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.     

PID控制器参数快速整定的新方法

本文分析了影响控制器参数整定的几个基本问题（控制目标、优化准则和被控过程的特性），提出了精确地确定被控过程模型参数的方法。通过计算机仿真，系统地提出了可适用于多容过程的ＰＩＤ控制器参数快速整定新方法。     

改善性能的PID控制器校正方法

提出了一种对于宽级线性自调节过程实现高性能的PID控制器设计方法,对于不同的动态过程,包括那些具有低阶和高阶、小的和大的延迟时间以及单调的和振荡的响应,均能获得满意的动态品质.研究的方法是基于一个二阶加延迟时间模型化技术和通过运用根轨迹图的一种闭环极点分布策略,此模型被证明对各种过程是有效的,并且在诸如振荡过程的频率响应中能够产生峰值.按照阻尼比和模型的延迟时间选择不同的闭环极点,并且为计算提供了简单的公式.提供的仿真结果表明,所设计的控制器在处理具有不同特性的过程中获得了理想的结果.     

A PI tuning rule for integrating plus dead time processes with parametric uncertainty

A novel method to tune a Proportional–Integral (PI) compensator for an integrating plus dead time (IPDT) process, in presence of interval parametric uncertainty, is presented. The design is based on optimization of load disturbance rejection with constraints on the magnitude of the sensitivity and complementary sensitivity functions, that must be satisfied for any element belonging to a set of plants. Instead of solving this problem with a brute force approach (grid the uncertainty set), we prove that this problem can be solved by considering only two plants. That lets us to obtain a tuning rule, after using some approximations. To conclude, some examples will be given in order to elucidate the usefulness of the proposed tuning rule.     

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.     

一类非自衡对象的最优PID控制

实际控制系统中输入控制对象的控制能量大小不可能是无限大的,本文对控制能量存在约束时一类非自衡对象的最优控制问题作了探讨.首先定义了一个包含跟踪误差和控制能量在内的积分平方性能指标,然后针对不同设计要求运用最优方法极小化该性能指标,从而导出2类PID控制器的解析设计方法,可使系统在控制能量约束条件下具有最优的控制性能.     

PI/PID controller design based on IMC and percentage overshoot specification to controller setpoint change

In this work, the normalized Internal Model Control (IMC) filter time constant is designed to achieve a specified value of the maximum sensitivity for stable first and second order plus time delay process models, respectively. Since a particular value of the maximum sensitivity results in an almost constant percentage overshoot to controller setpoint change, an empirical relationship between the normalized IMC filter time constant and percentage overshoot is presented. The main advantage of the proposed method is that only a user-defined overshoot is required to design a PI/PID controller. Simulation examples are given to demonstrate the value of the proposed method.     

大时滞不稳定对象的PID控制

对一阶大时滞不稳定对象的控制，普通的PID控制器很难满足要求，有时甚至无法实现系统的稳定。采用了双环控制结构，先构造内环状态反馈以改善对象动态特性，然后按照内模控制原理设计外环的控制器。仿真结果表明了该方法的有效性。     

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.     

PID controller tuning for the first-order-plus-dead-time process model via Hermite-Biehler theorem

This paper discusses PID stabilization of a first-order-plus-dead-time (FOPDT) process model using the stability framework of the Hermite-Biehler theorem. The FOPDT model approximates many processes in the chemical and petroleum industries. Using a PID controller and first-order Padé approximation for the transport delay, the Hermite-Biehler theorem allows one to analytically study the stability of the closed-loop system. We derive necessary and sufficient conditions for stability and develop an algorithm for selection of stabilizing feedback gains. The results are given in terms of stability bounds that are functions of plant parameters. Sensitivity and disturbance rejection characteristics of the proposed PID controller are studied. The results are compared with established tuning methods such as Ziegler-Nichols, Cohen-Coon, and internal model control.     

Guide lines for the tuning and the evaluation of decentralized and decoupling controllers for processes with recirculation

This paper gives guidelines for the pairing, the time response specification, and the tuning for processes with recirculation when decentralized controllers are used. This selection is based on the condition number, which is an indicator of the process directionality, and on the generalized dynamic relative gain (GDRG), which is a measure of the interaction. Simple tuning rules are developed and results are compared to algebraic controllers with decouplers. Performances are evaluated for set-point changes as well as disturbance rejection using the generalized step response (GSR). The GSR gives a 3D graphic of the system response as a function of the input direction.     

