Design of multiloop PI controllers based on quadratic optimal approach

The LQR methodology is extended to produce multiloop PI controllers in this study. With this method, a multivariable P controller is first obtained and then diagonalized using an iterative procedure. The resulting controller is further complemented with the integral action in a similar process. The proposed tuning process explores different values of the control weight matrix to balance the output error and control signal in both stages, and is refined through additional indices related with the error to reference tracking, disturbance rejection and the associated control use. In addition, the diagonalization procedure is generalized to obtain multiloop versions of existing multivariable PI controllers. The developed theory was applied to the design of multiloop controllers for a distillation column as well as the diagonalization of existing controllers for a nonlinear CSTR. The tuning procedure allowed the synthesis of multiloop PI controllers with performance indices comparable to those reported by other authors. Furthermore, diagonalized controllers exhibited a similar operation as the original multivariable ones.     

Development of characteristic equations and robust stability analysis for SISO move suppressed and shifted DMC

New controller and closed loop transfer functions for move suppressed and shifted dynamic matrix control were derived in order to compare the controller robustness on several plants as a function of tuning parameters lambda and m. The derivation of these transfer functions are for any order plant requiring its open loop step or impulse response. A generic control design algorithm was developed for selecting the controller tuning parameters using controller robustness as a performance index, in the presence of plant parameter variations and uncertainties. Shifted dynamic matrix control (DMC) was found to be more robust with respect to all plant parameter variations, and therefore more suited than move suppressed DMC to control plants with wide ranging parameters. This result was demonstrated on an experimental direct current servomotor system, and further verified on a plant having a cascade control structure with the (m , m) being the most robust to plant variations.     

Integration of advanced process control and full-scale dynamic simulation

In the process control industry, multivariable model predictive controller and dynamic simulation for operator training are usually available in separate packages. It is very difficult for the operators and plant engineers to find good tools for them to get trained in multivariable advanced process control. This paper presents a system, which integrates the advanced process control and full-scale dynamic simulation. The advanced process control uses multivariable model predictive control techniques. The model used in the predictive control algorithms is generated from the dynamic simulated process. The advanced process controller can control the simulated plant directly, or through a DCS system to control the simulated plant. The combined system provides an excellent environment for training operators in process operation with multivariable advanced process control. The same environment is also very useful for engineers in designing and tuning the advanced process controllers, and in testing communication between the advanced process controller and the DCS systems, or the other type of process control systems.     

Simultaneous gains tuning in boiler/turbine PID-based controller clusters using iterative feedback tuning methodology

Tuning a complex multi-loop PID based control system requires considerable experience. In today's power industry the number of available qualified tuners is dwindling and there is a great need for better tuning tools to maintain and improve the performance of complex multivariable processes. Multi-loop PID tuning is the procedure for the online tuning of a cluster of PID controllers operating in a closed loop with a multivariable process. This paper presents the first application of the simultaneous tuning technique to the multi-input-multi-output (MIMO) PID based nonlinear controller in the power plant control context, with the closed-loop system consisting of a MIMO nonlinear boiler/turbine model and a nonlinear cluster of six PID-type controllers. Although simplified, the dynamics and cross-coupling of the process and the PID cluster are similar to those used in a real power plant. The particular technique selected, iterative feedback tuning (IFT), utilizes the linearized version of the PID cluster for signal conditioning, but the data collection and tuning is carried out on the full nonlinear closed-loop system. Based on the figure of merit for the control system performance, the IFT is shown to deliver performance favorably comparable to that attained through the empirical tuning carried out by an experienced control engineer.     

Development of characteristic equations and robust stability analysis for MIMO move suppressed and shifted DMC

Discrete-time controller and closed-loop transfer functions were developed for move suppressed λ and the recently formulated m-shifted multiple-input-multiple-output (MIMO) dynamic matrix control (DMC). Using these transfer functions, robust analyses were conducted for MIMO plants by varying corresponding delay and gain ratios of the system. In all instances, robust plots indicate that the shifted DMC is less sensitive and hence more robust to variations in the plant parameters than move suppressed DMC. It was shown that the design of these MIMO DMC controllers depends on the plant closed-loop performance and overall stability, since the selection of λ and m directly influences the plant robustness and closed-loop dynamics.     

