Learning Control For Batch Processes Research Articles

Repetitive process based indirect-type iterative learning control for batch processes with model uncertainty and input delay

This paper develops an indirect iterative learning control scheme for batch processes with time-varying uncertainties, input delay, and disturbances. In this paper, a predictor based on a state observer is designed to estimate the future state and to compensate for the input delay. Then a feedback controller based on the estimated state and the set-point error is used to track the specified reference trajectory, where, of the options available, a robust H∞ controller is designed in the presence of time-varying uncertainties and load disturbances. Then a proportional plus derivative type iterative learning control law is designed. An injection molding process model demonstrates the new method’s effectiveness, and a comparison with a direct-type design is given.

A novel PID type iterative learning controller optimized by two‐dimensional infinite horizon linear quadratic iterative learning control for batch processes

AbstractAlthough a proportional integral derivative type iterative learning control (PIDILC) scheme can achieve good performance, its application is limited by open‐loop structure, parameter tuning, and initial state. In this paper, a novel PIDILC optimized by two‐dimensional infinite horizon linear quadratic regulator (PIDILC‐2D‐IHLQR) is proposed. First, by synthesizing the advantage of the conventional PIDILC method and proportional integral derivative (PID) strategy, a novel closed‐loop PIDILC scheme is obtained. Then, a novel two‐dimensional infinite horizon linear quadratic regulator (2D‐IHLQR) is developed to optimize the parameters of the PIDILC strategy. The limitations of parameter tuning and initial state are solved by this PIDILC‐2D‐IHLQR method. Therefore, the proposed method not only solves the aforementioned limitations but also inherits the advantages of PIDILC algorithm, PID method, and the novel 2D‐IHLQR scheme. Moreover, a stability condition is given based on Lyapunov theory and it can help judge whether the selection of control parameters meets the stability condition. The effectiveness of the proposed method is demonstrated by the case study on an injection modelling process.

Improved point-to-point iterative learning control for batch processes with unknown batch-varying initial state

In this article, the authors study and solve the problem of point-to-point iterative learning control (P2PILC), which only tracks certain key points with unknown batch-varying initial state, thereby eliminating the impact on the output of the initial state error at the final tracking time instants. By completely considering the degree of freedom in point-to-point (P2P) control, an update learning law is designed to compensate the initial state error, and the convergence of the error at the tracking points is proved. At last, the effectiveness of the proposed method is validated by simulation.

Optimal Iterative Learning Control for Batch Processes in the Presence of Time-Varying Dynamics

Optimal iterative learning control (OILC) has been recognized as an excellent model-based means for regulating batch process with abundant successful applications reported in the past decades but also received considerable criticisms for its poor robustness against model mismatch that is common for many industrial situations. Despite numerous attempts to address the issue, many of them are still not able to yield satisfactory control performance particularly in the presence of a possible combination of time-varying uncertainties and conservatively designed controllers, which may compromise the learning mechanism, hence rendering the robustness issue of OILC far from well explored. This article intends to investigate the aforementioned issue by proposing a new OILC method resting upon the minimization of a dynamic upper bound on tracking error which is distilled from better exploitation of the time variation of uncertainties. We also show that the problem can be formulated in the framework of convex–concave game that can be efficiently solved by a subgradient method with an excellent balance of optimality and computation time. Such a formulation enables us to gain: 1) guaranteed monotonic convergence on tracking error; 2) remarkably reduced conservatism on controller synthesis; and 3) controllable computation complexity. It is further shown that the proposed method is capable of handling nonlinearity, for example Volterra system, a classic representation of nonlinear process. The efficacy of the method is verified by numerical experiments on a continuous stirred tank reactor model.

