A direct method for multi-loop PI/PID controller design

Difficulties caused by the interactions are always encountered in the design of multi-loop control systems for MIMO processes. To overcome the difficulties, a multi-loop system is decomposed into a number of equivalent single loops for design. For each equivalent single loop, an effective open-loop process (EOP) is formulated without prior knowledge of controller dynamics in other loops, and, hence, controller can be designed directly and independently. Based on the derived EOPs, a model-based method aims at having reasonable gain margins (e.g. 2) and phase margins (e.g. ≈60°) are presented to derive multi-loop PI/PID controllers. This proposed method is formulated in details for the EOPs of 2-loop systems. Extension to higher dimensional systems needs further simplification and is illustrated with formulation for 3-loop systems. Simulation results show that this presented method is effective for square MIMO processes, especially, for low dimensional ones.     

A multivariable IMC-PID method for non-square large time delay systems using NPSO algorithm

Multiple time delays and strong interactions among different loops are the main problems in the design of multivariable controller for non-square systems. In this paper, the concept of effective open-loop transfer function (EOTF) is extended to non-square systems. By applying the internal model control (IMC) method, the controllers with equivalent models are designed. For practical applications, the NPSO algorithm is used to obtain the parameters of the incremental PID with first-order lag filter. This new method does not only avoid the complex computation caused by the procedure of decoupling first and then designing controllers but also employs the advantages of IMC-PID's suitable for large time delay systems and strong robustness. Simulation is carried out to demonstrate the effectiveness of the proposed method; also significant performance improvement has been achieved with the proposed method compared with other methods.     

Multi-loop design of multi-scale controllers for multivariable processes

Based on the recently proposed (SISO) multi-scale control scheme, a new approach is introduced to design multi-loop controllers for multivariable processes. The basic feature of the multi-scale control scheme is to decompose a given plant into a sum of basic modes. To achieve good nominal control performance and performance robustness, a set of sub-controllers are designed based on the plant modes in such a way that they are mutually enhanced with each other so as to optimize the overall control objective. It is shown that the designed multi-scale controller is equivalent to a conventional PID controller augmented with a filter. The multi-scale control scheme offers a systematic approach to designing multi-loop PID controllers augmented with filters. Numerical studies show that the proposed multi-loop multi-scale controllers provide improved nominal performance and performance robustness over some well-established multi-loop PID controller schemes.     

Design of decentralized controllers for MIMO processes

In this paper, the design of decentralized PID controller for interactive and delay time processes is proposed. Direct controller synthesis approach is used to obtain parameters of the multi-loop controllers. A detuning factor for each loop is specified based on the closed-loop time constant. Then appropriate controller settings are determined using the Maclaurin series expansion and the model of the process. The success of the proposed algorithm is based on the detuning parameter thus the selection of the desired closed-loop time constant is an important factor. The proposed method has no limitations regarding systems weak or strong interactions, multiple delays, and its operating behaviors such as monotonic or oscillatory. The proposed algorithm is simpler and improved performance of various processes are achieved as compared to some of the prevalent techniques. Simulation examples demonstrate the usefulness of the proposed method.     

Analytical method of PID controller design for parallel cascade control

An analytical method of PID controller design is proposed for parallel cascade control. Firstly, a general structure for parallel cascade control is proposed that takes both setpoint and load disturbance responses into account. Analytical tuning rules for the PID controllers are then derived for the general process model by employing the IMC design procedure. The proposed method offers a simple and effective way to obtain the PID controller rules for parallel cascade control system which takes into account the interaction between primary and secondary control loops. The simulation results illustrate the application of the proposed method and demonstrate its superiority compared to several alternatives.     

Fractional robust control of main irrigation canals with variable dynamic parameters

A new method is proposed for controlling main irrigation canals with variable dynamical parameters based on robust fractional order controllers. A methodology for designing PID controllers robust to changes in the time delay and the gain is presented first. Then this method is generalized to design fractional controllers that exhibit the same robustness as the previous PID to time delay and gain changes, but are noticeably more robust to variations in the dominant time constant of the process. This method is applied to control main irrigation canals. Extensive numerical simulations using the dynamic model of a real canal were carried out. Then experimental results were obtained in a prototype canal that proved the effectiveness of the proposed control method in terms of performance and robustness.     

