Tuning algorithms for fractional order internal model controllers for time delay processes

This paper presents two tuning algorithms for fractional-order internal model control (IMC) controllers for time delay processes. The two tuning algorithms are based on two specific closed-loop control configurations: the IMC control structure and the Smith predictor structure. In the latter, the equivalency between IMC and Smith predictor control structures is used to tune a fractional-order IMC controller as the primary controller of the Smith predictor structure. Fractional-order IMC controllers are designed in both cases in order to enhance the closed-loop performance and robustness of classical integer order IMC controllers. The tuning procedures are exemplified for both single-input-single-output as well as multivariable processes, described by first-order and second-order transfer functions with time delays. Different numerical examples are provided, including a general multivariable time delay process. Integer order IMC controllers are designed in each case, as well as fractional-order IMC controllers. The simulation results show that the proposed fractional-order IMC controller ensures an increased robustness to modelling uncertainties. Experimental results are also provided, for the design of a multivariable fractional-order IMC controller in a Smith predictor structure for a quadruple-tank system.     

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.     

Enhanced design of cascade control systems for unstable processes with time delay

In this paper, optimal H₂ internal model controller (IMC) is designed for control of unstable cascade processes with time delays. The proposed control structure consists of two controllers in which inner loop controller (secondary controller) is designed using IMC principles. The primary controller (master controller) is designed as a proportional-integral-derivative (PID) in series with a lead-lag filter based on IMC scheme using optimal H₂ minimisation. Selection of tuning parameter is important in any IMC based design and in the present work, maximum sensitivity is used for systematic selection of the primary loop tuning parameter. Simulation studies have been carried out on various unstable cascade processes. The present method provides significant improvement when compared to the recently reported methods in the literature particularly for disturbance rejection. The present method also provides robust closed loop performances for large uncertainties in the process parameters. Quantitative comparison has been carried out by considering integral of absolute error (IAE) and total variation (TV) as performance indices.     

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.     

一类非线性多变量对象的解耦内模控制

针对化工行业中常见的多变量非线性问题,提出了基于全局多模型的解耦内模控制方案。将非线性对象在工作区域的顶点线性化得到线性化模型,内部模型采用其加权形式,再用每个顶点模型求局部解耦控制器,最后加权得到全局控制器。与分散控制方案相对比,只需少数几个局部线性化模型就可设计解耦控制器,计算量小,并且实现了系统的解耦,有更好的实用性。仿真结果证明了该设计方法的可行性及其优点。     

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.     

An expert autotuner for multiloop SISO controllers

In this paper, an on-line expert autotuner for a class of 2-input-2-output multivariable process control applications is proposed. The autotuning controller, which uses a pattern-recognition technique is designed with a view to its practical implementation in multivariable processes. The main idea of the autotuning methodology is to use the observed multiloop responses with reference to the single-loop responses such that proper detuning of the SISO controllers is achieved. Customized identification techniques in SISO and MIMO environments based on closed-loop responses are developed for this application. Simulation results for a range of 2-input-2-output multivariable processes characterized by the Relative Gain (RG) and the relative dynamics are used to evaluate the performance of the autotuning controller under different conditions. The time response of the autotuning controller is compared to that of Biggest Log Modulus Tuning (BLT) method with a few distillation column models proposed in the literature.     

Independent design of multi-loop PI/PID controllers for interacting multivariable processes

The interactions between input/output variables are a common phenomenon and the main obstacle encountered in the design of multi-loop controllers for interacting multivariable processes. In this study, a novel method for the independent design of multi-loop PI/PID controllers is proposed. The idea of an effective open-loop transfer function (EOTF) is first introduced to decompose a multi-loop control system into a set of equivalent independent single loops. Using a model reduction technique, the EOTF is further approximated to the reduced-order form. Based on the corresponding EOTF model, the individual controller of each single loop is then independently designed by applying the internal model control (IMC)-based PID tuning approach for single-input/single-output (SISO) systems, while the main effects of the dynamic interactions are properly taken into account. Several illustrative examples are employed to demonstrate the effectiveness of the proposed method.     

