Analytical design of enhanced PID filter controller for integrating and first order unstable processes with time delay

An analytical design for a proportional-integral derivative (PID) controller cascaded with a first order lead/lag filter is proposed for integrating and first order unstable processes with time delay. The design algorithm is based on the internal model control (IMC) criterion, which has a single tuning parameter to adjust the performance and robustness of the controller. A setpoint filter is used to diminish the overshoot in the servo response. In the simulation study, the controllers were tuned to have the same degree of robustness by measuring the maximum sensitivity, Ms, in order to obtain a reasonable comparison. Furthermore, the robustness of the controller was investigated by inserting a perturbation uncertainty in all parameters simultaneously to obtain the worst case model mismatch, and the proposed method showed more robustness against process parameter uncertainty than the other methods. For the selection of the closed-loop time constant, λ, a guideline is also provided over a broad range of time-delay/time-constant ratios. The simulation results obtained for the suggested method were compared with those obtained for other recently published design methods to illustrate the superiority of the proposed method.     

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.     

Analysis of a predictor—regulator system

A high-performance control system called “predictor—regulator” is proposed, its governing laws are derived, and it is applied to simulated processes to evaluate its characteristics, and to real processes to demonstrate its feasibility. The proposed system is made up of a two-loop configuration[4]: a fast auxiliary loop consisting of a controller and a simple lag element, and a main loop provided with another controller operating on the process. Both the controllers are conventional PID type commercial controllers. Theoretical study reveals that, by suitable choice of the compensator parameters, the control arrangement could result in remarkably superior performance. While, for the key loads, both steady state and transient errors become practically zero with the aid of only two P-controllers, inclusion of integral action aids in achieving control against secondary (unmeasured) disturbances also. The design and performance of the regulator system are evaluated via simulation. Several practical aspects of the control problem are examined, and criteria for choosing the auxiliary lag, the modes of control, and the controller settings are established. Applicability of the technique to a wide range of processes (e.g. complex higher order and dead time processes) is also discussed. The results obtained confirm that the control approach could match combined feedforward—feedback regulation in its performance, and classical feedback in design simplicity and ease of implementation.     

Bounded robust control of constrained multivariable nonlinear processes

This work focuses on control of multi-input multi-output (MIMO) nonlinear processes with uncertain dynamics and actuator constraints. A Lyapunov-based nonlinear controller design approach that accounts explicitly and simultaneously for process nonlinearities, plant-model mismatch, and input constraints, is proposed. Under the assumption that all process states are accessible for measurement, the approach leads to the explicit synthesis of bounded robust multivariable nonlinear state feedback controllers with well-characterized stability and performance properties. The controllers enforce stability and robust asymptotic reference-input tracking in the constrained uncertain closed-loop system and provide, at the same time, an explicit characterization of the region of guaranteed closed-loop stability. When full state measurements are not available, a combination of the state feedback controllers with high-gain state observes and appropriate saturation filters, is employed to synthesize bounded robust multivariable output feedback controllers that require only measurements of the outputs for practical implementation. The resulting output feedback design is shown to inherit the same closed-loop stability and performance properties of the state feedback controllers and, in addition, recover the closed-loop stability region obtained under state feedback, provided that the observer gain is sufficiently large. The developed state and output feedback controllers are applied successfully to non-isothermal chemical reactor examples with uncertainty, input constraints, and incomplete state measurements. Finally, we conclude the paper with a discussion that attempts to put in perspective the proposed Lyapunov-based control approach with respect to the nonlinear model predictive control (MPC) approach and discuss the implications of our results for the practical implementation of MPC, in control of uncertain nonlinear processes with input constraints.     

On‐Line PEMFC Control Using Parameterized Nonlinear Model‐Based Predictive Control

In this work, a fast nonlinear model‐based predictive control (NMPC) strategy is designed and experimentally validated on‐line on a real fuel cell. Regarding NMPC strategies, the most challenging part remains to achieve on‐line implementation, especially when dealing with fast dynamic systems. As previously demonstrated in a recent work, the proposed control strategy is ideally suited to address this problem. Indeed, it is 30 times faster than classical NMPC controllers. This strategy relies on a specific parameterization of the control actions to reduce the computational time and achieve on‐line implementation. Due to its short computational time compared to mechanistic models, an artificial neural network model is designed and experimentally validated. This model is employed as internal model in the NMPC controller to predict the system behavior. To confirm the applicability and the relevance of the proposed NMPC controller varying control scenarios are investigated on a test bench. The built‐in controller is overridden and the NMPC controller is implemented externally and executed on‐line. Experimental results exhibit the outstanding tracking capability and robustness against model‐process mismatch of the proposed strategy. The parameterized NMPC controller turns out to be an excellent candidate for on‐line applications.     

