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.     

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.     

卡尔曼滤波器在PID控制器中的应用研究

本文建立球杆系统模型并分析系统中噪声,采用卡尔曼滤波器来克服球杆系统中的测量噪声和控制噪声对控制性能的影响,并在MATLAB环境下进行对比仿真试验,验证了滤波器对噪声的有效抑制作用。     

Dominant pole placement with fractional order PID controllers: D-decomposition approach

Dominant pole placement is a useful technique designed to deal with the problem of controlling a high order or time-delay systems with low order controller such as the PID controller. This paper tries to solve this problem by using D-decomposition method. Straightforward analytic procedure makes this method extremely powerful and easy to apply. This technique is applicable to a wide range of transfer functions: with or without time-delay, rational and non-rational ones, and those describing distributed parameter systems. In order to control as many different processes as possible, a fractional order PID controller is introduced, as a generalization of classical PID controller. As a consequence, it provides additional parameters for better adjusting system performances. The design method presented in this paper tunes the parameters of PID and fractional PID controller in order to obtain good load disturbance response with a constraint on the maximum sensitivity and sensitivity to noise measurement. Good set point response is also one of the design goals of this technique. Numerous examples taken from the process industry are given, and D-decomposition approach is compared with other PID optimization methods to show its effectiveness.     

Tuning PID controllers for higher-order oscillatory systems with improved performance

In this paper, model based design of PID controllers is proposed for higher-order oscillatory systems. The proposed method has no limitations regarding systems order, time delays and oscillatory behavior. The reduced model is achieved based on third-order modeling and selection of coefficients through the use of frequency responses. The tuning of the PID parameters are obtained from a reduced third-order model; the procedure seems to be simple and effective, and improved performance of the overall system can be achieved. Three simulation examples and one real-time experiment are included to demonstrate the effectiveness and applicability of the proposed method to systems with oscillatory behavior.     

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.     

An improved auto-tuning scheme for PID controllers

An improved auto-tuning scheme is proposed for Ziegler–Nichols (ZN) tuned PID controllers (ZNPIDs), which usually provide excessively large overshoots, not tolerable in most of the situations, for high-order and nonlinear processes. To overcome this limitation ZNPIDs are upgraded by some easily interpretable heuristic rules through an online gain modifying factor defined on the instantaneous process states. This study is an extension of our earlier work [Mudi RK., Dey C. Lee TT. An improved auto-tuning scheme for PI controllers. ISA Trans 2008; 47: 45–52] to ZNPIDs, thereby making the scheme suitable for a wide range of processes and more generalized too. The proposed augmented ZNPID (AZNPID) is tested on various high-order linear and nonlinear dead-time processes with improved performance over ZNPID, refined ZNPID (RZNPID), and other schemes reported in the literature. Stability issues are addressed for linear processes. Robust performance of AZNPID is observed while changing its tunable parameters as well as the process dead-time. The proposed scheme is also implemented on a real time servo-based position control system.     

一类时滞系统的PID稳定控制器设计

针对工业控制过程中常见的时滞系统,给出了快速计算PI和PID控制器所有稳定参数集的方法。推导了系统开环不稳定情形下稳定控制器存在的必要性条件．通过在该稳定参数区域上进行性能指标寻优,可以得到满足控制器设计性能指标要求的PID控制器参数区域。仿真实例表明了该方法的优越性。     

Thermal response simulation for tuning PID controllers in a 1016 mm guarded hot plate apparatus

A mathematical model has been developed and used to simulate the controlled thermal performance of a large guarded hot-plate apparatus. This highly specialized apparatus comprises three interdependent components whose temperatures are closely controlled in order to measure the thermal conductivity of insulation materials. The simulation model was used to investigate control strategies and derive controller gain parameters that are directly transferable to the actual instrument. The simulations take orders-of-magnitude less time to carry out when compared to traditional tuning methods based on operating the actual apparatus.The control system consists primarily of a PC-based PID control algorithm that regulates the output voltage of programmable power amplifiers. Feedback parameters in the form of controller gains are required for the three heating circuits. An objective is to determine an improved set of gains that meet temperature control criteria for testing insulation materials of interest.The analytical model is based on aggregated thermal capacity representations of the primary components and includes the same control algorithm as used in the actual hot-plate apparatus. The model, accounting for both thermal characteristics and temperature control, was validated by comparisons with test data.The tuning methodology used with the simulation model is described and results are presented. The resulting control algorithm and gain parameters have been used in the actual apparatus without modification during several years of testing materials over wide ranges of thermal conductivity, thickness, and insulation resistance values.     

