COMPENSATOR FOR CONSTANT RELATIVE STABILITY IN PROCESS CONTROL SYSTEMS

Process control systems are designed for a closed-loop peak magnitude of 2 dB, which corresponds to a damping coefficient (ζ) of 0.5 approximately. With this specified constraint, the designer should choose and/or design the loop components to maintain a constant relative stability. However, the manipulative variable in almost all chemical processes will be the flow rate of a process stream. Since the gains and the time constants of the process will be functions of the manipulative variable, a constant relative stability cannot be maintained. Up to now, this problem has been overcome either by selecting proper control valve flow characteristics or by gain scheduling of controller parameters. Nevertheless, if a wrong control valve selection is made then one has to account for huge loss in controllability or eventually it may lead to an unstable control system. To overcome these problems, a compensator device that can bring back the relative stability of the control system was proposed. This compensator is similar to a dynamic nonlinear controller that has both online and offline information on several factors related to the control system. The design and analysis of the proposed compensator is discussed in this article. Finally, the performance of the compensator is validated by applying it to a two-tank blending process. It has been observed that by using a compensator in the process control system, the relative stability could be brought back to a great extent despite the effects of changes in manipulative flow rate.     

Two-degree-of-freedom output feedback controllers for nonlinear processes

In this work, a nonlinear output feedback control algorithm is proposed, in the spirit of model-state feedback control. The structure provides state estimates using a process model, the measured output, and the residual between the model output and the measured output. These estimates will track the process states at a rate determined by a set of tunable parameters. An algebraic transformation of the state estimates is incorporated in the control structure to ensure that the input/output gain of the observer matches the model upon which the static state feedback control law is based. The transformed states are then used in the control law. This leads to a controller of minimal order possessing integral action. The control structure is shown to have the same properties as the standard model-state feedback structure. The resulting algorithm is a two-degree of freedom control law, in the sense that the control action is not a function of the error only, but the output and the set point are processed in different ways. Finally, a simulation example using an exothermic CSTR operating at an open-loop unstable steady state is used to demonstrate the closed-loop performance of the proposed method.     

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.     

Two-degree-of-freedom output feedback controllers for discrete-time nonlinear systems

A discrete-time, model-based output feedback control structure for nonlinear processes is developed in the present work. The structure makes use of a closed-loop observer, while at the same time it guarantees that the overall feedback controller possesses integral action. An algebraic transformation is applied on the observer states to insure that the input/output gain of the observer matches the model upon which the static state feedback control law is based. The resulting control algorithm is a two-degree-of-freedom control law, in the sense that the output and the set point are processed in different ways. The control structure is shown not only to have the same properties as the standard model-state feedback structure, but also that it emerges from a model algorithmic control framework. Finally, a simulation example using an exothermic CSTR operating at an open-loop unstable steady state is used to evaluate the closed-loop performance of the proposed method.     

Model predictive control for multivariable unstable processes with constraints on manipulated variables

The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steady states. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input-multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control. Linear Quadratic Regulator (LQR) with integral action.     

ADAPTIVE NEURAL-NETWORK PREDICTIVE CONTROL FOR NONMINIMUM-PHASE NONLINEAR PROCESSES

An adaptive neural-network predictive control strategy for a class of nonlinear processes, which exhibit input multiplicities and change in the sign of steady-state gains, is presented. According to the graphic-based determination associated with prescribed input/output patterns, the feed-forward neural network (FNN) is attributed to reconstruct dynamic and steady-state characteristics of minimum-phase modes with specified operating ranges. The flexible predictive control strategy using on-line neuro-based adaptation is developed for enhancing the predictive capability of neural network. Finally, the proposed FNN-based implementation is illustrated on simulations of both isothermal and adiabatic CSTR systems.     

Input Multiplicity Analysis in a Non‐Isothermal CSTR for Acid‐Catalyzed Hydrolysis of Acetic Anhydride

Multiplicity analysis gives practical guidance for process design to eliminate difficult operating regions associated with input and output multiplicities. Continuous stirred tank reactors (CSTRs) present challenging operational problems due to complex behavior such as input and output multiplicities, ignition/extinction, parametric sensitivity, and nonlinear oscillations. In the absence of a unified mathematical theory for representing various nonlinear system characteristics, the present study was aimed at understanding the dynamic behavior of CSTRs by means of experiments and to link the experimental data to theoretical considerations for further detection and elimination of operating problems. Theoretical modeling and analysis of a non‐isothermal CSTR with acid‐catalyzed hydrolysis of an acetic anhydride system for input multiplicity are discussed. Theoretical modeling of a non‐isothermal CSTR using a root‐finding technique was carried out for predicting steady‐state temperatures. Alternatively, a mathematical model for a non‐isothermal CSTR using unsteady‐state mass and energy balance equations is proposed. Computer‐based simulation was carried out using a program developed in MATLAB for final transient temperature and time‐temperature data of the CSTR system under investigation. The results of a theoretical analysis conducted for confirming the existence of input multiplicity in non‐isothermal CSTRs with acid‐catalyzed hydrolysis of acetic anhydride were compared with experimental investigations for validation.     