Controller adjustment for improved nominal performance and robustness—II. Robust geometric control of a distillation column

In Part I of this paper a general frequency domain method to adjust multivariable controllers with respect to both nominal performance and robustness are presented. In Part II this method is used to examine and improve the control of a binary distillation column. The selected control strategies are conventional PI control and geometric control. The PI controller is adjusted in order to obtain satisfactory robustness properties. The basic geometric controller is extended with feedback from state variables which do not alter the nominal disturbance rejection. Both constant gain feedback and integration are examined. The included control parameters are adjusted for improved nominal performance and for robustness. The major result is that the adjusted geometric controller has a robustness which equals that of the adjusted conventional PI controller. However, the nominal performance of the geometric controller is superior to that of conventional PI control. Thus we expect the adjusted geometric controller to have improved performance on a real column compared to that of conventional PI control.     

Multi‐controller scheme for load rejection and set‐point tracking

To acheive complete compensation for loads, a novel multi‐controller scheme with feedforward control is proposed. This scheme has four controllers, a set‐point controller, two load controllers, and a feedforward controller. This results in the separation of the load response from the set‐point response in a closed‐loop system. These four controllers can then be designed independently to achieve good system performance for both set‐point tracking and load rejection. One of the load controllers can be chosen as a proportional controller; this guarantees physical realizability and provides excellent compensation. The results of simulation and real time control show that the proposed multi‐controller scheme is superior to a double‐controller system and a Smith predictor in the presence of large uncertainty in process dynamics especially for load disturbances.     

Nonlinear internal model control strategy for neural network models

A nonlinear internal model control (NIMC) strategy based on neural network models is proposed for SISO processes. The neural network model is identified from input—output data using a three-layer feedforward network trained with a conjugate gradient algorithm. The NIMC controller consists of a model inverse controller and a robustness filter with a single tuning parameter. The proposed strategy includes time delay compensation in the form of a Smith predictor and ensures offset-free performance. Extensions for measured disturbances are also presented. The NIMC approach is currently restricted to processes with stable inverses. Two alternative implementations of the control law are discussed and simulations results for a continuous stirred tank reactor and pH neutralization process are presented. The results for these two highly-nonlinear processes demonstrate the ability of the new strategy to outperform conventional PID control.     

Context-kernel support vector machines (KSVM) based run-to-run control for nonlinear processes

Past studies on multi-tool and multi-product (MTMP) processes have focused on linear systems. In this paper, a novel run-to-run control (RtR) methodology designed for nonlinear semiconductor processes is presented. The proposed methodology utilizes kernel support vector machines (KSVM) to perform nonlinear modeling. In this method, the original variables are mapped using a kernel function into a feature space where linear regression is done. To eliminate the effects of unknown disturbances and drifts, the KSVM expression for the KSVM controller is modified to include constants that are updated in a manner similar to the weights used in double exponential weighting moving average method and the control law for KSVM controllers is derived. Illustrative examples are presented to demonstrate the effectiveness of KSVM and its method in process modeling and control of processes. Even if there is limited data in process modeling, KSVM still has the good capability of characterizing the nonlinear behavior. The performance of the proposed KSVM control algorithm is highly satisfactory and is superior to the other MTMP control algorithms in controlling MTMP processes.     

Simulated nonlinear control studies of five-effect evaporator models

This paper is devoted to the simulated nonlinear control studies of two dynamic models of an industrial five-effect evaporator of an alumina refinery. The simulated control studies were carried out to ascertain the performance and robustness of nonlinear control techniques on the five-effect evaporator prior to its implementation on-site. The nonlinear control structure used in the studies was the multi-input multi-output (MIMO) globally linearizing control (GLC) structure of Kravaris and Soroush (1990). The I/O linearizing controller was implemented in a cascade arrangement with the industrial coded velocity form of proportional-integral (PI) controllers in the simulation. The design parameters were chosen such that the desired decoupling control of the ill-conditioned evaporator models was achieved, and such that cascade arrangement of the nonlinear controller was possible. Simulated results indicates that the MIMO GLC structure provides superior servo and regulatory control to multi-loop single-input single-output (SISO) PI controllers that are currently being used to regulate the five-effect evaporator on-site.     