Design and implementation of a new fuzzy PID controller for networked control systems

This paper presents a practical network platform to design and implement a networked-based cascade control system linking a Smar Foundation Fieldbus (FF) controller (DFI-302) and a Siemens programmable logic controller (PLC-S7-315-2DP) through Industrial Ethernet to a laboratory pilot plant. In the presented network configuration, the Smar OPC tag browser and Siemens WinCC OPC Channel provide the communicating interface between the two controllers. The paper investigates the performance of a PID controller implemented in two different possible configurations of FF function block (FB) and networked control system (NCS) via a remote Siemens PLC. In the FB control system implementation, the desired set-point is provided by the Siemens Human-Machine Interface (HMI) software (i.e, WinCC) via an Ethernet Modbus link. While, in the NCS implementation, the cascade loop is realized in remote Siemens PLC station and the final element set-point is sent to the Smar FF station via Ethernet bus. A new fuzzy PID control strategy is then proposed to improve the control performances of the networked-based control systems due to an induced transmission delay degradation effect. The proposed strategy utilizes an innovative idea based on sectionalizing the error signal of the step response into three different functional zones. The supporting philosophy behind these three functional zones is to decompose the desired control objectives in terms of rising time, settling time and steady-state error measures maintained by an appropriate PID-type controller in each zone. Then, fuzzy membership factors are defined to configure the control signal on the basis of the fuzzy weighted PID outputs of all three zones. The obtained results illustrate the effectiveness of the proposed fuzzy PID control scheme in improving the performances of the implemented NCS for different transportation delays.     

新型连续变速积分控制算法研究及应用

提出一种新的改进PID控制算法--连续变速积分控制算法.对其进行了仿真,与常规PID算法进行了比较,并将其应用于小型电加热炉的控制中.仿真及实际应用结果表明,该算法可提高控制质量,克服了常规PID算法容易造成超调与积分饱和的问题,且易于进行参数整定,特别适用于间歇生产过程及程序温度控制.     

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.     

基于改进型灰色预测大时滞过程的自适应PID控制研究

针对传统PID控制对大时滞控制效果不佳的情况,提出一种基于改进灰色预测模型的自适应PID控制系统。采用等维新信息、改变初始条件和精指数拟合法对G（1,1）模型进行改进,将改进后的G（1,1）模型与传统PID结合,组成灰色预测控制系统。用预测结果代替被控对象测量值,克服了大时滞系统控制效果不能及时反馈的不足,并在控制运算中,沿二次型性能指标的负梯度方向对加权系数进行在线修改,实现了自适应PID的优化控制。仿真结果表明了该预测控制算法的响应速度快、鲁棒性强,有较好的适应性。     

气动比例位置系统优化模糊PID控制方法的研究

在建立气动比例位置控制系统数学模型和分析其特性的基础上,设计了常规比例-积分-微分(PID)控制器,引入优化设计理论,通过不断的仿真实验,获得一组优化的PID控制参数,以此作为初始值,设计模糊PID控制器.基于LabVIEW设计了系统实时控制程序,通过实验研究,不仅可以实现PID的在线自整定控制,而且实验结果证明所设计的控制器可行,具有较好的控制效果.     

An analytical method for PID controller tuning with specified gain and phase margins for integral plus time delay processes

In this paper, an analytical method is proposed for proportional-integral/proportional-derivative/proportional-integral-derivative (PI/PD/PID) controller tuning with specified gain and phase margins (GPMs) for integral plus time delay (IPTD) processes. Explicit formulas are also obtained for estimating the GPMs resulting from given PI/PD/PID controllers. The proposed method indicates a general form of the PID parameters and unifies a large number of existing rules as PI/PD/PID controller tuning with various GPM specifications. The GPMs realized by existing PID tuning rules are computed and documented as a reference for control engineers to tune the PID controllers.     

Optimal controller synthesis for second order time delay systems with at least one RHP pole

An optimal H₂ minimization framework is proposed in this paper for devising a controller of PID in nature, based on a refined IMC filter configuration. The tuning strategy is for controlling time delay system with at least one pole which falls on the right half of the s-plane. An underdamped model based filter is used in place of the unity damping ratio (critically damped) filter available in the literature to improve the reset action. The method has a single adjustable closed loop tuning parameter. Guidelines have been provided for choosing the pertinent tuning parameter based on the sensitivity function. Simulation work has been executed on diverse unstable models to support the advantages of the proposed scheme. The proposed controller yields improved performances over other recently reported tuning techniques in the literature. Experimental implementation is carried out on an inverted pendulum for demonstrating the practical applicability of the present method. The efficacy of the intended controller design is quantitatively analyzed using the time integral performance index.     

Design of a new PID controller using predictive functional control optimization for chamber pressure in a coke furnace

An improved proportional-integral-derivative (PID) controller based on predictive functional control (PFC) is proposed and tested on the chamber pressure in an industrial coke furnace. The proposed design is motivated by the fact that PID controllers for industrial processes with time delay may not achieve the desired control performance because of the unavoidable model/plant mismatches, while model predictive control (MPC) is suitable for such situations. In this paper, PID control and PFC algorithm are combined to form a new PID controller that has the basic characteristic of PFC algorithm and at the same time, the simple structure of traditional PID controller. The proposed controller was tested in terms of set-point tracking and disturbance rejection, where the obtained results showed that the proposed controller had the better ensemble performance compared with traditional PID controllers.