Article

Robust Hybrid Controller Design for Batch Processes with Time Delay and Its Application in Industrial Processes

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Abstract

A new design method of two-dimensional (2D) controller for multi-phase batch processes with time delay and disturbances is proposed to ensure the stability of the control system and realize efficient production in industry. The batch process is first converted to an equivalent but different dimensional 2D-FM switched system. Based on the 2D system framework, then sufficient conditions of a controller existence expressed by linear matrix inequalities (LMIs) that stabilizing system is given by means of the average dwell time method. Meanwhile, robust hybrid 2D controller design containing extended information is proposed and the minimum runtime lower bound of each sub-system is accurately calculated. The design advantages of the controller depend on the size of the time delay so it has a certain degree of robustness. At the same time, considering the exponential stability, the system can have a faster rate of convergence. In addition, the introduction of extended information has improved the control performance of the system to some extent. The acquisition of minimum time at different phases will promote certain production efficiency and thus reduce energy consumption. Finally, an injection process in industrial production process has been taken as an example to verify effectiveness of the proposed method.

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Actuator faults commonly exist in process control systems. Due to these faults, the controller may not achieve the required target, so the control performance may degrade. In this paper, the fault-tolerant control is designed through a predictive functional control framework to deal with partial actuator faults and unknown disturbances, which exist widely in process control systems. Based on a new state space formulation of the process models, an improved predictive functional control scheme is proposed, where satisfactory closed-loop control performance is achieved even with unknown disturbances and actuator faults. With the actuator faults, the system becomes a process with parameter uncertainties. Hence, a sufficient condition that guarantees closed-loop robust stability is presented. Simulations are given to illustrate the feasibility and effectiveness of the proposed scheme.
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As often experienced in industrial practice, a fixed-parameter PID can do a good job, even for potentially challenging problems such as open-loop unstable processes. However in such cases, considerable a priori process knowledge may be required in order to adequately tune the controller and make the control performance robust to changes in operating conditions. Adaptive schemes, on the other hand, require less prior plant information but they should not be regarded as magic solutions to control problems. In this study, alternative adaptive control schemes are presented for the temperature control of an open-loop unstable batch chemical reactor in which the sequential exothermic reactions A→B→C are carried out. The performance of such control systems are compared with that of a PID controller, designed using IMC-based rules, and detuned to ensure robustness to process parameter changes along the temperature trajectory. Since the required detuning results in poor disturbance rejection, one would expect that the adoption of adaptive strategies should improve performance. However, the fact that a fixed-parameter PID controller can be designed to perform reasonably well does not imply that a self-tuning version will do at least as well. A self-tuning scheme combined with a parametric control approach can successfully deal with the reactor start-up and the regulatory problem, provided that the adaptive scheme's process model order is adequately selected. Thus, a self-tuning PID controller, which is based on a second-order model, is liable to failure if the true process is effectively of higher order.
Article
A robust iterative learning control (ILC) scheme for batch processes with uncertain perturbations and initial conditions is developed. The proposed ILC design is transformed into a robust control design of a 2-D Fornasini–Marchsini model with uncertain parameter perturbations. The concepts of robust stabilities and convergences along batch and time axes are introduced. The proposed design leads to nature integration of an output feedback control and a feedforward ILC to guarantee the robust convergence along both the time and the cycle directions. This design framework also allows easy enhancement of the feedback and/or feedforward controls of the system by extending the learning information along the time and/or the cycle directions. The proposed analysis and design are formulated as matrix inequality conditions that can be solved by an algorithm based on linear matrix inequality. Application to control injection packing pressure shows the proposed ILC scheme and its design are effective. © 2006 American Institute of Chemical Engineers AIChE J, 2006
Article
Injection velocity, a key variable in injection molding, was controlled via an adaptive controller using a self-tuning regulator (STR) scheme. The pole-placement design was employed first, together with the performance enhancement techniques of anti-windup estimation, feed-forward control, and cycle-to-cycle adaptation. The pole-placement design with the enhancement techniques was found experimentally to work very well over different molding conditions. However, this design was also found to be sensitive to the model mismatch. To overcome this problem, a new adaptive controller based on a generalized predictive control (GPC) principle was designed to make the controller more robust. Experiments have shown that the adaptive GPC control of injection velocity has inherently good set-point tracking performance and excellent tolerance to model structure mismatch.
Article
A robust H∞ control for uncertain linear systems with a state-delay is described. Systems with norm-bounded parameter uncertainties are considered and linear memoryless state feedback controllers are obtained. Firstly, a delay-dependent bounded real lemma for systems with a state-delay is presented in terms of linear matrix inequalities (LMIs). By taking a new Lyapunov–Krasovsii functional, neither model transformation nor bounding for cross terms is required to obtain delay-dependent results. Secondly, based on the bounded real lemma obtained, delay-dependent condition for the existence of robust H∞ control is presented in terms of nonlinear matrix inequalities. In order to solve these nonlinear matrix inequalities, an iterative algorithm involving convex optimization is proposed. Numerical examples show that the proposed methods are much less conservative than existing results.
Article