Optimized Model Based Controller with Model Plant Mismatch for NMP Mitigation in Boost Converter

In this paper, an optimized Genetic Algorithm (GA) based internal model controller-proportional integral derivative (IMC-PID) controller has been designed for the control variable to output variable transfer function of dc-dc boost converter to mitigate the effect of non-minimum phase (NMP) behavior due to the presence of a right-half plane zero (RHPZ). This RHPZ limits the dynamic performance of the converter and leads to internal instability. The IMC PID is a streamlined counterpart of the standard feedback controller and easily achieves optimal set point and load change performance with a single filter tuning parameter λ. Also, this paper addresses the influences of the model-based controller with model plant mismatch on the closed-loop control. The conventional IMC PID design is realized as an optimization problem with a resilient controller being determined through a genetic algorithm. Computed results suggested that GA–IMC PID coheres to the optimum designs with a fast convergence rate and outperforms conventional IMC PID controllers.     

IMC-based iterative learning control for batch processes with uncertain time delay

Based on the internal model control (IMC) structure, an iterative learning control (ILC) scheme is proposed for batch processes with model uncertainties including time delay mismatch. An important merit is that the IMC design for the initial run of the proposed control scheme is independent of the subsequent ILC for realization of perfect tracking. Sufficient conditions to guarantee the convergence of ILC are derived. To facilitate the controller design, a unified controller form is proposed for implementation of both IMC and ILC in the proposed control scheme. Robust tuning constraints of the unified controller are derived in terms of the process uncertainties described in a multiplicative form. To deal with process uncertainties, the unified controller can be monotonically tuned to meet the compromise between tracking performance and control system robust stability. Illustrative examples from the recent literature are performed to demonstrate the effectiveness and merits of the proposed control scheme.     

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。     

一类非最小相位过程内模控制系统设计

非最小相位过程是较难控制的一类过程。针对一类自衡二阶非最小相位过程 ,采用内模控制系统结构 ,使系统具有良好的抗扰性和鲁棒性。给出了在希望的幅值和相角裕量下控制器参数的计算方法。设计例子与仿真结果表明 ,根据该方法设计的系统有比较理想的稳定性和鲁棒性     

Nonlinear internal model controller design for wastegate control of a turbocharged gasoline engine

Internal Model Control (IMC) has a great appeal for automotive powertrain control in reducing the control design and calibration effort. Motivated by its success in several automotive applications, this work investigates the design of nonlinear IMC for wastegate control of a turbocharged gasoline engine. The IMC design for linear time-invariant (LTI) systems is extended to nonlinear systems. To leverage the available tools for LTI IMC design, the quasi-linear parameter-varying (quasi-LPV) models are explored. IMC design through transfer function inverse of the quasi-LPV model is ruled out due to parameter variability. A new approach for nonlinear inversion, referred to as the structured quasi-LPV model inverse, is developed and validated. A fourth-order nonlinear model which sufficiently describes the dynamic behavior of the turbocharged engine is used as the design model in the IMC structure. The controller based on structured quasi-LPV model inverse is designed to achieve boost-pressure tracking. Finally, simulations on a validated high-fidelity model are carried out to show the feasibility of the proposed IMC. Its closed-loop performances are compared with a well-tuned PI controller with extensive feedforward and anti-windup built in. Robustness of the nonlinear IMC design is analyzed using simulations.     

IMC based Controller Design for Automatic Generation Control of Multi Area Power System via Simplified Decoupling

This paper deals with design of integer and non-integer IMC based controllers for automatic generation control of two area power system using the simplified decoupling technique. A two area non-reheated interconnected thermal power system is considered for decentralised controller design. The coupling among areas are the main hurdle encountered in the design of controller. Hence, the idea of simplified decoupling technique is introduced to decouple the two area power system into two equivalent independent SISO systems. Integer and non-integer internal model control (IMC), are independently designed for each area based on decoupled systems. The performance of two area power system equipped with proposed controller is analysed through MATLAB. Simulation results show that proposed controller maintains robust performance and can minimize the load fluctuations. Finally, the method is extended to three area power system.     