Well-conditioned model predictive control

Model-based predictive control is an advanced control strategy that uses a move suppression factor or constrained optimization methods for achieving satisfactory closed-loop dynamic responses of complex systems. While these approaches are suitable for many processes, they are formulated on the selection of certain parameters that are ambiguous and also computationally demanding which makes them less suited for tight control of fast processes. In this paper, a new dynamic matrix control (DMC) algorithm is proposed that reduces inherent ill-conditioning by allowing the process prediction time step to exceed the control time step. The main feature, that stands in contrast with current DMC approaches, is that the original open-loop data are used to evaluate a "shifting factor" m in the controller matrix where m replaces the move suppression coefficient. The new control algorithm is practically demonstrated on a fast reacting process with better control being realized in comparison with DMC using move suppression. The algorithm also gives improved closed-loop responses for control simulations on a multivariable nonlinear process having variable dead-time, and on other models found in the literature. The shifting factor m is generic and can be effectively applied for any control horizon.     

Multi-model direct adaptive decoupling control with application to the wind tunnel system

In this paper, a new multi-model direct adaptive decoupling controller is presented for multivariable processes, which includes multiple fixed optimal controllers, one free-running adaptive controller, and one re-initialized adaptive controller. The fixed controllers provide initial control to the process if its model lies in the corresponding region. For each controller selected, the re-initialized adaptive controller uses the values of this particular controller to improve the adaptation speed. This controller may replace the fixed controller at a later stage according to the switching criterion which is to select the best one among all controllers. A free-running adaptive controller is also added to guarantee the overall system stability. Different from the multiple models adaptive control structure proposed in Narendra, Balakrishnan, and Ciliz [Adaptation and learning using multiple models, switching, and tuning. IEEE Control Syst. Mag. 15, 37-51 (1995)], the method not only is applicable to the multi-input multi-output processes but also identifies the decoupling controller parameters directly, which reduces both the computational burden and the chances of a singular matrix during the process of determining controller parameters. Several examples for a wind tunnel process are given to demonstrate the effectiveness and practicality of the proposed method.     

Simple method of designing centralized PI controllers for multivariable systems based on SSGM

A method is given to design multivariable PI/PID controllers for stable and unstable multivariable systems. The method needs only the steady state gain matrix (SSGM). The method is based on the static decoupler design followed by SISO PI/PID controllers design and combining the resulted decoupler and the diagonal PI(D) controllers as the centralized controllers. The result of the present method is shown to be equivalent to the empirical method proposed by Davison EJ. Multivariable tuning regulators: the feed-forward and robust control of general servo-mechanism problem. IEEE Trans Autom Control 1976;21:35–41. Three simulation examples are given. The performance of the controllers is compared with that of the reported centralized controller based on the multivariable transfer function matrix.     

Learning control for batch thermal sterilization of canned foods

A control technique based on Reinforcement Learning is proposed for the thermal sterilization of canned foods. The proposed controller has the objective of ensuring a given degree of sterilization during Heating (by providing a minimum temperature inside the cans during a given time) and then a smooth Cooling, avoiding sudden pressure variations. For this, three automatic control valves are manipulated by the controller: a valve that regulates the admission of steam during Heating, and a valve that regulate the admission of air, together with a bleeder valve, during Cooling. As dynamical models of this kind of processes are too complex and involve many uncertainties, controllers based on learning are proposed. Thus, based on the control objectives and the constraints on input and output variables, the proposed controllers learn the most adequate control actions by looking up a certain matrix that contains the state-action mapping, starting from a preselected state-action space. This state-action matrix is constantly updated based on the performance obtained with the applied control actions. Experimental results at laboratory scale show the advantages of the proposed technique for this kind of processes.     

