Data-driven two-dimensional integrated control for nonlinear batch processes

Design and Analysis of Integrated Predictive Iterative Learning Control for Batch Process Based on Two-dimensional System Theory

This work focuses on the model-free iterative learning control (ILC) design with good transient performance and fast convergence rate that is employed for precision control of a wafter stage. First, the experimental setup, the mathematical model, and the desired reference are introduced. Notice that the desired reference and its internal model (IM) are known in advance. Then, based on the internal model principle (IMP), a new ILC scheme, named as 1M-based ILC, is proposed by incorporating the 1M of the reference. The proposed 1M-based ILC is model-free, that is, independent on the system model of the controlled plant. The 1M -based ILC is carefully constructed to track the reference along the time axis while tracking/rejecting repetitive variations along the iteration axis. Precisely because of the tracking capability along the time axis in every iteration, the 1M-based ILC can achieve satisfactory performance even in the 0th iteration and improve the transient performance and the convergence speed. In addition, the 2-D $H_{\infty}$ theory is used to establish the design criterion for the 1M-based ILC. Finally, in the experiments, the efficiency of the 1M-based ILC is illustrated by comparing with a P-type ILC and a model-based one.

The injection stretch blow moulding (ISBM) process is widely used to manufacture plastic bottles for the beverage and consumer goods industry. The majority of the production processes are open-loop systems, often suffering from high raw material and energy waste. In this paper, a heuristic based norm-optimal terminal iterative learning control (ILC) method is proposed to control the preform temperature profiles in the reheating process. The reheating process is a batch process, and ILC can achieve improved tracking performance in a fixed time interval. The terminal ILC (TILC) is a useful strategy when only the terminal temperature profile can be measured in a batch process like the preform reheating in ISBM. To balance the control performance and energy cost, a norm-optimal method is applied, leading to a proposal of the new norm-optimal TILC method in this paper. Heuristic methods including the swarm optimisation (PSO), differential evolution (DE) and teaching-learning based optimization (TLBO) are used to calculate the sequence of norm-optimal control inputs for this non-linear batch process. Simulation results confirm the efficacy of the proposed control strategy.

ABSTRACTIn this article, to tackle with the iteration-varying trail lengths and random initial state shifts, an average operator-based PD-type iterative learning control (ILC) law is firstly presented for linear discrete-time multiple-input multiple-output (MIMO) systems with vector relative degree. The proposed PD-type ILC law includes an initial rectifying action against initial state shifts, and pursues the reference trajectory tracking beyond the initial time points. As special cases of the PD-type ILC law, P-type and D-type ILC laws are then introduced. It is proved that for linear discrete-time MIMO systems with vector relative degree, the three proposed ILC laws can drive the varying trail lengths-based ILC tracking errors to zero in mathematical expectation beyond the initial time points. A numerical example is used to illustrate the effectiveness of the proposed ILC laws.

The tracking performance of two iterative learning control algorithms is compared to that, which can be achieved by an optimal feedback controller. P-type iterative Learning Control in parallel with a proportional feedback controller is compared with norm-optimal iterative learning control, then both ILC systems are compared with the performance achieved by an optimal feedback controller. Considering that the ILC plus proportional controller requires no prior modelling of the plant and minimal adjustment of gains, the tracking performance in terms of mean squared error (mse) per iteration can be reduced by two orders of magnitude further than can be achieved with the optimal feedback controller. However, the Norm-Optimal ILC improves upon this performance by reducing the mse by an extra order of magnitude. The experimental results are derived from tests performed on a gantry robot.

A novel control technique is proposed by combining P-type Iterative learning control (ILC) and model predictive control (MPC) with updating-reference for point-to-point tracking problem of batch process. In this paper, a batch-to-batch updating-reference, which passes through the desired points, is designed as the tracking trajectory within batch. The update law consists of two parts: P-type ILC and MPC. Based on the updating-reference, MPC can suppress effectively model perturbations and disturbances. Comparing with other point-to- point tracking algorithms, the proposed algorithm performs better in robustness. Furthermore, updating-reference relaxes the output constraints, and it also leads to faster convergence and more extensive range of application than the fixed-reference control algorithms. Simulation results of a numerical case show better performance of the proposed approach.

This paper presents a P-type iterative learning control (ILC) scheme for a class of fractional order distributed parameter switched systems. First, by analyzing of the control and learning processes, a discrete system for P-type ILC is established and the ILC design problem is then converted to a stabilization problem for such a discrete system. Next, a sufficient condition for the convergence of the tracking errors is obtained, which is less conservative than the existing one. Finally, the validity of the proposed method is verified by a numerical example.

The feedback control based on the model and method of iterative learning control, which in turn is based on the macroscopic fundamental diagram (MFD), mostly belongs to the classification of single-layer boundary control method. However, the feedback control method has the problem of time delay. Therefore, a feedforward feedback iterative learning control (FFILC) method based on MFD of the multi-layer boundary of single-area oversaturated intersections is proposed. The FFILC method can improve the effectiveness of boundary control and avoid the time-delay problem of feedback control. Firstly, MFD theory is used to determine the MFD of the control area; the congestion zone and the transition zone of the control area are identified; and the two-layer boundary of the control area is determined. Then, the FFILC controllers are established at the two-layer boundary of the control area. When the control area enters into a congestion state, the control ratio of traffic flow in and out of the two-layer boundary is adjusted. The cumulative number of vehicles in the control area continues to approach the optimal cumulative number of vehicles, and it maintains high traffic efficiency with high flow rates. Finally, The actual road network is taken as the experimental area, and the road network simulation platform is built. The controller of the feedforward iterative learning control (FILC) is selected as the comparative controller and used to analyse the iterative effect of FFILC. Improvements in the use of traffic signal control indicators for the control area are analysed after the implementation of the FFILC method. Results show that the FFILC method considerably reduces the number of iterations, and it can effectively improve convergence speed and the use of traffic signal evaluation indicators for the control area.

