Low-gain internal model control PID controller design based on second-order filter

A design method is proposed for low-gain internal model control (IMC) proportional-integral-derivative (PID) controllers based on the second-order filter. The PID parameters are obtained by approximating the feedback form of the IMC controller with a Maclaurin series, in which the second-order filter is applied using the IMC approach to achieve a low-gain PID controller that is suitable for model mismatch problems. Analytical PID tuning rules based on the second-order filter are derived for several common-use process models. The second-order filter is designed from the desired time domain performances of maximum overshoot and settling time. Furthermore, the robustness of the IMC PID controller based on the second-order filter is analyzed, and results show that its robustness performance is better than the first-order filter under certain conditions. Finally, three categories of models divided by the ration of time constant and time delay are presented in the comparative numerical simulations to validate the effectiveness and generality of the proposed PID controller design method.     

Adaptive Internal Model Control of a High‐Purity Heat‐Integrated Air Separation Column

An internal model control scheme based on a second‐order internal model (SI‐IMC) is proposed for the heat‐integrated air separation column (HIASC). An adaptive internal model control (ASI‐IMC) scheme is further presented to make the model more accurate. The IMC scheme based on the first‐order model (F‐IMC) and the multi‐loop PID (M‐PID) scheme are also explored as the comparison basis of ASI‐IMC and SI‐IMC schemes. Comparative researches among these four control schemes are carried out in detail. The results indicate that ASI‐IMC presents the best performances among the four control schemes in both servo control and regulatory control, which proves the improvement of ASI‐IMC over the SI‐IMC and the superiority of ASI‐IMC for the high‐purity HIASC.     

燃煤电站锅炉主蒸汽压力滑模预测控制(英文)

Since the combustion system of coal-fired boiler in thermal power plant is characterized as time varying, strongly coupled, and nonlinear, it is hard to achieve a satisfactory performance by the conventional proportional integral derivative (PID) control scheme. For the characteristics of the main steam pressure in coal-fired power plant boiler, the sliding mode control system with Smith predictive structure is proposed to look for performance and robustness improvement. First, internal model control (IMC) and Smith predictor (SP) is used to deal with the time delay, and sliding mode controller (SMCr) is designed to overcome the model mismatch. Simulation results show the effectiveness of the proposed controller compared with conventional ones.     

Investigating Control Schemes for an Ideal Thermally Coupled Distillation Column (ITCDIC)

The control schemes of an ITCDIC are addressed. A modified IMC scheme (M‐IMC) is proposed to overcome model/plant mismatch of the Internal Model Control scheme (IMC). Predictive PID control (P‐PID) and Adaptive Predictive control (AP‐PID) schemes are also presented to improve effectively the response speed of the multi‐loop PID control (M‐PID) and eliminate its residual error. A detailed comparative investigation on the above five control schemes was performed. Simulation results demonstrate all the schemes are able to keep two end products within their specifications. M‐IMC is the best one with the fastest response speed. AP‐PID is the second choice since it is better at dealing with sudden set‐point transitions and complex external disturbances than P‐PID. M‐PID cannot compete with AP‐PID and P‐PID due to its slow servo response speed and large residual error. IMC ranks last as it is extremely sensitive to changes in the operating conditions.     

Robust continuous velocity control of convective spatially distributed systems

In this work a robust nonlinear scheme is proposed to control spatially distributed convective systems described by first-order hyperbolic partial differential equations by manipulating the flow velocity. The proposed scheme is designed after the method of characteristics is used to establish key structural properties of the system dynamics. The resulting feedback control, which can be seen as a proportional integral controller with variable integration time, does not require measurements for several axial points nor infinite dimensional state estimations. The proposed controller is applied successfully to two heat exchange simulation examples and a nonisothermical plug flow reactor. It is shown that it is robust in the face of uncertain parameters and load disturbances. Finally, the performance of the robust controller is compared to other control applications.     

Polypropylene degradation control during reactive extrusion

In this work, a proportional‐integral‐derivative (PID) control scheme with two different tuning methods to control the degree of degradation of polypropylene (PP) during reactive extrusion is proposed. The concentration of dicumyl peroxide is taken as the manipulated variable. The molten viscosity of PP under processing is taken as the controlled variable. The degree of degradation is determined by a viscosity function derived by an off‐line identification. A first‐order‐plus‐time‐delay empirical model is identified to simulate the system plant. Both Ziegler–Nichols tuned PID and internal model control (IMC)‐based PID controllers are implemented on the system. Better performances in settling time and precision can be achieved using the IMC‐based PID controller. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 95: 280–289, 2005     

多变量多时滞非方系统的解耦内模控制

多变量复杂控制系统不仅具有多耦合和多时滞性,还具有结构上的复杂性,即输入输出不等,传递函数为奇异矩阵。传统的多变量内模控制是基于对非奇异对象求逆来进行的,因此很难解决这类问题。针对该情况引入矩阵论中的广义逆概念,通过求对象的广义逆矩阵来设计解耦内模控制器,打破了内模控制只能对方系统进行控制的局限性,并利用泰勒近似很好地解决了多滞后的问题,最后通过设计特殊形式的滤波器,不仅能够消除由纯滞后近似引入的不稳定极点,保证系统的稳定性,且能够保证系统的正则性。仿真结果表明,该方法不仅跟踪迅速,且继承了内模控制的无余差和强鲁棒性,动态解耦效果良好,仅对时滞变化较为敏感。由于系统基于内模控制设计,故模型匹配度越高,系统响应越好。     