A novel tuning strategy for multivariable model predictive control

Model predictive control (MPC) has established itself as the most popular form of advanced multivariable control in the chemical process industry. However, the benefits of this technology cannot be realized unless the controller can be operated with desirable performance for an extended period of time. The objective of this work is to present an easy-to-use and reliable tuning strategy that enables the control practitioner to maintain MPC at peak performance with minimal effort. A novel analytical expression that computes the move suppression coefficients, guidelines to select the additional adjustable parameters, and their demonstration in an overall tuning strategy are some of the significant contributions of this work. The compact form for the analytical expression that computes the move suppression coefficients is derived as a function of a first order plus dead time (FOPDT) model approximation of the process dynamics. With tuning parameters computed. MPC is then implemented in the classical fashion using an internal model formulated from step response coefficients of the actual process. Just as a FOPDT model approximation has proved a valuable tool in tuning rules such as Cohen-Coon. ITAE and IAE for PID implementations, the tuning strategy presented here is significant because it offers an analogous approach for multivariable MPC.     

Centralized PI control for high dimensional multivariable systems based on equivalent transfer function

This article presents a new scheme to design full matrix controller for high dimensional multivariable processes based on equivalent transfer function (ETF). Differing from existing ETF method, the proposed ETF is derived directly by exploiting the relationship between the equivalent closed-loop transfer function and the inverse of open-loop transfer function. Based on the obtained ETF, the full matrix controller is designed utilizing the existing PI tuning rules. The new proposed ETF model can more accurately represent the original processes. Furthermore, the full matrix centralized controller design method proposed in this paper is applicable to high dimensional multivariable systems with satisfactory performance. Comparison with other multivariable controllers shows that the designed ETF based controller is superior with respect to design-complexity and obtained performance.     

Simplified filtered Smith predictor for MIMO processes with multiple time delays

This paper proposes a simplified tuning strategy for the multivariable filtered Smith predictor. It is shown that offset-free control can be achieved with step references and disturbances regardless of the poles of the primary controller, i.e., integral action is not explicitly required. This strategy reduces the number of design parameters and simplifies tuning procedure because the implicit integrative poles are not considered for design purposes. The simplified approach can be used to design continuous-time or discrete-time controllers. Three case studies are used to illustrate the advantages of the proposed strategy if compared with the standard approach, which is based on the explicit integrative action.     

SISO extended predictive control-formulation and the basic algorithm

A new predictive controller is developed that represents a significant change from conventional model predictive control. The method termed extended predictive control (EPC) uses one tuning parameter, the condition number of the system matrix to provide an easy-to-follow tuning procedure. EPC drastically improves the system matrix conditionality resulting in faster closed-loop response without oscillatory transients. The control performance of EPC is compared with the original move suppressed and recently derived shifted predictive controllers, with improved results.     

Multi-loop decentralized PID control based on covariance control criteria: an LMI approach

PID control is well known and widely applied in industry and many design algorithms are readily available in the literature. However, systematic design of multi-loop or decentralized PID control for multivariable processes to meet certain objectives simultaneously is still a challenging task. Designing multi-loop PID controllers such that the process variables satisfy the generalized covariance constraints is studied in this paper. A convergent computational algorithm is proposed to calculate the multi-loop PID controller for a process with stable disturbances. This algorithm is then extended to a process with random-walk disturbances. The feasibility of the proposed algorithm is verified by applying it to several simulation examples.     

Relay-enhanced multi-loop PI controllers

In this paper, the development of relay-enhanced multi-loop PI controllers is described for multivariable processes. The control system employs a relay in series with the controller. The relay can ensure a satisfactory level of closed-loop performance and it also yields oscillations for tuning of the PI controller based on an equivalent process model for each loop. A simulation example [on a two-inputs-two-outputs (TITO) process] is provided to illustrate the effectiveness of the proposed method and to compare its performance to an existing method.     

