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 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.     

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。     

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.     

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.     

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.     

一种模糊规范化PID控制器混沌优化设计

基于混沌变量，提出了一种FNPID参数混沌优化设计。文中将混沌动力学特性与退火策略结合起来实现混沌优化搜索，体现出具有更强的FNPID参数全局最优值的搜索能力。仿真实验表明能有效地实现FNPID控制器参数优化，控制结果具有稳定、无振荡、无超调、响应快、调节时间短的优点，算法结构简单，编程容易。     

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。     

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.     

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.     

A fuzzy model based adaptive PID controller design for nonlinear and uncertain processes

We develop a novel adaptive tuning method for classical proportional–integral–derivative (PID) controller to control nonlinear processes to adjust PID gains, a problem which is very difficult to overcome in the classical PID controllers. By incorporating classical PID control, which is well-known in industry, to the control of nonlinear processes, we introduce a method which can readily be used by the industry. In this method, controller design does not require a first principal model of the process which is usually very difficult to obtain. Instead, it depends on a fuzzy process model which is constructed from the measured input–output data of the process. A soft limiter is used to impose industrial limits on the control input. The performance of the system is successfully tested on the bioreactor, a highly nonlinear process involving instabilities. Several tests showed the method's success in tracking, robustness to noise, and adaptation properties. We as well compared our system's performance to those of a plant with altered parameters with measurement noise, and obtained less ringing and better tracking. To conclude, we present a novel adaptive control method that is built upon the well-known PID architecture that successfully controls highly nonlinear industrial processes, even under conditions such as strong parameter variations, noise, and instabilities.     

Design of a fractional order PID controller using GBMO algorithm for load–frequency control with governor saturation consideration

Load–frequency control is one of the most important issues in power system operation. In this paper, a Fractional Order PID (FOPID) controller based on Gases Brownian Motion Optimization (GBMO) is used in order to mitigate frequency and exchanged power deviation in two-area power system with considering governor saturation limit. In a FOPID controller derivative and integrator parts have non-integer orders which should be determined by designer. FOPID controller has more flexibility than PID controller. The GBMO algorithm is a recently introduced search method that has suitable accuracy and convergence rate. Thus, this paper uses the advantages of FOPID controller as well as GBMO algorithm to solve load–frequency control. However, computational load will higher than conventional controllers due to more complexity of design procedure. Also, a GBMO based fuzzy controller is designed and analyzed in detail. The performance of the proposed controller in time domain and its robustness are verified according to comparison with other controllers like GBMO based fuzzy controller and PI controller that used for load–frequency control system in confronting with model parameters variations.     

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.     

Fixed, low-order controller design with time response specifications using non-convex optimization

In this paper, we present a new algorithm for designing a fixed, low-order controller with time response specifications for a linear time invariant (LTI), single input single output (SISO) plant. For a two-parameter feedback configuration, the problem of finding a fixed or low-order controller to meet the desired time response specification is reduced to the least square estimation (LSE) in the sense of partial model matching (PMM), which minimizes a quadratic cost function. The closed-loop stability condition imposed on the controller parameters is formulated by the polynomial matrix inequality (PMI) constraint associated with the cost function. When the cascade feedback structure is considered, the zeros of the controller may be a substantial obstacle when designing a controller that has a good time response. This problem can also be formulated using polynomial constraints. Consequently, it is shown that the total problem here can be formulated as an optimization problem with a quadratic objective function and several polynomial constraints in the controller parameter space. We show that the SeDuMi with YALMIP interface [L?fberg J. YALMIP: A toolbox for modeling and optimization in MATLAB, in: Proceedings of the IEEE symposium on computer aided control systems design 2004. p. 284-9. http://control.ee.ethz.ch/~joloef/yalmip.php] can be used for solving this problem. Finally, several illustrative examples are given.     

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.     

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.     

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.     

Optimal supplementary frequency controller design using the wind farm frequency model and controller parameters stability region

In most of the existing studies, the frequency response in the variable speed wind turbines (VSWTs) is simply realized by changing the torque set-point via appropriate inputs such as frequency deviations signal. However, effective dynamics and systematic process design have not been comprehensively discussed yet. Accordingly, this paper proposes a proportional-derivative frequency controller and investigates its performance in a wind farm consisting of several VSWTs. A band-pass filter is deployed before the proposed controller to avoid responding to either steady state frequency deviations or high rate of change of frequency. To design the controller, the frequency model of the wind farm is first characterized. The proposed controller is then designed based on the obtained open loop system. The stability region associated with the controller parameters is analytically determined by decomposing the closed-loop system's characteristic polynomial into the odd and even parts. The performance of the proposed controller is evaluated through extensive simulations in MATLAB/Simulink environment in a power system comprising a high penetration of VSWTs equipped with the proposed controller. Finally, based on the obtained feasible area and appropriate objective function, the optimal values associated with the controller parameters are determined using the genetic algorithm (GA).     

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.     

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.