基于改进VRFT算法的PID控制器参数整定

分析虚拟参考反馈参数整定（VRFT）设计方法和内模控制（IMC）方法的内在关系,提出一种改进的VRFT—PID参数整定方法。该方法的基本思想是将运行一段时间的过程输入输出数据添加到原始数据序列中,用来更新传统VRFT设计方法中的离线数据。然后利用VRFT使性能指标最小时的参数即为控制器参数的设计思想来整定PID控制器。仿真结果表明,改进的VRFT-PID整定方法优于传统的VRFT-PID方法。     

A unified approach to the design of advanced proportional-integral-derivative controllers for time-delay processes

A unified approach for the design of proportional-integral-derivative (PID) controllers cascaded with first-order lead-lag filters is proposed for various time-delay processes. The proposed controller’s tuning rules are directly derived using the Padé approximation on the basis of internal model control (IMC) for enhanced stability against disturbances. A two-degrees-of-freedom (2DOF) control scheme is employed to cope with both regulatory and servo problems. Simulation is conducted for a broad range of stable, integrating, and unstable processes with time delays. Each simulated controller is tuned to have the same degree of robustness in terms of maximum sensitivity (Ms). The results demonstrate that the proposed controller provides superior disturbance rejection and set-point tracking when compared with recently published PID-type controllers. Controllers’ robustness is investigated through the simultaneous introduction of perturbation uncertainties to all process parameters to obtain worst-case process-model mismatch. The process-model mismatch simulation results demonstrate that the proposed method consistently affords superior robustness.     

基于内模控制的Smith反向解耦控制器设计

针对多变量时滞系统提出了一种基于内模控制(Internal Model Control,IMC)的Smith动态解耦控制器设计方法。其中,Smith补偿器被应用在该控制结构中,包含带有时滞项和不带时滞项的补偿结构,以解决不能完全补偿的问题,通过反向解耦设计实现多变量时滞系统动态解耦。多变量系统被解耦成一系列互相独立的单回路对象,通过内模控制原理对Smith控制器进行参数整定,并分析了系统的鲁棒性。仿真实例表明了该方法的有效性,能够较好地克服系统参数扰动导致的干扰,并具有较好的动态性能。     

Decoupling internal model control for multivariable systems with multiple time delays

In this paper, the decoupling internal model control (IMC) with stability is investigated for multivariable stable processes with multiple time delays. All the stabilizing IMC controllers which solve this decoupling problem and the resulting closed-loop systems are characterized in terms of the open-loop system's time delays and non-minimum phase zeros. It shows that the inclusion of some time delays and non-minimum phase zeros might be necessary to make a decoupling solution realizable and stabilizing. Based on this characterization, a control design method for best achievable performance is presented. However, owing to the high complexity of the theoretical controller, a practical controller design procedure is developed with the help of the proposed model reduction algorithm. Examples are given to illustrate our analysis and design. Significant performance improvement over the existing multivariable Smith predictor control has been achieved with the proposed approach.     

Nonlinear recursive feedback control for the regulation of substrate concentration in a fixed bed bioreactor

In this work, a recursive nonlinear feedback control law for the regulation of the outlet substrate concentration for a fixed bed bioreactor with immobilized biomass is designed. The control algorithm is based on a reduced order model related with ordinary differential equations and only made use of a discrete substrate outlet concentration for its implementation. It is shown that the proposed control algorithm is robust against disturbances in the input substrate concentration. The performance of the proposed regulation scheme is illustrated by means of numerical simulations. © 1999 Society of Chemical Industry     

ENHANCED IMC-PID CONTROLLER DESIGN WITH LEAD-LAG FILTER FOR UNSTABLE AND INTEGRATING PROCESSES WITH TIME DELAY

In this article, a design method for a PID controller is proposed based on IMC principles for control of open loop integrating and unstable first-order processes with time delay. The design is based on H₂ optimal closed-loop transfer function for set point changes and step input disturbances. The method has one tuning parameter, and systematic guidelines are provided for the selection of this tuning parameter based on peak value of the sensitivity function. The performance of the designed controller is verified on various integrating and unstable processes, and it is observed that nominal and robust control performance is achieved with the proposed design method. Improved closed-loop performance was obtained when compared to other methods recently reported in the literature. Further, the proposed method provides good closed-loop performance even when there are large uncertainties in the process parameters.     