Disturbance observer based multi-variable control of ball mill grinding circuits

Ball mill grinding circuits are essentially multi-variable systems characterized with couplings, time-varying parameters and time delays. The control schemes in previous literatures, including detuned multi-loop PID control, model predictive control (MPC), robust control, adaptive control, and so on, demonstrate limited abilities in control ball mill grinding process in the presence of strong disturbances. The reason is that they do not handle the disturbances directly by controller design. To this end, a disturbance observer based multi-variable control (DOMC) scheme is developed to control a two-input-two-output ball mill grinding circuit. The systems considered here are with lumped disturbances which include external disturbances, such as the variations of ore hardness and feed particle size, and internal disturbances, such as model mismatches and coupling effects. The proposed control scheme consists of two compound controllers, one for the loop of product particle size and the other for the loop of circulating load. Each controller includes a PI feedback part and a feed-forward compensation part for the disturbances by using a disturbance observer (DOB). A rigorous analysis is also given to show the reason why the DOB can effectively suppress the disturbances. Performance of the proposed scheme is compared with those of the MPC and multi-loop PI schemes in the cases of model mismatches and strong external disturbances, respectively. The simulation results demonstrate that the proposed method has a better disturbance rejection property than those of the MPC and PI methods in controlling ball mill grinding circuits.     

OPTIMIZATION OF DECENTRALIZED PI/PID CONTROLLERS BASED ON GENETIC ALGORITHM

In this paper, an optimization method of tuning decentralized PI/PID controllers based on genetic algorithms is presented. First, the existence of decentralized PI controllers with integrity is examined. Then, stable regions of each PI/PID controller parameters are calculated as the feasible area to be exploited, and the optimal PI/PID controllers are obtained by using a real‐coded genetic algorithm with elitist strategy, to meet the design specifications for the whole control system. The proposed method is applied to six examples from literature. Simulation results demonstrate that the proposed decentralized PI control is compatible to the referenced method while the decentralized PID control is better than the referenced method, and the proposed method is feasible for more complicated control systems optimizations.     

A DESIGN OF MULTILOOP PID CONTROLLERS WITH A NEURAL‐NET BASED DECOUPLER

In process industries, PID control schemes have been widely used due to their simple structures and easiness of comprehending the physical meanings of control parameters. However, the good control performance cannot be obtained by simply using PID controlschemes, since most processes are considered as nonlinear multivariable systems with mutual interactions. In this paper, a design method of multiloop PID controllers neural‐net based decoupler is proposed for nonlinear multivariable systems with mutual interactions. The proposed method consists of a decoupler given by the sum of a static decoupler and a neural‐net based decoupler, and multi‐loop PID controllers. Finally, the effectiveness of the proposed control scheme is evaluated on the simulation examples.     

ISE tuning rule revisited

The integral square error (ISE) method is applied to approximate the internal model control (IMC) system by the PID control system. Simulations show that the proposed method to design PID controllers can relieve some disadvantages of the original ISE method and IMC-based PID controller design methods.     

The Mimo Predictive Pid Controller Design

This paper is concerned with the design of Multi‐Inputs and Multi‐Outputs (MIMO) predictive PID controllers, which have similar performance to that obtainable from model‐based predictive controllers. A new PID control structure is defined which incorporates the prediction of future outputs and uses future set point. A method is proposed to calculate the optimal values of the PID gains from generalised predictive control results. A decentralized version of the predictive PID controllers is presented and the stability of the closed loop system is studied. Simulation studies demonstrate the superior performance of the proposed controller compared with a conventional PID controller. The results are also compared with generalised predictive control solutions.     

Robust ℋ︁∞ PID control for multivariable networked control systems with disturbance/noise attenuation

In this paper, we study the design problem of PID controllers for networked control systems (NCSs) with polyhedral uncertainties. The load disturbance and measurement noise are both taken into account in the modeling to better reflect the practical scenario. By using a novel technique, the design problem of PID controllers is converted into a design problem of output feedback controllers. Our goal of this paper is two‐fold: (1) To design the robust PID tracking controllers for practical models; (2) To develop the robust ??_∞ PID control such that load and reference disturbances can be attenuated with a prescribed level. Sufficient conditions are derived by employing advanced techniques for achieving delay dependence. The proposed controller can be readily designed based on iterative suboptimal algorithms. Finally, four examples are presented to show the effectiveness of the proposed methods. Copyright © 2011 John Wiley & Sons, Ltd.     