High-purity control of internal thermally coupled distillation columns based on nonlinear wave model

Internal thermally coupled distillation column (ITCDIC) is a frontier of energy saving distillation researches, which is a great improvement on conventional distillation column (CDIC). However its high degree thermal coupling makes the control design a bottleneck problem, where data-driven model leads to obvious mismatch with the real plant in the high-purity control processes, and a first-principle model which is comprised of complex mass balance relations and thermally coupled relations could not be directly used as control model for the bad online computing efficiency. In the present work, wave theory is extended to the control design of ITCDIC with variable molar flow rates, where a general nonlinear wave model of ITCDIC processes based on the profile trial function of the component concentration distribution is proposed firstly; combined with the thermally coupled relations, a novel wave model based generic model controller (WGMC) of ITCDIC processes is developed. The benzene-toluene system for ITCDIC is studied as illustration, where WGMC is compared with another generic model controller based on a data-driven model (TGMC) and an internal model controller (IMC). In the servo control and regulatory control, WGMC exhibits the greatest performances. Detailed research results confirm the efficiency of the proposed wave model and the advantage of the proposed WGMC control strategy.     

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.     

Maximum sensitivity based fractional IMC–PID controller design for non-integer order system with time delay

A simple approach with a small number of tuning parameters is a key goal in fractional order controller design. Recently there have been a number of limited attempts to bring about improvements in these areas. In this paper, a new design method for a fractional order PID controller based on internal model control (IMC) is proposed to handle non-integer order systems with time delay. In order to reduce the number of tuning parameters and mitigate the impact of time delay, the fractional order internal model control scheme is used. Considering the robustness of the control system with respect to process variations and model uncertainty, maximum sensitivity is applied to the tuning of the parameters. The resulting controller has the structure of a fractional order PID which is cascaded with a filter. This is named a fractional IMC–PID controller. Numerical results are given to show the efficiency of the proposed controller.     

Theoretical analysis of unconstrained nonlinear model predictive control

Model predictive control (MPC) is a well-established controller design strategy for linear process models. Because many chemical and biological processes exhibit significant nonlinear behaviour, several MPC techniques based on nonlinear process models have recently been proposed. The most significant difference between these techniques is the computational approach used to solve the nonlinear model predictive control (NMPC) optimization problem. Consequently, analysis of NMPC techniques is often connected to the computational approach employed. In this paper, a theoretical analysis of unconstrained NMPC is presented that is independent of the computational approach. A nonlinear discrete-time, state-space model is used to predict the effects of future inputs on future process outputs. It is shown that model inverse, pole-placement, and steady-state controllers can be obtained by suitable selection of the control and prediction horizons. Moreover, the NMPC optimization problem can be modified to yield nonlinear internal model control (NIMC). The computational requirements of NIMC are considerably less than NMPC, but the NIMC approach is currently restricted to nonlinear models with well-defined and stable inverses. The NIMC controller is shown to provide superior servo and regulatory performance to a linear IMC controller for a continuous stirred tank reactor.     

IMC design for unstable processes with time delays

A modified IMC structure is proposed for unstable processes with time delays. The structure extends the standard IMC structure for stable processes to unstable processes and controllers do not have to be converted to conventional ones for implementation. An advantage of the structure is that setpoint tracking and disturbance rejection can be designed separately. A method is proposed to tune the modified IMC structure with an emphasis on the robustness of the structure. Design for some typical delayed unstable processes shows that the control structure can be tuned easily and achieve good tradeoff between time-domain performance and robustness.     

NCS系统中二自由度内模控制器的优化设计

针对网络化控制系统中网络时滞与对象模型不确定性,提出了一种二自由度内模控制器的优化设计方法。该控制器能够实现设定值跟踪与扰动抑制过程解耦,同时在对象模型失配情况下,系统具有较强的鲁棒稳定性。对于控制器的参数采用了混沌算法进行优化,以直线伺服系统为对象的仿真实验证实了此方法的可行性。