtained, and the designed piecewise-constant controller ensures that the closed-loop NCS achieves a prescribed H(∞) disturbance attenuation level. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method.     

基于LMI的永磁直线电机H∞鲁棒控制器设计

针对永磁直线同步电机(PMLSM)伺服控制中存在的模型摄动和外部干扰问题,保证闭环控制系统的鲁棒稳定和鲁棒性能,将基于状态反馈的H∞鲁棒控制器应用到永磁直线同步电机的速度环和电流环设计中,通过建立伺服系统鲁棒控制的状态空间模型,将H∞标准设计问题转化为线性矩阵不等式(LMI)的最优解求解问题,利用Matlab LMI工...     

Vehicle active steering control research based on two-DOF robust internal model control

Because of vehicle’s external disturbances and model uncertainties, robust control algorithms have obtained popularity in vehicle stability control. The robust control usually gives up performance in order to guarantee the robustness of the control algorithm, therefore an improved robust internal model control(IMC) algorithm blending model tracking and internal model control is put forward for active steering system in order to reach high performance of yaw rate tracking with certain robustness. The proposed algorithm inherits the good model tracking ability of the IMC control and guarantees robustness to model uncertainties. In order to separate the design process of model tracking from the robustness design process, the improved 2 degree of freedom(DOF) robust internal model controller structure is given from the standard Youla parameterization. Simulations of double lane change maneuver and those of crosswind disturbances are conducted for evaluating the robust control algorithm, on the basis of a nonlinear vehicle simulation model with a magic tyre model. Results show that the established 2-DOF robust IMC method has better model tracking ability and a guaranteed level of robustness and robust performance, which can enhance the vehicle stability and handling, regardless of variations of the vehicle model parameters and the external crosswind interferences. Contradiction between performance and robustness of active steering control algorithm is solved and higher control performance with certain robustness to model uncertainties is obtained.     

Robust controller synthesis for high order unstable processes with time delay using mirror mapping technique

In this note, a general scheme is proposed for the high order unstable delay process with one or more positive poles, using the mirror mapping technique. The Nyquist criteria is employed to establish a systematic methodology to tune the parameter. The stabilizing parameter region could guarantee the prespecified robustness specification. In the scheme, a control law is designed based on the all-pole Padé approximated model. The unstable process was first mapped into a minimum-phase system, and the actual control is obtained by the closed-loop gain shaping algorithm (CGSA). The advantages are that one has a concise design procedure and can achieve good performance such as disturbance rejection and robustness. Finally, three highly cited examples are used to illustrate the effectiveness of the proposed method.     

A novel composite adaptive flap controller design by a high-efficient modified differential evolution identification approach

The optimal tuning of adaptive flap controller can improve adaptive flap control performance on uncertain operating environments, but the optimization process is usually time-consuming and it is difficult to design proper optimal tuning strategy for the flap control system (FCS). To solve this problem, a novel adaptive flap controller is designed based on a high-efficient differential evolution (DE) identification technique and composite adaptive internal model control (CAIMC) strategy. The optimal tuning can be easily obtained by DE identified inverse of the FCS via CAIMC structure. To achieve fast tuning, a high-efficient modified adaptive DE algorithm is proposed with new mutant operator and varying range adaptive mechanism for the FCS identification. A tradeoff between optimized adaptive flap control and low computation cost is successfully achieved by proposed controller. Simulation results show the robustness of proposed method and its superiority to conventional adaptive IMC (AIMC) flap controller and the CAIMC flap controllers using other DE algorithms on various uncertain operating conditions. The high computation efficiency of proposed controller is also verified based on the computation time on those operating cases.     

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.     

光电跟踪系统鲁棒自调整内模控制设计与分析

光电跟踪系统广泛应用于制导武器、航空航天观测设备以及靶场光电测量仪器等领域。针对光电成像测量时滞和模型不确定性,设计了一种鲁棒自调整内模控制算法。给出基于相位裕度和幅值裕度指标的系统控制器整定方程,分析得到了模型失配情况下的系统鲁棒稳定条件以及参数的设计准则,引入基于二次型性能指标的优化方法在线自适应调整控制滤波器参数来提高系统的控制性能和鲁棒性。在光电跟踪转台上的实验结果表明,所设计算法可有效地克服光电图像跟踪器测量时滞所造成的跟踪偏差,跟踪精度小于1密位,保证了成像传感器对目标的快速准确跟踪。     

Extension of IMC tuning correlations for non-self regulating (integrating) processes

The filter term of a PID with Filter controller reduces the impact of measurement noise on the derivative action of the controller. This impact is quantified by the controller output travel defined as the total movement of the controller output per unit time. Decreasing controller output travel is important to reduce wear in the final control element. Internal Model Control (IMC) tuning correlations are widely published for PI, PID, and PID with Filter controllers for self regulating processes. For non-self regulating (or integrating) processes, IMC tuning correlations are published for PI and PID controllers but not for PID with Filter controllers. The important contribution of this work is that it completes the set of IMC tuning correlations with an extension to the PID with Filter controller for non-self regulating processes. Other published correlations (not based upon the IMC framework) for PID with Filter controllers fix the filter time constant at one-tenth the derivative time regardless of the model of the process. In contrast, the novel IMC correlations presented in this paper calculate a filter time constant based upon the model of the process and the user's choice for the closed-loop time constant. The set point tracking and disturbance rejection performance of the proposed IMC tunings is demonstrated using simulation studies and a bench-scale experimental system. The proposed IMC tunings are shown to perform as well as various PID correlations (with and without a filter term) while requiring considerably less controller action.     