Extremum seeking control using a partial sum of input-output product

Recent extremum seeking control that uses a continuous perturbation and the integral feedback of perturbation- output product is based on a static nonlinear process. The method can be applied to dynamic nonlinear processes for tracking and maintaining the optimal operating points. It has several tuning parameters, such as the integral controller gain and the magnitude and frequency of the continuous perturbation signal. The frequency of the continuous perturbation signal should be low enough to ensure the time-scale separation between the real-time optimization and the process dynamics for the closed-loop stability. However, for some processes, fast perturbations are preferred because they can be attenuated easily in subsequent processes such as buffers and storages. For this, we propose an extremum seeking control method where the partial sum of perturbation-output product is used for a faster squarewave perturbation. Simulations for two processes of parallel competing reactions have been given, and a simple liquid level system to test extremum seeking control methods is suggested.     

Double-command feedforward-feedback control of a nonlinear plant

A design approach is proposed for feedforward-feedback control systems. The basis of the proposed approach is a steady state control law which maintains the desired control output of the system and is employed as the feedforward controller. With this feedforward controller, for a wide class of systems, the stability of the control system is proved if the feedback controller is a gain with an arbitrarily high value; that is, the only limit for the feedback (transient) control command is the actuator’s practical limit. Moreover, in continuous domain, there will be no overshoot. In this article, the proposed method has been applied to a catalytic stirred tank reactor (CSTR) to control the output concentration through adjusting the flow of two valves simultaneously and resulted in an excellent control response.     

反应精馏过程中的多稳态分析

Reactive distillation processes for synthesis of ethylene glycol （EG） and ethyl tert-butyl ether （ETBE） were modeled with the simulation package ASPEN PLUS. The input multiplicity and output multiplicity were discussed with the method of sensitivity analysis for both cases. In EG production process, steady state multiplicities were studied in terms of effective liquid holdup volume and boil-up ratio. In ETBE synthesis process, the user kinetic subroutine was supplied into ASPEN PLUS firstly, and then the composition, temperature and reaction-rate profiles within the reactive distillation column were presented in detail. A set of stable solution branches based on distinct initial guesses for a range of boil-up ratio were found in EG synthesis. Input multiplicities were observed for a range of reboiler duty at several values of reflux ratio for ETBE synthesis process. These results can be used to avoid excessive energy consumption and achieve optimum design of reactive distillation column.     

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.     

Improved infinite horizon LQ tracking control for injection molding process against partial actuator failures

Focusing on injection molding processes with partial actuator failures, a new design of infinite horizon linear quadratic control is introduced. A new state space process model is first derived through input–output process data. Furthermore, an improved infinite horizon linear quadratic control scheme, whereby the process state variables and tracking error can both be regulated separately, is proposed to show enhanced control performance against partial actuator failures and unknown disturbances. Under the circumstances of actuator faults, the closed-loop system is indeed a process with uncertain parameters. Hence, a sufficient condition is proposed to guarantee robust stability is presented using Lyapunov theory. The proposed concepts are illustrated in an injection velocity control case study to show the effectiveness.     

Steady state multiplicity in an UOP FCC unit with high-efficiency regenerator

The possibility of existence of multiple steady states in fluid catalytic cracking (FCC) units has a major impact in the supervision of these systems. The origins of these behaviours are usually due to the exothermicity of the catalyst regeneration reactions and to the strong interactions between the reactor and the regenerator system.Prior work has focused on modelling and control problems of different operating FCC units. However, none of these studies have considered a high-efficiency regenerator. This paper presents an analysis of the existence of output and input multiple steady states in an UOP FCC unit with a high-efficiency regenerator.The influence of unit disturbances and model uncertainties, such as coke composition and cracking enthalpy, in the output multiplicity, was studied and the results show that the high-efficiency regenerator exhibits at least three multiple output steady states and a maximum of five output steady states, in the operating range considered. Moreover, the state multiplicity analysis revealed that input multiplicity can be present in this FCC unit, depending on the choice of the control structure, and that operating the unit in full combustion mode can prevent instabilities due to input and output multiplicities. Therefore, these results can be used to guide the design of the most appropriate control structures in industrial applications. For the FCC unit with high-efficiency regenerator the most appropriate control structure corresponds to the control of the riser reactor temperature and the oxygen level in the flue gas, with the catalyst circulation rate and the combustion air flow rate, respectively.     

SUDDEN DESTABILIZATION OF CONTROLLED CHEMICAL PROCESSES

Input multiplicity occurs when more than one set of inputs can produce the same set of outputs. Input multiple steady states are divided into compatible steady states having process gains of similar sign, and opposed steady stales with process gains of opposite sign. For a system controlled with reset action, only the compatible steady states satisfy the necessary condition for stability. Any disturbance which drives the controlled system from the designed steady state to a less stable or unstable compatible steady state can cause sudden destabilization of the process. Several examples are given of the possible types of behavior resulting from this phenomenon.

