PID controller tuning for integrating processes

Minimizing the integral squared error (ISE) criterion to get the optimal controller parameters results in a PD controller for integrating processes. The PD controller gives good servo response but fails to reject the load disturbances. In this paper, it is shown that satisfactory closed loop performances for a class of integrating processes are obtained if the ISE criterion is minimized with the constraint that the slope of the Nyquist curve has a specified value at the gain crossover frequency. Guidelines are provided for selecting the gain crossover frequency and the slope of the Nyquist curve. The proposed method is compared with some of the existing methods to control integrating plant transfer functions and in the examples taken it always gave better results for the load disturbance rejection whilst maintaining satisfactory setpoint response. For ease of use, analytical expressions correlating the controller parameters to plant model parameters are also given.     

A simple nonlinear PD controller for integrating processes

Many industrial processes are found to be integrating in nature, for which widely used Ziegler–Nichols tuned PID controllers usually fail to provide satisfactory performance due to excessive overshoot with large settling time. Although, IMC (Internal Model Control) based PID controllers are capable to reduce the overshoot, but little improvement is found in the load disturbance response. Here, we propose an auto-tuning proportional-derivative controller (APD) where a nonlinear gain updating factor α continuously adjusts the proportional and derivative gains to achieve an overall improved performance during set point change as well as load disturbance. The value of α is obtained by a simple relation based on the instantaneous values of normalized error (e_N) and change of error (Δe_N) of the controlled variable. Performance of the proposed nonlinear PD controller (APD) is tested and compared with other PD and PID tuning rules for pure integrating plus delay (IPD) and first-order integrating plus delay (FOIPD) processes. Effectiveness of the proposed scheme is verified on a laboratory scale servo position control system.     

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.     

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.     

Performance assessment of PID and IMC tuning methods for a mixing process with time delay

A flow process with time delay has been considered for modeling and control. A dilute solution of sodium chloride is used as tracer and an online conductivity measurement unit as sensor and recorder. The objective of the current study is to design control algorithms and present corresponding robust control analysis for the process. The control methodologies considered are (i) conventional PID control and (ii) internal model control (IMC). The control structures are comparatively analyzed using standard robustness measures for stability and performance. Of the two control algorithms, conventional PID and IMC, IMC exhibits faster settling time, no overshoot, better set-point tracking and disturbance rejection, and good robust performance than the PID control scheme.     

Parameter estimation of integrating and time delay processes using single relay feedback test

Autotuning using relay feedback is widely used to identify low order integrating plus dead time (IPDT) systems as the method is simple and is operated in closed-loop without interrupting the production process. Oscillatory responses from the process due to ideal relay input are collected to calculate ultimate properties of the system that in turn are used to model the responses as functions of system model parameters. These theoretical models of relay response are validated. After adjusting the phase shift, input and output responses are used to find land mark points that are used to formulate algorithms for parameter estimation of the process model. The method is even applicable to distorted relay responses due to load disturbance or measurement noise. Closed-loop simulations are carried out using model based control strategy and performances are calculated.     

Intuitive robust stability metric for PID control of self-regulating processes

Published methods establish how plant-model mismatch in the process gain and dead time impacts closed-loop stability. However, these methods assume no plant-model mismatch in the process time constant. The work presented here proposes the robust stability factor metric, RSF, to examine the effect of plant-model mismatch in the process gain, dead time, and time constant. The RSF is presented in two forms: an equation form and a visual form displayed on robustness plots derived from the Bode and Nyquist stability criteria. This understanding of robust stability is reinforced through visual examples of how closed-loop performance changes with various levels of plant-model mismatch. One example shows how plant-model mismatch in the time constant can impact closed-loop stability as much as plant-model mismatch in the gain and/or dead time. Theoretical discussion shows that the impact is greater for small dead time to time constant ratios. As the closed-loop time constant used in Internal Model Control (IMC) tuning decreases, the impact becomes significant for a larger range of dead time to time constant ratios. To complete the presentation, the RSF is used to compare the robust stability of IMC-PI tuning to other PI, PID, and PID with Filter tuning correlations.     

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.     

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.     

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.     

Smith predictor based-sliding mode controller for integrating processes with elevated deadtime

An approach to control integrating processes with elevated deadtime using a Smith predictor sliding mode controller is presented. A PID sliding surface and an integrating first-order plus deadtime model have been used to synthesize the controller. Since the performance of existing controllers with a Smith predictor decrease in the presence of modeling errors, this paper presents a simple approach to combining the Smith predictor with the sliding mode concept, which is a proven, simple, and robust procedure. The proposed scheme has a set of tuning equations as a function of the characteristic parameters of the model. For implementation of our proposed approach, computer based industrial controllers that execute PID algorithms can be used. The performance and robustness of the proposed controller are compared with the Matausek-Mici? scheme for linear systems using simulations.     