PI based indirect-type iterative learning control for batch processes with time-varying uncertainties: A 2D FM model based approach

A robust PI based indirect-type iterative learning control (ILC) is proposed in this paper for industrial batch processes with time-varying uncertainties, based on a two-dimensional (2D) Fornasini-Marchesini (FM) model description of the batch process dynamics. An important merit is that the proposed ILC design is independent of the PI tuning in the closed-loop system, owing to that the ILC updating law is only implemented through tuning the set-point of the closed-loop system. By introducing a specified pole location of the closed-loop system, a robust PI controller design is firstly given with the H infinity performance index to maintain the closed-loop robust stability. Then by developing a 2D FM description of the batch operation with the designed PI controller, the control objective of minimizing the tracking error along both the time and batch directions is formulated based on the 2D robust H infinity control theory, such that a robust ILC updating law is determined by solving the linear matrix inequality (LMI) conditions established for holding the 2D system stability. Moreover, the batch-direction convergence rate can be separately tuned via the performance index in the above LMI conditions. An illustrative application to batch injection molding is given to demonstrate the effectiveness and merit of the proposed method.

Probability Based Stochastic Iterative Learning Control for Batch Processes With Actuator Faults

This paper proposes a new stochastic composite iterative learning control for batch processes with actuator faults that happen with a certain kind of probability. The main contribution lies in the fact that stochastic control theory is used to analyze the stability issues and consider controller designs of batch processes with actuator faults that happen under various kinds of probability, which paves the way for reliable control theory. Firstly, the batch process is represented as a system with stochastic uncertainty for iterative learning control design; and with the state and output error, it is further treated into a two dimensions (2D) Rosser system with stochastic errors. Using such transformation, the iterative learning control design is transformed into the updating control law design. Secondly, 2D Lyapunov stochastic theory is used to design the controller with actuator faults under various kinds of probability, together with the stability results of the control system in terms of LMI conditions. Finally, the proposed method is tested on the injection molding process to demonstrate the effectiveness.

2D Terminal Constrained Model Predictive Iterative Learning Control of Batch Processes With Time Delay

In this paper, a 2D terminal constrained model predictive iterative learning control method of batch processes with time delay is proposed to deal with time delay, input and output constraints, and disturbances in batch processes. Firstly, an iterative learning control law is designed for the given batch process; then the state error and output tracking error are introduced, and the original state-space model is converted to an equivalent 2D-FM model. In the meantime, an optimal performance index with terminal constraints is introduced, and an update law is designed to minimize the objective function under input and output constraints. The robust constraint set is adopted that the system state is converged to this set round the desired point. Then, based on the designed optimal performance index and Lyapunov stability theory, the MPC problem is transformed into a linear matrix inequality problem and a sufficient condition is given to ensure the robust asymptotically stability of the closed-loop system. Finally, the validity of the proposed method is proved by the simulation on a stirred tank.

Nonlinear Monotonically Convergent Iterative Learning Control for Batch Processes

Iterative learning control (ILC) has been successfully applied to numerous batch processes over the past decades. Monotonic convergence of tracking error is a desired characteristic that attracts much attention in academia. Many factors arising in industrial practice, such as strong nonlinearity and parameter uncertainty, have challenged the most existing monotonically convergent ILC approaches. This motivates the development of the nonlinear monotonically convergent ILC (NMC-ILC) in this paper. The proposed NMC-ILC is an optimization-based control strategy, in which the original nonlinear process is linearly approximated to reduce the complexity of the optimization problem accompanied. An upper bound of the tracking error is derived by considering the effects of model mismatches that consist of two components: structural mismatch induced by the linearization and parametric mismatch arising from the indetermination of process parameters. The NMC-ILC is then devised by minimizing this upper bound. Numerical experiments are conducted on an ILC-testing benchmark and the velocity control in an injection molding process.

A tube feedback iterative learning control for batch processes

Optimization-based iterative learning control (OILC) has been widely applied to batch processes due to its fast convergence, good control performance and ability to handle constraints. However, how to guarantee constraint satisfaction and convergence of tracking error in the presence of unknown system nonlinearity remains open in the framework of OILC. It is important to address this issue since unknown nonlinearity is common in practice and detrimental to good control performance. In this paper, we propose a tube feedback OILC to investigate the applicability of linear-model based control strategy on batch processes with an unknown nonlinear term. First, a state feedback control law is designed to stabilize the system. The stabilized system is then decomposed into two subsystems: repeatable and unrepeatable subsystems; Second, an invariant set of states corresponding to the unrepeatable subsystem is computed, based on which an OILC is further developed for the repeatable subsystem to improve the control performance. Meanwhile, the feedback controller steers the states within a tube around the trajectory of OILC. In this way, convergence and constraint satisfaction are ensured simultaneously. Compared with the currently existing methods, the proposed method has the following advantages: (1) generality covering both stable and unstable systems; (2) low computation complexity; and (3) rigorous stability. The simulation results on injection molding velocity control demonstrate that the proposed method has superior performance.