This paper investigates robust stability of uncertain linear systems with interval time-varying delay. The time-varying delay is assumed to belong to an interval and is a fast time-varying function. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. A new Lyapunov–Krasovskii functional, which makes use of the information of both the lower and upper bounds of the interval time-varying delay, is proposed to drive some new delay-dependent stability criteria. In order to obtain much less conservative results, a tighter bounding for some term is estimated. Moreover, no redundant matrix variable is introduced. Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria.
Article
Based on a two-dimensional (2D) system description of a batch process in industry, a robust closed-loop iterative learning control (ILC) scheme is proposed for batch processes with state delay and time-varying uncertainties. An important merit is that the proposed ILC method can be used for on-line optimization against batch-to-batch process uncertainties to realize robust tracking of setpoint trajectory in both the time (during a cycle) and batchwise (from cycle to cycle) directions. Only measured output errors of current and previous cycles are used to design a synthetic ILC controller consisting of dynamic output feedback plus feedforward control, for the convenience of implementation. By introducing a comprehensive 2D difference Lyapunov function that can lead to monotonical state energy decrease in both the time and batchwise directions, sufficient conditions are established in terms of linear matrix inequality (LMI) constraints for holding robust stability of the closed-loop ILC system. By solving these LMI constraints, the ILC controller is explicitly formulated, together with an adjustable robust H infinity performance level. An illustrative example of injection molding is given to demonstrate effectiveness and merits of the proposed ILC method.
Article
A new support vector machine based nonlinear predictive functional control design method has been developed and applied to an industrial coking furnace, which leads to the improvement of regulatory capacity for both reference input tracking and load disturbance rejection compared with traditional PFC and PID control strategies. The nonlinear process is first treated into a linear part plus a nonlinear part, then a convergent overall linear predictive functional control law is designed. The method gives a direct and effective multi-step predicting method and uses linear methods to get the control law which avoids the complicated nonlinear optimization. Comparison results and application to the temperature control of the industrial heavy oil coking furnace are presented in the article showing the efficiency of the method.
Article
In this paper, iterative learning control (ILC) system is modeled and designed from a two-dimensional (2D) system point of view. Based on a 2D cost function defined over a single-cycle or multi-cycle prediction horizon, two ILC schemes, referred respectively as single-cycle and multi-cycle generalized 2D predictive ILC (2D-GPILC) schemes, have been proposed and formulated in the GPC framework for the 2D system. Analysis shows that the resulted control schemes are the combination of a time-wise GPC and a cycle-wise ILC optimized in 2D sense. Guidelines for parameter tuning have been proposed based on the ultimate performance analysis for the control system. Simulation shows that the multi-cycle 2D-GPILC outperforms the single-cycle 2D-GPILC in term of cycle-wise convergence.
Article
To improve stability and convergence, feedback control is often incorporated with iterative learning control (ILC), resulting in feedback feed-forward ILC (FFILC). In this paper, a general form of FFILC is studied, comprising of two feedback controllers, a state feedback controller and a tracking error compensator, for the robustness and convergence along time direction, and an ILC for performance along the cycle direction. The integrated design of this FFILC scheme is transformed into a robust control problem of an uncertain 2D Roesser system. To describe the stability and convergence quantitatively along the time and the cycle direction, the concepts of robust stability and convergence along the two axes are introduced. A series of algorithms are established for the FFILC design. These algorithms allow the designer to balance and choose optimization objectives to meet the FFILC performance requirements. The applications to injection molding velocity control show the good effectiveness and feasibility of the proposed design methods.
Article
Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon open-loop optimal control problem, using the current state of the plant as the initial state; the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant. An important advantage of this type of control is its ability to cope with hard constraints on controls and states. It has, therefore, been widely applied in petro-chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls. In this review, we focus on model predictive control of constrained systems, both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and/or time-varying systems. We concentrate our attention on research dealing with stability and optimality; in these areas the subject has developed, in our opinion, to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control. We distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature. In some cases the finite horizon optimal control problem solved on-line is exactly equivalent to the same problem with an infinite horizon; in other cases it is equivalent to a modified infinite horizon optimal control problem. In both situations, known advantages of infinite horizon optimal control accrue.
Conference Paper
Time-optimal control strategies of the on-off type can be used to bring batch reactor temperature to the set point in the minimum time. A practical controller implementing this control strategy in industry is the dual-mode controller. When well tuned, this controller shows excellent system performance for various batch reactors. However, because time-optimal control is a kind of open loop control strategy, the dual-mode controller may be sensitive to process variations. For robust control, the dual-mode controller is modified here with an iterative learning technique. This iterative learning dual-mode controller requires minimal information from the previous batch runs and can be incorporated in the existing dual-mode controller with minimal effort.
Article
The problem of robust state feedback control using delta operator approach for a class of linear fractional uncertain systems with time-varying delays is investigated. Based on Lyapunov-Krasovskii functional in delta domain, a new delay-dependent state feedback controller is presented in terms of linear matrix inequalities. The sampling-period T is an explicit parameter, and thus it is easy to observe and analyse the effect of the state feedback controller with different sampling periods. The proposed method can unify some previous related continuous and discrete systems into the framework of delta operator systems. Numerical examples are given to illustrate the effectiveness of the developed techniques.