Set point weighted modified Smith predictor for integrating and double integrating processes with time delay

A simple method of designing the controllers for a modified form of Smith predictor is proposed for integrating and double integrating processes with time delay. The modified Smith predictor has two controllers, namely, a set point tracking controller and a load disturbance rejection controller for obtaining good set point tracking and load disturbance rejection, respectively. The set point tracking controller is designed using the classical direct synthesis method based on the process model without considering the time delay. The disturbance rejection controller is considered as a proportional-derivative (PD) controller and is designed using optimal gain and phase margin approaches. Set point weighting is considered for reducing undesirable overshoots and settling times in the modified Smith predictor. Guidelines are provided for selection of the desired closed loop tuning parameter in the direct synthesis method and the set point weighting parameter. The method gives significant load disturbance rejection performances. Illustrative examples are considered to show the performances of the proposed method. A significant improvement in control performance is obtained when compared to recently reported methods.     

Improved automatic tuning of PID controller for stable processes

This paper presents an improved automatic tuning method for stable processes using a modified relay in the presence of static load disturbances and measurement noise. The modified relay consists of a standard relay in series with a PI controller of unity proportional gain. The integral time constant of the PI controller of the modified relay is chosen so as to ensure a minimum loop phase margin of 30. A limit cycle is then obtained using the modified relay. Hereafter, the PID controller is designed using the limit cycle output data. The derivative time constant is obtained by maintaining the above mentioned loop phase margin. Minimizing the distance of Nyquist curve of the loop transfer function from the imaginary axis of the complex plane gives the proportional gain. The integral time constant of the PID controller is set equal to the integral time constant of the PI controller of the modified relay. The effectiveness of the proposed technique is verified by simulation results.     

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。     

一种新的积分过程PID控制器整定方法

针对积分过程，提出了一种简单、实用的PID控制器。该方法首先通过PD控制器对积分过程建立内部反馈控制回路，将内部闭环系统近似为二阶加纯滞后模型；然后，根据有效的模型，基于鲁棒性能指标设计外部反馈回路的PID控制器；最后，简化控制系统的结构，采用设定值加权PID控制器控制积分过程。仿真结果表明了设定值加权PID控制器的有效性和可行性。     

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.     

Iterative tuning of modified uncertainty and disturbance estimator for time-delay processes: A data-driven approach

Uncertainty and disturbance widely exist in the process industry, which may deteriorate control performance if not well handled. The uncertainty and disturbance estimator (UDE) emerges as a promising solution by treating the external disturbances and internal uncertainties simultaneously as a lumped term. To overcome its limitation caused by time delay, a modified UDE (MUDE) has been proposed recently. However, its parameter tuning relies heavily on trial-and-error, thus being time-consuming in balancing the robustness and performance. To this end, this paper aims to develop an automatic tuning procedure for the MUDE-based control system. The quantitative relationship between system performance and the scaled parameters is empirically built. Iterative Feedback Tuning (IFT) is utilized to approximate the nominal model towards actual process. Through the empirical formula and optimized model, an automatic design procedure is proposed after taking into account the system robustness and output performance simultaneously. Simulation results show the superiority of the closed-loop performance over the original MUDE controllers. The experimental results validate the feasibility of the method proposed in this paper, depicting a promising prospect in the practical application.     

A generic method for servo tuning based on dynamic modeling and task description

In robotics or machining, task quality is strongly linked to servo tuning. Indeed, geometrical and dynamic behavior of the mechanical structure could be degraded when a coarse tuning is achieved. Several P/PI or PID tuning methods can be used but generally uncorrelated with industrial context or mechanical considerations. In this paper, we propose a generic tuning method based on dynamic modeling of the mechanical structure and model parameters experimental identification. Therefore, the proposed tuning is adapted to the real dynamic behavior of the mechanical structure under task load while being sufficiently simple to be implemented in an industrial context. The method is illustrated on a vertical axis.     

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.     

Design and robust tuning of control scheme based on the PD controller plus Disturbance Observer and low-order integrating first-order plus dead-time model

This paper presents an effective design and robust tuning method for the control structure based on a series PD controller and a simple Disturbance Observer. All elements of the proposed controller are directly obtained from the low-order Integrating First-Order Plus Dead-Time (IFOPDT) model, used to approximate essential dynamic characteristics of lag-dominant stable, integrating and unstable plants. The structure of the proposed controller is an effective, easy to implement and tune, extension of the series PID controller. For the same robustness, a better disturbance rejection response is obtained by the proposed controller than that of the PID, by adjusting only two parameters with a clear meaning. A comparison with well-tuned PIDs, done by simulations, and the experimental results, obtained on a real thermal power plant, confirm that high performance and robustness are obtained, for dynamic characteristics common to industrial processes.