Fuzzy Iterative Learning Control for Batch Processes with Interval Time-Varying Delays

In this paper, a T-S model-based fuzzy delay-range-dependent iterative learning control (ILC) scheme is developed for highly nonlinear batch processes with interval time-varying delays. The two-dimensional (2D) T-S time-delay model is constructed to remedy the disadvantage that the overall linear model cannot sufficiently describe the nonlinear batch process. Then, exploiting the repetitive nature of batch processes, a 2D fuzzy delay-range-dependent iterative learning control is designed. The delay-range-dependent stabilization problem and H∞ control are studied by using 2D Lyapunov function under a 2D system framework. At the same time, the controller gain design is given and its gain can be obtained in terms of LMIs. A water tank is taken as a simulation case to demonstrate the effectiveness of the proposed fuzzy iterative learning control scheme.

Dynamic R-parameter based integrated model predictive iterative learning control for batch processes

A novel integrated model predictive iterative learning control (MPILC) strategy with dynamic R-parameter for batch processes is proposed in this paper. It systematically integrates batch-axis information and time-axis information into one uniform frame, namely the iterative learning controller (ILC) in the domain of batch-axis, while a model predictive controller (MPC)with time-varying prediction horizon in the domain of time-axis. As a result, the operation policy of batch process can be regulated during one batch, which leads to superior tracking performance and better robustness against disturbance and uncertainty. Moreover, both model identification and dynamic R-parameter are employed to eliminate the model-plant mismatch and make zero-error tracking possible. Next, the convergence and tracking performance of the proposed integrated model predictive learning control system are given rigorous description and proof. Lastly, the effectiveness of the proposed method is verified by one example.

Robust iterative learning control for batch processes with input delay subject to time‐varying uncertainties

A robust iterative learning control (ILC) method is proposed for industrial batch processes with input delay subject to time-varying uncertainties, based on a two-dimensional (2D) system description of batch process operation. To compensate the input delay, a 2D state predictor is established to predict the augmented system states, such that a 2D ILC design is developed for the ‘delay-free’ 2D system based on using only the measured output errors of current and previous cycles. Delay-dependent stability conditions for the resulting 2D system are established in terms of matrix inequalities by defining a comprehensive 2D Lyapunov–Krasovskii functional candidate along with free-weighting matrices. By solving these matrix inequalities using a cone complementarity linearisation method, the ILC controller is explicitly derived together with an adjustable H infinity performance index. An important merit is that perfect tracking can be realised for a batch process with arbitrarily long input delay if the delay-free part of the 2D system can be stabilised, in no presence of time-varying uncertainties. Moreover, the time integral of tracking error can be added as an extended 2D system state for ILC design to eliminate steady-state output error for all batches. An illustrative example of injection moulding process is given to demonstrate the effectiveness of the proposed method.

Robustness of reinforced gradient-type iterative learning control for batch processes with Gaussian noise

In this paper, a reinforced gradient-type iterative learning control profile is proposed by making use of system matrices and a proper learning step to improve the tracking performance of batch processes disturbed by external Gaussian white noise. The robustness is analyzed and the range of the step is specified by means of statistical technique and matrix theory. Compared with the conventional one, the proposed algorithm is more efficient to resist external noise. Numerical simulations of an injection molding process illustrate that the proposed scheme is feasible and effective.

Robust PID based indirect-type iterative learning control for batch processes with time-varying uncertainties

Based on the proportional-integral-derivative (PID) control structure widely used in engineering applications, a robust indirect-type iterative learning control (ILC) method is proposed for industrial batch processes subject to time-varying uncertainties. An important merit is that the proposed ILC design is independent of the PID tuning that aims primarily to hold robust stability of the closed-loop system, owing to the fact that the ILC updating law is implemented through adjusting the setpoint of the closed-loop PID control structure plus a feedforward control to the plant input from batch to batch. According to the robust H infinity control objective, a robust discrete-time PID tuning algorithm is given in terms of the plant state-space model description to accommodate for time-varying process uncertainties. For the batchwise direction, a robust ILC updating law is developed based on the two-dimensional (2D) control system theory. Only measured output errors of current and previous cycles are used to implement the proposed ILC scheme for the convenience of practical application. An illustrative example from the literature is adopted to demonstrate the effectiveness and merits of the proposed ILC method.