基于自适应遗传算法的异步电机矢量控制参数优化与仿真

自动控制领域中PID参数的整定是一个极其重要的问题。为解决工程人员凭经验对异步电机控制器参数整定难寻到最优解的问题,将速度误差积分型作为目标函数,采用惩罚措施,利用自适应遗传算法对异步电机速度控制器的参数进行优化、仿真,并与利用常规PID参数整定获得的速度曲线相对比,实验结果表明,用自适应遗传算法优化的参数,可以提高系统的控制精度、动态性能。     

基于改进模型预测控制的加热炉温控系统研究

模型预测控制具有鲁棒性强、跟踪快速性好等特点,能够解决复杂工业过程控制中的大时滞问题。该文提出了一种改进的模型预测控制器,基于事先设定的期望响应,实现参考轨迹在预测时域内最大限度地渐进期望轨迹,使系统响应能够准确地跟踪期望轨迹。该文以硅单晶体加热炉为控制对象,分别采用PID、DMC和改进DMC三种控制方法进行预测控制。仿真结果表明改进的DMC控制方法比传统的预测控制方法具有更好的动态响应性能和跟踪效果。     

Move Suppression Calculations for Well-Conditioned MPC

Several popular tuning strategies applicable to Model Predictive Control (MPC) schemes such as GPC and DMC have previously been developed. Many of these tuning strategies require an approximate model of the controlled process to be obtained, typically of the First Order Plus Dead Time type. One popular method uses such a model to analytically calculate an approximate value of the move suppression coefficient to achieve a desired condition number for the regularized system dynamic matrix; however it is not always accurate and tends to under-estimate the required value. In this paper an off-line method is presented to exactly calculate the move suppression coefficient required to achieve a desired condition number directly from the unregularized system dynamic matrix. This method involves an Eigendecomposition of the system dynamic matrix - which may be too unwieldy in some cases –and a simpler analytical expression is also derived. This analytical expression provides a guaranteed tight upper bound on the required move suppression coefficient yielding a tuning formula which is easy to apply, even in on-line situations. Both methods do not require the use of approximate or reduced order process models for their application. Simulation examples and perturbation studies illustrate the effectiveness of the methods in both off-line and on-line MPC configurations. It is shown that accurate conditioning and improved closed loop robustness can be achieved.     

Experimental evaluation of control performance of MPC as a regulatory controller

Proportional-integral-derivative (PID) control is widely practised as the base layer controller in the industry due to its robustness and design simplicity. However, a supervisory control layer over the base layer, namely a model predictive controller (MPC), is becoming increasingly popular with the advent of computer process control. The use of a supervisory layer has led to different control structures. In this study, we perform an objective investigation of several commonly used control structures such as ‘Cascaded PI controller’, ‘DMC cascaded to PI’ and ‘Direct DMC’. Performance of these control structures are compared on a pilot-scale continuous stirred tank heater (CSTH) system. We used dynamic matrix control (DMC) algorithm as a representative of MPC. In the DMC cascaded to PI structure, the flow-loops are regulated by the PI controller. On top of that a DMC manipulates the set-points of the flow-loops to control the temperature and the level of water in the tank. The ‘Direct DMC’ structure, as its name suggests, uses DMC to manipulate the valves directly. Performance of all control structures were evaluated based on the integrated squared error (ISE) values. In this empirical study, the ‘Direct DMC’ structure showed a promise to act as regulatory controller. The selection of control frequency is critical for this structure. The effect of control frequency on controller performance of the ‘Direct DMC’ structure was also studied.     

一种改进的DMC算法及其应用

在分析PID算法和动态矩阵控制算法的基础上,将动态矩阵控制算法的性能指标构造成PID形式,并推导了改进的PIDDMC算法。通过对参数选取范围的研究,在时域内分析了PIDDMC控制器的参数选择对控制性能的影响。最后通过在电厂的过热汽温控制系统中的仿真事例分析,同基本的DMC控制算法对比,结果表明PIDDMC算法具有更好的控制性能,将会有较好的工程应用前景。