Explicit analytical tuning rules for digital PID controllers via the magnitude optimum criterion

Analytical tuning rules for digital PID type–I controllers are presented regardless of the process complexity. This explicit solution allows control engineers 1) to make an accurate examination of the effect of the controller's sampling time to the control loop's performance both in the time and frequency domain 2) to decide when the control has to be I, PI and when the derivative, D, term has to be added or omitted 3) apply this control action to a series of stable benchmark processes regardless of their complexity. The former advantages are considered critical in industry applications, since 1) most of the times the choice of the digital controller's sampling time is based on heuristics and past criteria, 2) there is little a–priori knowledge of the controlled process making the choice of the type of the controller a trial and error exercise 3) model parameters change often depending on the control loop's operating point making in this way, the problem of retuning the controller's parameter a much challenging issue. Basis of the proposed control law is the principle of the PID tuning via the Magnitude Optimum criterion. The final control law involves the controller's sampling time T_s within the explicit solution of the controller's parameters. Finally, the potential of the proposed method is justified by comparing its performance with the conventional PID tuning when controlling the same process. Further investigation regarding the choice of the controller's sampling time T_s is also presented and useful conclusions for control engineers are derived.     

Tuning of an optimal fuzzy PID controller with stochastic algorithms for networked control systems with random time delay

An optimal PID and an optimal fuzzy PID have been tuned by minimizing the Integral of Time multiplied Absolute Error (ITAE) and squared controller output for a networked control system (NCS). The tuning is attempted for a higher order and a time delay system using two stochastic algorithms viz. the Genetic Algorithm (GA) and two variants of Particle Swarm Optimization (PSO) and the closed loop performances are compared. The paper shows that random variation in network delay can be handled efficiently with fuzzy logic based PID controllers over conventional PID controllers.     

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。     

基于模糊自整定PID的注水流量控制系统

针对注水流量控制系统的控制对象数学模型难建立,同时由于井下环境复杂,控制系统存在严重的非线性的问题,采用模糊自整定PID控制算法,设计了基于TMS320F2812模糊自整定PID控制器。该验结果表明模糊自整定PID控制能够满足系统的控制精度要求,具有动态和稳态性能好等优点。     

Robust stabilizing first-order controllers for a class of time delay systems

In this paper, stabilizing regions of a first-order controller for an all poles system with time delay are computed via parametric methods. First, the admissible ranges of one of the controller’s parameters are obtained. Then, for a fixed value of this parameter, stabilizing regions in the remaining two parameters are determined using the D-decomposition method. Phase and gain margin specifications are then included in the design. Finally, robust stabilizing first-order controllers are determined for uncertain plants with an interval type uncertainty in the coefficients. Examples are given to illustrate the effectiveness of the proposed method.     

具有指定性能的不稳定时滞对象H2控制器

本文基于H2最优控制理论针对一类不稳定对象推导了具有指定性能的控制器整定公式。设计过程分为两步。首先根据闭环系统渐近跟踪约束寻找满足要求的控制器集合，然后定义H2最优性能指标，利用有理近似副近控制对象中的纯滞后，进行控制器推导，最后，分析了系统的性能和稳定性，给出了判定的充要条件，在给出了例子中比较了新的控制器和其它控制器的性能。     

Design and implementation of a 2-DOF PID compensation for magnetic levitation systems

This paper employs a 2-DOF (degree of freedom) PID controller for compensating a physical magnetic levitation system. It is shown that because of having a feedforward gain in the proposed 2-DOF PID control, the transient performance of the compensated system can be changed in a desired manner unlike the conventional 1-DOF PID control. It is also shown that for a choice of PID parameters, although the theoretical loop robustness is the same for both the compensated systems, in real-time, 2-DOF PID control may provide superior robustness if a suitable choice of the feedforward parameter is made. The results are verified through simulations and experiments.     

IMC-PID-fractional-order-filter controllers design for integer order systems

One of the reasons of the great success of standard PID controllers is the presence of simple tuning rules, of the automatic tuning feature and of tables that simplify significantly their design. For the fractional order case, some tuning rules have been proposed in the literature. However, they are not general because they are valid only for some model cases. In this paper, a new approach is investigated. The fractional property is not especially imposed by the controller structure but by the closed loop reference model. The resulting controller is fractional but it has a very interesting structure for its implementation. Indeed, the controller can be decomposed into two transfer functions: an integer transfer function which is generally an integer PID controller and a simple fractional filter.     

基于LPC2103的模糊PID温度控制器设计

为使温度控制器的动态性能和稳态精度满足控制系统的要求,控制器采用了一种新型的模糊PID控制算法;温度测量采用Pt100,信号调理采用高精度运算放大器OP07,采用控制器LPC2103处理器制作了温度控制器;温度控制器采用PWM控制,控制器经模糊PID控制算法确定PWM脉冲宽度。为更好确定电阻炉温度控制系统的控制参数,采用实验的方法对电阻炉的数学模型进行了识别。在matlab仿真的基础上确定模糊PID控制参数,电阻炉的温度控制实验结果表明该温度控制器满足系统控制要求。     

PLC闭环控制系统中PID控制器的实现

本文介绍了针对西门子S7-200PLC闭环控制系统中PID控制器的实现,PID数字控制器的原理和使用方法及编程实例,对PID在工业控制中的应用很有参考价值。