积分和不稳定时滞对象的改进内模控制

针对化工过程中一阶积分和不稳定时滞对象,基于内模控制提出了两自由度控制方案。首先根据鲁棒控制理论H2最优性能指标设计设定值跟踪控制器,然后采用期望闭环补灵敏度函数确定扰动抑制控制器。设定值跟踪控制器和扰动抑制控制器可通过性能参数独立调节而无需再取折衷,同时保证系统具有较好的鲁棒稳定性。最后通过仿真实例验证了该控制方案的有效性。     

A method for robustness analysis of controlled nonlinear systems

This paper presents an approach to analyzing robustness properties of nonlinear systems under feedback control. The core idea is to apply numerical bifurcation analysis to the closed-loop process, using the controller/observer tuning parameters, the set points, and parameters describing model uncertainty (parametric as well as unmodeled dynamics) as bifurcation parameters. By analyzing the Hopf bifurcation and saddle-node bifurcation loci with respect to these parameters, bounds on the controller tuning are identified which can serve as a measure for the robustness of the controlled system. These bounds depend upon the type as well as the degree of mismatch that exists between the plant and the model used for controller design.The method is illustrated by analyzing three control systems which are applied to a continuously operated stirred tank reactor: a state feedback linearizing controller and two output feedback linearizing controllers. While model uncertainty has only a minor effect on the tuning of the state feedback linearizing controller, this does not represent a very realistic scenario. However, when an observer is implemented in addition to the controller and an output feedback linearizing scheme is investigated, it is found that the plant-model mismatch has a much more profound impact on the tuning of the observer than it has on the controller tuning. In addition, two observer designs with different level of complexity are investigated and it is found that a scheme which makes use of additional knowledge about the system will not necessarily result in better stability properties as the level of uncertainty in the model increases. These investigations are carried out using the robustness analysis scheme introduced in this paper.     

Smith predictor based fractional-order PI control for time-delay processes

A new fractional-order proportional-integral controller embedded in a Smith predictor is systematically proposed based on fractional calculus and Bode’s ideal transfer function. The analytical tuning rules are first derived by using the frequency domain for a first-order-plus-dead-time process model, and then are easily applied to various dynamics, including both the integer-order and fractional-order dynamic processes. The proposed method consistently affords superior closed-loop performance for both servo and regulatory problems, since the design scheme is simple, straightforward, and can be easily implemented in the process industry. A variety of examples are employed to illustrate the simplicity, flexibility, and effectiveness of the proposed SP-FOPI controller in comparison with other reported controllers in terms of minimum the integral absolute error with a constraint on the maximum sensitivity value.     

On-line optimization: a hierarchical scheme for distallation column control

This paper presents a hiererchical on-line optimization and nonlinear control of a distillation column using a new semirigorous model which drastically reduces the problem dimensions compared to a rigorous model without significantly compromising with accuracy. Single level control is often found to be inadequate since optimization using highly nonlinear physical models cannot be performed in the very short real times available between controller actions. A two level approach can effectively overcome this difficulty with optimization being carried out using more realistic nonlinear physical models at the supervisory level. The nominal control vector trajectory generated at this level using a nonlinear analytical model predictive control (NAMPC) is passed on to the regulatory level where an LQ type neighbouring optimal control action is generated. Simulation results showed that a two level control can effectively deal with process-model mismatch in the presence of disturbances. Experimentation on pilot scale distillation column vindicated the simulation results and demonstrated the superiority of the hierarchical control scheme.     

Analytical design of PID controller cascaded with a lead-lag filter for time-delay processes

An analytical method for the design of a proportional-integral-derivative (PID) controller cascaded with a second-order lead-lag filter is proposed for various types of time-delay process. The proposed design method is based on the IMC-PID method to obtain a desired, closed-loop response. The process dead time is approximated by using the appropriate Pade expansion to convert the ideal feedback controller to the proposed PID·filter structure with little loss of accuracy. The resulting PID·filter controller efficiently compensates for the dominant process poles and zeros and significantly improves the closed-loop performance. The simulation results demonstrate the superior performance of the proposed PID·filter controller over the conventional PID controllers. A guideline for the closed-loop time constant, λ, is also suggested for the FOPDT and SOPDT models.     