多变量多时滞系统的前馈补偿解耦及IMC-PID控制

多变量系统控制器设计中遇到的主要难题是多时滞和强铰链耦合问题;对于非奇异方阵系统,根据解耦理论通过串级前馈时滞补偿器将原系统解耦为多个单变量小时滞系统,运用模型降阶技术,将解耦后的复杂单变量小时滞系统逼近为FOPDT(一阶环节+延时)形式,采用IMC控制策略实现多个单变量系统单位反馈控制,运用了麦克劳林级数展开式,通过相应项系数的比对得到了传统PID控制器;仿真分析表明了该方法能够有效性地补偿系统时滞,同时现实解耦;解决了多变量多时滞系统控制器设计复杂性的难题,有一定的工程参考价值。     

Equivalent transfer function based multi-loop PI control for high dimensional multivariable systems

A new equivalent transfer function (ETF) parameterization algorithm to incorporate the loop interaction effect into the design of multi-loop PI controllers for high dimensional multivariable processes is presented in this paper. The design scheme consists of two stages. In the first, by exploiting the relationship between the equivalent closed-loop transfer function and the inverse of open-loop transfer function, the analytical expression of ETF is derived. In the second stage, based on the ETF, controller parameters for each loop are determined by utilizing the existing PI tuning rules and the simple internal model control method. The proposed ETF parameterization algorithm is more accurate and reasonable compared to the conventional ETF model approximation methods. Furthermore, the advantage of the multi-loop PI controller designed by the proposed ETF is more significant when applied to higher dimensional processes with complicated interaction modes. Several typical industrial process examples show the well-balanced and robust response with the minimum integral absolute error.     

多变量解耦控制的工业过程运行层次控制方法

基于多变量解耦控制技术,提出了一种工业过程运行的层次控制方法,用于实现表征过程整体运行性能的工艺指标.底层回路控制系统采用多回路PI/PID控制技术进行设计,用于将关键工艺参数控制在给定的工作点.针对中被控过程和底层回路控制系统构成的文义对象,采用扩展的单位反馈解耦方法设计上层回路设定控制器,该回路设定控制器能够克服系...     

Equivalent transfer function method for PI/PID controller design of MIMO processes

In this paper, a novel engineering oriented control system design method for multivariable processes is presented. By employing the concepts of energy transmission ratio and effective relative gain, an equivalent transfer function matrix for closed loop control system can be obtained. Based on the equivalent transfer function matrix, both off-diagonal decoupling controllers and main loop diagonal controllers can be easily designed using the existing PI/PID tuning rules. The main advantages of the method are that: (1) the overall control system performance is better compared with the existing decoupling control methods; (2) it is very simple which can be easily understood and implemented by field control engineers; and (3) the control system is robust, it can still work with satisfactory performance even under significant model mismatches. Several multivariable industrial processes with different interaction characteristics are employed to demonstrate the simplicity and effectiveness of the design method.     

统计过程监测与反馈控制的整合: 状态空间下的一般方法

将状态空间模型引入统计过程监测,选取状态变量为统计过程控制(SPC)统计量,以解决自相关过程的统计监测问题.在分析常用的最小均方误差(MMSE)和PID控制器的基础上,提出了工业过程控制(EPC)反馈控制器的一般设计方法和基本设计原则.作为演绎示例,给出了两组新型反馈控制器,并与MMSE和PID的反馈调整进行比较,当过程均值发生阶跃扰动时,可进一步提高统计监测效果.     

Design of fuzzy PID controllers using modified triangular membership functions

A design method for fuzzy proportional-integral-derivative (PID) controllers is investigated in this study. Based on conventional triangular membership functions used in fuzzy inference systems, the modified triangular membership functions are proposed to improve a system’s performance according to knowledge-based reasonings. The parameters of the considered controllers are tuned by means of genetic algorithms (GAs) using a fitness function associated with the system’s performance indices. The merits of the proposed controllers are illustrated by considering a model of the induction motor control system and a higher-order numerical model.     

基于改进Smith预估控制结构的二自由度PID控制

针对工业过程中的二阶不稳定时滞过程, 基于改进史密斯预估控制结构提出了一种简单的两自由度控制方案.设定值跟踪控制器和扰动抑制控制器采用同一设计程序, 并基于内模控制原理提出了控制器解析设计方案.设定值跟踪控制器和抗扰动控制器可分别通过单性能参数独立调节和优化, 每个控制器都具有PID形式, 给出了控制器调整参数的选择范围和扰动抑制闭环保证鲁棒稳定性的条件.仿真实例验证了提出方法对于近期其他方法的优越性.