Controller design for high-frequency cutting using a piezo-driven microstage

Controller design consists of a feedforward and a feedback controller to support a microstage with flexure hinge structure driven by piezoelectric ceramic actuator for high-frequency nanoscale cutting is developed in this article. The feedforward controller is designed based on a hysteresis dynamic model in order to reduce the nonlinear hysteresis effect of piezoelectric actuator. The position feedback controller is designed based upon an exponentially weighted moving average (EWMA) method embedded in an internal model control (IMC) structure constructing a run-to-run IMC (RtR-IMC) control scheme in order to deal with system bias or modeling inaccuracy. Also, disturbance due to temperature rise will influence actuator's performance, hence an additional compensator is included in the IMC structure. Surfaces dimple micro-machining utilizes piezoelectric-driven microstage for high-speed cutting is selected as an example to investigate system performance. The developed control algorithm is implemented on a DSP-based system to provide 1 kHz operating speed. In experiment, the proposed feedforward and feedback controller is verified to be able to overcome those negative factors efficiently and preserve good positioning accuracy.     

Takagi–Sugeno fuzzy model based robust dissipative control for uncertain flexible spacecraft with saturated time-delay input

In this paper, the problem of robust dissipative control is investigated for uncertain flexible spacecraft based on Takagi–Sugeno (T–S) fuzzy model with saturated time-delay input. Different from most existing strategies, T–S fuzzy approximation approach is used to model the nonlinear dynamics of flexible spacecraft. Simultaneously, the physical constraints of system, like input delay, input saturation, and parameter uncertainties, are also taken care of in the fuzzy model. By employing Lyapunov–Krasovskii method and convex optimization technique, a novel robust controller is proposed to implement rest-to-rest attitude maneuver for flexible spacecraft, and the guaranteed dissipative performance enables the uncertain closed-loop system to reject the influence of elastic vibrations and external disturbances. Finally, an illustrative design example integrated with simulation results are provided to confirm the applicability and merits of the developed control strategy.     

Observer-based reliable stabilization of uncertain linear systems subject to actuator faults,saturation, and bounded system disturbances

A matrix inequality approach is proposed to reliably stabilize a class of uncertain linear systems subject to actuator faults, saturation, and bounded system disturbances. The system states are assumed immeasurable, and a classical observer is incorporated for observation to enable state-based feedback control. Both the stability and stabilization of the closed-loop system are discussed and the closed-loop domain of attraction is estimated by an ellipsoidal invariant set. The resultant stabilization conditions in the form of matrix inequalities enable simultaneous optimization of both the observer gain and the feedback controller gain, which is realized by converting the non-convex optimization problem to an unconstrained nonlinear programming problem. The effectiveness of proposed design techniques is demonstrated through a linearized model of F-18 HARV around an operating point.     

Intelligent modified internal model control for speed control of nonlinear uncertain heavy duty vehicles

The objective of this paper is to control the speed of heavy duty vehicle (HDV) through angular position of throttle valve. Modified internal model control (IMC) schemes with fuzzy supervisor as an adaptive tuning are proposed to control the speed of HDV. Internal model (IM) plays a key role in design of various IMC structures with robust and adaptive features. The motivation to design an IM is to produce nearly stable performance as of the system itself. Clustering algorithm and Hankel approximation based model order reduction techniques are used for the design of suitable IM. The time domain performance specifications such as overshoot, settling time, rise time and integral error performance indices such as the integral of the absolute error and the integral of the square of error are taken into consideration for performance analysis of HDV for various uncertainties.     

Predictive directional compensator for systems with input constraints

Nonlinearity caused by actuator constraint plays a destructive role in the overall performance of a control system. A model predictive controller can handle the problem by implementing a constrained optimization algorithm. Due to the iterative nature of the solution, however, this requires high computation power. In the present work we propose a new method to approach the problem by separating the constraint handling from the predictive control job. The input constraint effects are dealt with in a newly defined component called a predictive directional compensator, which works based on the directionality and predictive concepts. Through implementation of the proposed method, the computational requirement is greatly reduced with the least degradation of the closed-loop performance. Meanwhile, a new characteristic matrix has been defined by which directionality of SISO as well as nonminimum phase systems can be determined.     

基于CAN总线技术的IMC在驱动系统中的运用与实现

依托一种智能分布式系统，基于CAN总线技术来实现增益内模控制，在上位机与各控制节点之间实现了控制通信，并进行了驱动系统闭环实验，实控结果表明较好地解决了因通信周期较长而导致实时控制不好的难题。     

Optimal solution,quantitative performance estimation,and robust tuning of the simplifying controller

Recently, a simplifying controller has been proposed based on the principal of simplification of the control system transfer functions, which offers improved control for processes with a large time delay. It is the purpose of this complementary paper to give a comprehensive analysis on the scheme. First, the relationship among the simplifying controller, the Smith predictor, and the internal model control are discussed. Second, an analytical design procedure is developed based on internal model control (IMC) and optimal solution is derived. Third, the problem of estimating the time domain performance of the closed loop system, quantitatively, is discussed. Fourth, a simple robust tuning procedure is presented. Numerical examples are provided to illustrate the proposed method.