EXTENDED KALMAN FILTER CONTROLLER: FIRST PRINCIPLES MODELS TO NEURAL NETWORKS

Extended Kalman filters (EKF) have been widely employed for state and parameter estimation in chemical engineering systems. Gao et al. [Gao, F., Wang, F. and Li, M. (1999). Ind. Eng. Chem. Res., 38, 2345-2349] have proposed the use of EKF for control computation using a neural network representation of the system in a discrete-time framework. In the present study, an EKF controller is proposed in a continuous time framework with models incorporating different levels of process knowledge. The problem of process-model mismatch is handled by incorporating EKF-based state and/or parameter estimation along with control computation. A batch reactor temperature control problem for a highly exothermic reaction between maleic anhydride and hexanol to form hexyl monoester of maleic acid is considered as a test bed to evaluate the performance of the proposed control schemes. Three different models are considered, namely the first principles model, a reduced-order process model, and an artificial neural network (ANN) model for formulation of the control schemes. The performance of the proposed control scheme using first principles model is compared to that of generic model control, and a similar performance is achieved. The present study illustrates the usefulness of the proposed control schemes and can be easily extended to general chemical engineering systems.     

Set point weighted modified Smith predictor with PID filter controllers for non-minimum-phase (NMP) integrating processes

A simple modified Smith predictor design for the control of non-minimum-phase integrating processes with/without a zero is proposed. The method consists of two controllers, one for set point tracking and the other for disturbance rejection. The controllers are designed based on direct synthesis approach. The set point tracking controller is designed as a proportional-integral-derivative (PID) with lag filter and the disturbance rejection controller is designed as a proportional-derivative (PD) with lead lag structure. Typical types of integrating processes with/without zero are considered and the controllers are designed in a unified approach for all the types of integrating processes. Extensive simulation studies have been carried out on various integrating processes with/without zero. The present method gives good disturbance rejection response and significant improvement when compared to the recently reported methods in the literature.     

Control of milk pasteurization process using model predictive approach

A milk pasteurization process, a nonlinear process and multivariable interacting system, is difficult to control by the conventional on–off controllers since the on–off controller can handled the temperature profiles for milk and water oscillating over the plant requirements. The multi-variable control approach with model predictive control (MPC) is proposed in this study. The proposed algorithm was tested for control of a milk pasteurization process in four cases of simulation such as set point tracking, model mismatch, difference control and prediction horizons, and time sample. The results for the proposed algorithm show the well performance in keeping both the milk and water temperatures at the desired set points without any oscillation and overshoot and giving less drastic control action compared to the cascade generic model control (GMC) strategy.     

Performance analysis of three advanced controllers for polymerization batch reactor: An experimental investigation

The performances of three advanced non-linear controllers are analyzed for the optimal set point tracking of styrene free radical polymerization (FRP) in batch reactors. The three controllers are the artificial neural network-based MPC (NN-MPC), the artificial fuzzy logic controller (FLC) as well as the generic model controller (GMC). A recently developed hybrid model (Hosen et al., 2011a. Asia-Pac. J. Chem. Eng. 6(2), 274) is utilized in the control study to design and tune the proposed controllers. The optimal minimum temperature profiles are determined using the Hamiltonian maximum principle. Different types of disturbances are introduced and applied to examine the stability of controller performance. The experimental studies revealed that the performance of the NN-MPC is superior to that of FLC and GMC.     

基于同址训练递推最小二乘支持向量机的分批补料生物反应器中溶氧浓度的非线性广义预测控制(英文)

In this study, Saccharomyces cerevisiae (baker’s yeast) was produced in a fed-batch bioreactor at the optimal dissolved oxygen concentration (DOC) and growth medium temperature. However, it is very difficult to control the DOC using conventional controllers because of the poorly understood and constantly changing dynamics of the bioprocess. A generalized predictive controller (GPC) based on a nonlinear autoregressive integrated moving average exogenous (NARIMAX) model is presented to stabilize the DOC by manipulation of air flow rate. The NARIMAX model is built by an improved recursive least-squares support vector machine, which is trained by an in-place computation scheme and avoids the computation of the inverse of a large matrix and memory reallocation. The proposed nonlinear GPC algorithm requires little preliminary knowledge of the fermentation process, and directly obtains the nonlinear model in matrix form by using iterative multiple modeling instead of linearization at each sampling period. By application of an on-line bioreactor control, experimental results demonstrate the robustness, effectiveness and advantages of the new controller.