Multiple steady states also occur for systems with proportional controllers. For single-input-single-output systems with continuous process characteristics, whether or not reset action is used, two steady states positioned next to each other cannot both be stable under closed-loop control. However, under proportional control, opposed steady states for which 1 + K_cK_p is positive can be stable.     

Simplified design of proportional-integral-derivative (PID) controller to give a time domain specification for high order processes

An efficient simplified method is proposed for the time domain design of industrial proportional-integral-derivative (PID) controllers and lead-lag compensators for high order single input single output (SISO) systems. The proposed analytical method requires no trial error steps for a lead-lag compensator design in the time domain by using the root-locus method. A practical PID controller design method was obtained based on the corresponding lead-lag compensator to give a required time-domain specification. Simulation studies were carried out to illustrate the control performance of the controllers by the proposed method. The proposed PID controller and lead-lag compensator directly satisfied time domain control specifications such as damping ratio, maximum overshoot, settling time and steady sate error without trial and error steps. The suggested algorithm can easily be integrated with a toolbox in commercial software such as Matlab.     

Internal model control design for input‐constrained multivariable processes

Multivariable plants under input constraints such as actuator saturation are liable to performance deterioration due to control windup and directionality change. A two‐stage internal model control (IMC) antiwindup design for open loop stable plants is presented. The design is based on the solution of two low‐order quadratic programs at each time step, which addresses both transient and steady‐state behaviors of the system. For analyzing the robust stability of such systems against any infinity‐norm bounded uncertainty, stability test have also been developed. In particular, we note that the controller input‐output mappings satisfy certain integral quadratic constraints. Simulated examples show that the two‐stage IMC has superior performance when compared with other existing optimization‐based antiwindup methods. The stability test is illustrated for a plant with left matrix fraction uncertainty. A scenario where the proposed two‐stage IMC competes favorably with a long prediction horizon model predictive control is described. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Tuning digital PI controllers for minimal variance in manipulated input moves applied to imbalanced systems with delay

Determining the discrete-time proportional plus integral (PI) controller tuning parameters to achieve the smallest possible variance in the manipulated input moves, for a given variance in the controlled output, is the subject of this article. Previous researchers have developed tuning rules for PI and PI permutated nonlinear controllers to achieve what is commonly referred to as “level-flow smoothing”, or “averaging level control”, on imbalanced or integrating processes with delay, such as liquid level and gas pressure systems. The intent of this note is to demonstrate a new and simple technique of tuning digital PI controllers which utilizes either open or closed-loop historical data to estimate the process gain, dead-time and expected flow disturbance magnitude from which the digital PI tuning constants can be easily derived. By parameterizing the closed-loop system as a function of the PI tuning constants, we can simultaneously minimize the expected variation in the process input move and output responses while at the same time ensuring nominal stability of the overall system. In order to demonstrate the technique, an illustrative example is included which highlights the new procedure on an oil refinery liquid surge drum level process.     

Model predictive control for multivariable unstable processes with constraints on manipulated variables

The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steadystates. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input-multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control. Linear Quadratic Regulator (LQR) with integral action.     

GRAPHICS-BASED CONTROL DESIGNS FOR NONMINIMUM-PHASE NONLINEAR SYSTEMS SUBJECT TO INPUT AND OUTPUT CONSTRAINTS

This article deals with the output regulation of nonminimum-phase systems subject to input and output constraints. Through the off-line static data reconciliation algorithm for a class of stable nonlinear bioreactors, the static feedforward control can ensure constant disturbance attenuation in spite of input multiplicities and actuators constraints. Under the pseudo-steady-state error diagnoses and a graphics-based mechanism for disturbance estimation, the proposed error feedback control scheme will induce the piecewise output regulation. Based on the “intelligent” algorithm for tuning improvement, the closed-loop simulation shows that the piecewise control strategy turns out to be robust against the unknown disturbances.     

GRAPHICS-BASED CONTROL DESIGNS FOR NONMINIMUM-PHASE NONLINEAR SYSTEMS SUBJECT TO INPUT AND OUTPUT CONSTRAINTS

This article deals with the output regulation of nonminimum-phase systems subject to input and output constraints. Through the off-line static data reconciliation algorithm for a class of stable nonlinear bioreactors, the static feedforward control can ensure constant disturbance attenuation in spite of input multiplicities and actuators constraints. Under the pseudo-steady-state error diagnoses and a graphics-based mechanism for disturbance estimation, the proposed error feedback control scheme will induce the piecewise output regulation. Based on the “intelligent” algorithm for tuning improvement, the closed-loop simulation shows that the piecewise control strategy turns out to be robust against the unknown disturbances.