In practical applications, the durations of operations in uncertain batch processes may fluctuate due to security considerations, physical constraints, and environmental changes. Regarding this issue, this paper addresses iterative learning control (ILC) for a class of uncertain single‐input single‐output (SISO) batch processes with nonuniform batch lengths. The aim is to develop an optimization‐based ILC scheme that guarantees robustness while meeting input constraints requirements. Two robust optimal ILC algorithms resting upon the modified error update model are proposed for the nonuniform batch length problem, where the linear matrix inequality (LMI) optimization techniques are employed to deal with polytopic and ellipsoidal model uncertainties. Hence, the ILC design requirements are reduced to a convex optimization method involving LMIs, which results in iterative input update signals at the end of each batch. Also, the theoretical analyses of the proposed algorithms are presented. Finally, two numerical cases for batch processes are simulated to testify the feasibility and performance of the proposed methods.

The problem of iterative learning control is considered for linear discrete-time systems with multiple time delays. In this paper, it is assumed that the initial condition for discrete time-delay systems is unknown at each iteration. For such a class of discrete time-delay systems, a method is presented whereby a class of P-type discrete iterative learning control schemes can be constructed. It is shown that under some given conditions, the constructed iterative learning controllers can guarantee the asymptotic convergence of the output error between the given desired output and the actual output through the iterative learning process. Finally, a numerical example is given to demonstrate the validity of the results.

Load simulator is a kind of hardware in the loop (HIL) simulation equipment, which is used to simulate the real load of the actuator in the laboratory environment. The main goal of the load simulator is to eliminate the surplus torque caused by the movement of the tested actuator and track the load spectrum accurately. When the load simulator tracks the high-frequency load signal, the feedback based control method has a serious lag, which can be avoided by using iterative learning control. However, iterative learning control is suitable for the case of constant reference trajectory and cannot deal with non-repetitive reference trajectory. B-spline decomposition based iterative learning control method is proposed. The reference load spectrum signal is decomposed into the basic spline signal, and the corresponding basic input is obtained by iterative learning control, the final control input is synthesized for tracking reference load spectrum. The simulation and experimental results show that compared with the traditional control method, this method can effectively improve the loading accuracy. The main contribution of this paper is to apply iterative learning control to non repetitive trajectory tracking.

Swinging up a pendulum on a cart is a well-known demonstration example for trajectory tracking in a nonlinear system. The standard realtime feedback control approach fails if the plant output is not available in real time, e.g. due to large or variable measurement delays. However, the task can be solved in multiple trials by applying feedforward inputs that are improved from trial to trial by Iterative Learning Control (ILC). Our examination demonstrates that an ILC can be used for trajectory tracking close to the singularities and the unstable equilibrium of a non-linear system. Specifically, we present an ILC algorithm for pendulum swing-up by angle trajectory tracking. The controller design is based on a modified plant inversion approach that restricts the learning process to trajectory segments with small tracking errors and sufficient input sensitivity. We show that these restrictions lead to improved learning progress in contrast to conventional learning from the complete trajectory. Controller performance is evaluated in an experimental testbed. The ILC starts from a zero-input trajectory and learns to swing up the pendulum within six iterations. Robustness is analyzed experimentally, and the performance is compared to literature results. The convergence is at least two orders of magnitude faster than the one achieved by other methods that avoid feedback and do not rely on a suitable initial input trajectory.

In this paper, an improved feedback-feedforward model-free adaptive iterative learning control with high-order estimation (FF-HOE-MFAILC) is proposed for the discrete-time nonlinear system. A novel pseudo-partial derivatives (PPD) estimation algorithm is derived based on the high-order optimization input criterion function with a proof derivation. Then, the model-free adaptive control with PPD high-order estimation is used as the feedback control term. Moreover, to improve the rapidity and accuracy of convergence, a P-type iterative learning control is employed into the proposed improved MFAC as the feedforward control term. This algorithm is essential a data-driven control method involved the repetitive iterative learning ability for nonlinear system. Numerical simulations are conducted to demonstrate the effectiveness of the proposed FF-HOE-MFAILC. Compared with the existing improved-MFAC (i-MFAC) and MFAC-based feedback-feedforward ILC (MFAC+ILC), our FF-HOE-MFAILC is proven by some comparative analyses that, the convergent speed is increased and the tracking error is decreased significantly.

This work presents a new application of iterative learning control (ILC) in two respects. Firstly, the output signal is generated by a machine vision system. Secondly, ILC is applied to the extrusion process in micro robotic deposition (muRD), directly addressing the end product quality instead of contributors to end product quality such as position tracking. A P-type and model inversion learning function are both applied to the extrusion process, a system that has nonlinear dynamics and no readily available volumetric flowrate sensor. Theoretical and experimental results show that the nominal system is first order with a pure time delay. Both P-type and model inversion ILC improve the dynamics, with both systems providing better reference tracking. The ILC compensates for the unmodeled nonlinearities, realizing a reduction of RMS error to less than 20% of the initial value for the model inversion approach. Experiments are performed, displaying the ability to extrude precise and seamless closed shapes with the model inversion ILC. This is a necessary requirement for transitioning materials and embedding sensors in multi- material muRD.

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