A DIRECT NONLINEAR ADAPTIVE CONTROL OF STATE FEEDBACK LINEARIZABLE SYSTEMS

A direct nonlinear adaptive control of state feedback linearizable single-input single-output systems is proposed in the case when parametric uncertainties are represented linearly in the unknown parameters. The main feature of the proposed nonlinear adaptive control system is that the linearizing coordinate transformation and the state feedback are updated by parametric adaptive law, derived using the second method of Lyapunov. The proposed adaptive control scheme is relatively straightforward and simple in the sense that it does not use the concept of augmented error. This adaptive control scheme is numerically applied to an exothermic chemical reactor system and is compared with the nonadaptive stale feedback linearization which has an integral action. The simulation shows that the proposed adaptive control scheme can be applied effectively to highly nonlinear, uncertain chemical systems.     

Design and control of extractive distillation for the separation of methyl acetate-methanol-water

The azeotrope of methyl acetate methanol and water was isolated using extractive distillation with water as entrainer. The pressure-swing extractive distillation (PSED) process and vapor side-stream distillation column (VSDC) with the rectifier process were designed to separate the methyl acetate, methanol and water mixture. It was revealed that the VSDC with the rectifier process had a reduction in energy consumption than the PSED process. Four control schemes of the two process were investigated: Double temperature control scheme (CS1), Q_R/F feedforward control of reboiler duty scheme for PESD (CS2), Q_R/F feedback control scheme for VSDC (CS3), the feedback control scheme of sensitive plate temperature of side-drawing distillation column to dominate the compressor shaft speed (CS4). Feed flow and composition disturbance were used to evaluate the dynamic performance. As a result, CS4 is a preferable choice for separation of methyl acetate-methanol-water mixture. A control scheme combining the operating parameters of dynamic equipment with the control indicators of static equipment was proposed in this paper. It means using the sensitive plate temperature of side-drawing column to control the compressor shaft speed. This is a new control scheme for extractive distillation.     

Design of a multivariable internal model controller based on singular value decomposition

In this article, a novel internal model control (IMC) approach based on singular value decomposition (SVD) is proposed for the control of multiple‐input–multiple‐output (MIMO) systems with multiple time delays. This approach achieves decoupling using a compensation term and improves the robustness using SVD in the inverse of the steady‐state gain matrix of process. Meanwhile, a novel filter is designed for decoupling and fast response speed of multivariable systems with multiple delays. The design of the controller can be extended to non‐square systems where there are more inputs than outputs. Examples are included to illustrate the effectiveness of the method. © 2012 Canadian Society for Chemical Engineering     

基于ARX-PLS解耦框架下的多回路约束迭代模型预测控制方法(英文)

A multi-loop constrained model predictive control scheme based on autoregressive exogenous-partial least squares （ARX-PLS） framework is proposed to tackle the high dimension, coupled and constraints problems in industry processes due to safety limitation, environmental regulations, consumer specifications and physical restric-tion. ARX-PLS decoupling character enables to turn the multivariable model predictive control （MPC） controller design in original space into the multi-loop single input single output （SISO） MPC controllers design in latent space. An idea of iterative method is applied to decouple the constraints latent variables in PLS framework and recursive least square is introduced to identify ARX-PLS model. This algorithm is applied to a non-square simulation system and a stirred reactor for ethylene polymerizations comparing with adaptive internal model control （IMC） method based on ARX-PLS framework. Its application has shown that this method outperforms adaptive IMC method based on ARX-PLS framework to some extent.     

基于动态PLS框架的多回路内模控制器设计(英文)

In this paper, a multi-loop internal model control (IMC) scheme in conjunction with feed-forward strategy based on the dynamic partial least squares (DyPLS) framework is proposed. Unlike the traditional methods to decouple multi-input multi-output (MIMO) systems, the DyPLS framework automatically decomposes the MIMO process into a multi-loop system in the PLS subspace in the modeling stage. The dynamic filters with identical structure are used to build the dynamic PLS model, which retains the or-thogonality among the latent variables. To address the model mismatch problem, an off-line least squares method is applied to obtain a set of optimal filter parameters in each latent space. Without losing the merits of model-based control, a simple and easy-tuned IMC structure is readily carried over to the dynamic PLS control framework. In addition, by projecting the measurable disturbance into the latent subspace, a multi-loop feed-forward control is yielded to achieve better performance for disturbance rejection. Simulation re-sults of a distillation column are used to further demonstrate this new strategy outperforms conventional control schemes in servo behavior and disturbance rejection.     

蒸汽裂解模拟装置的二自由度内模控制

针对中石化某裂解装置的控制问题,通过实测模型,根据内模控制理论,提出一种二自由度的内模控制器的设计和参数整定方法.通过参数整定,所设计的控制器可以控制系统,同时具有良好的设定值跟踪特性和抑制干扰特性.将该二自由度控制器设计方法应用于蒸汽裂解装置中,减小了装置升温过程的波动,克服了保温过程的扰动,并且缩短了升温时间,提高...     

基于VRFT的IMC-PID方法及其在水厂浊度控制中的仿真研究

针对城市供水出水浊度过程的大惯性、大时滞、非线性以及时变等特点,将虚拟参考反馈整定数据驱动方法引入到IMC-PID控制器的整定中来,提出了一种不基于模型参数的VRFT-IMC参数整定方法.该方法集合了内模控制鲁棒性强和数据驱动控制的自适应性两方面的优点,仿真表明其控制性能优于普通IMC-PID控制器,可望用于出水浊度等...