Delay-range-dependent robust 2D iterative learning control for batch processes with state delay and uncertainties

This paper proposes the design of the integrated output feedback and iterative learning control (ILC) for batch processes with uncertain perturbations and interval time-varying delays, where the main idea is to transform the design into a robust delay-range-dependent H∞ control of a 2D system described by a state-space model with varying delays. A sufficient criterion for delay-dependent H∞ noise attenuation is derived through linear matrix inequality (LMI) by introducing a comprehensive 2D difference Lyapunov–Krasovskii functional candidate and adding a differential inequality to the difference in the Lyapunov function for the 2D system. Based on the criterion obtained, the delay-range-dependent output feedback controller combined with ILC is then developed. The developed system ensures that the closed-loop system for all admissible uncertainties is asymptotically stable and has a prescribed H∞ performance level in terms of the LMI constraint. The controller is obtained by solving an LMI optimization problem with simple calculations and less constraint conditions. Moreover, the conditions can also be directly extended from delay-range-dependent to general delay-dependent stability. Applications in injection velocity control demonstrate the effectiveness and feasibility of the proposed method.

Model-Based Iterative Learning Control for Batch Processes Using Generalized Hinging Hyperplanes

A model-based iterative learning control (ILC) strategy using the generalized hinging hyperplanes (GHH) is proposed to track the product quality trajectory in the batch process. As an empirical mod...

Deterministic vs. stochastic performance assessment of iterative learning control for batch processes

The performance assessment of linear time‐invariant batch processes when iterative learning control (ILC) is implemented has been discussed. Previous literatures show that conventional performance assessment cannot be directly applied to batch processes due to the nature of batch operations. Chen and Kong have suggested a new method to assess the control performance of batch processes using optimal ILC as the benchmark. In their work, ILC controllers are assumed to affect either stochastic or deterministic performance but without considering their interaction. This work elaborates the controllers effects on both stochastic and deterministic control performance of batch processes. It is shown that the optimal solution based on the minimum variance control law has a trade‐off between deterministic and stochastic performance, which can be shown by a trade‐off curve. Furthermore, a method is proposed to estimate this curve from routine operating data, against which the performance of ILC controllers can be assessed. Simulation studies are conducted to verify the proposed method. © 2012 American Institute of Chemical Engineers AIChE J, 59: 457–464, 2013

Robust design of feedback integrated with iterative learning control for batch processes with uncertainties and interval time-varying delays

A robust feedback integrated with iterative learning control (FILC) scheme for batch processes with uncertain perturbations and interval time-varying delay is developed. The batch process is modeled as a two-dimensional (2D) Rosser system with a delay varying in a range. The design of FILC scheme is transformed into a robust control problem of uncertain 2D system. New delay-range-dependent stability criteria and stabilization conditions are derived in terms of linear matrix inequalities (LMIs), which depend on not only the difference between the upper and lower delay bounds but also the upper delay bound of the interval time-varying delay. Parameterized characterizations for stabilizing the controller are given in terms of the feasibility solutions to the LMIs. Applications to injection velocity control show that the proposed FILC achieve the design objectives well.

Two-dimensional Iterative Learning Control for Batch Processes With State Delay and Time-varying Uncertainties

AbstractBased on a two-dimensional (2D) system description of a batch process, a robust closed-loop iterative learning control (ILC) scheme is proposed for batch processes with 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 the setpoint trajectory in both the time (during a cycle) and batchwise (from cycle to cycle) directions. Only measured output errors of the current and previous cycles are used to design a synthetic ILC controller consisting of dynamic output feedback plus feedforward control. 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 is given to demonstrate effectiveness and merits of the proposed ILC method.

Robust two-dimensional iterative learning control for batch processes with state delay and time-varying uncertainties

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.