Iterative Nonlinear Control of a Semibatch Reactor. Stability Analysis

This paper presents the application of Iterative Nonlinear Model Predictive Control, INMPC, to a semibatch chemical reactor. The proposed control approach is derived from a model-based predictive control formulation which takes advantage of the repetitive nature of batch processes. The proposed controller combines the good qualities of Model Predictive Control (MPC) with the possibility of learning from past batches, that is the base of Iterative Control. It uses a nonlinear model and a quadratic objective function that is optimized in order to obtain the control law. A stability proof with unitary control horizon is given for nonlinear plants that are affine in control and have linear output map. The controller shows capabilities to learn the optimal trajectory after a few iterations, giving a better fit than a linear non-iterative MPC controller. The controller has applications in repetitive disturbance rejection, because they do not modify the model for control purposes. In this application, some experiments with a disturbance in inlet water temperature has been performed, getting good results.Ministerio de Ciencia y Tecnología DPI2004-07444-C04-0

An Adaptive Periodic-Disturbance Observer for Periodic-Disturbance Suppression

Repetitive operations are widely conducted by automatic machines in industry. Periodic disturbances induced by the repetitive operations must be compensated to achieve precise functioning. In this paper, a periodic-disturbance observer (PDOB) based on the disturbance observer (DOB) structure is proposed. The PDOB compensates a periodic disturbance including the fundamental wave and harmonics by using a time delay element. Furthermore, an adaptive PDOB is proposed for the compensation of frequency-varying periodic disturbances. An adaptive notch filter (ANF) is used in the adaptive PDOB to estimate the fundamental frequency of the periodic disturbance. Simulations compare the proposed methods with a repetitive controller (RC) and the DOB. Practical performances are validated in experiments using a multi-axis manipulator. The proposal provides a new framework based on the DOB structure to design controllers using a time delay element.Comment: 11 pages, 22 figures, journa

Multi-Input Multi-Output Repetitive Control Theory And Taylor Series Based Repetitive Control Design

Repetitive control (RC) systems aim to achieve zero tracking error when tracking a periodic command, or when tracking a constant command in the presence of a periodic disturbance, or both a periodic command and periodic disturbance. This dissertation presents a new approach using Taylor Series Expansion of the inverse system z-transfer function model to design Finite Impulse Response (FIR) repetitive controllers for single-input single-output (SISO) systems, and compares the designs obtained to those generated by optimization in the frequency domain. This approach is very simple, straightforward, and easy to use. It also supplies considerable insight, and gives understanding of the cause of the patterns for zero locations in the optimization based design. The approach forms a different and effective time domain design method, and it can also be used to guide the choice of parameters in performing in the frequency domain optimization design. Next, this dissertation presents the theoretical foundation for frequency based optimization design of repetitive control design for multi-input multi-output (MIMO) systems. A comprehensive stability theory for MIMO repetitive control is developed. A necessary and sufficient condition for asymptotic stability in MIMO RC is derived, and four sufficient conditions are created. One of these is the MIMO version of the approximate monotonic decay condition in SISO RC, and one is a necessary and sufficient condition for stability for all possible disturbance periods. An appropriate optimization criterion for direct MIMO is presented based on minimizing a Frobenius norm summed over frequencies from zero to Nyquist. This design process is very tractable, requiring only solution of a linear algebraic equation. An alternative approach reduces the problem to a set of SISO design problems, one for each input-output pair. The performances of the resulting designs are studied by extensive examples. Both approaches are seen to be able to create RC designs with fast monotonic decay of the tracking error. Finally, this dissertation presents an analysis of using an experiment design sequence for parameter identification based on the theory of iterative learning control (ILC), a sister field to repetitive control. This is suggested as an alternative to the results in optimal experiment design. Modified ILC laws that are intentionally non-robust to model errors are developed, as a way to fine tune the use of ILC for identification purposes. The non-robustness with respect to its ability to improve identification of system parameters when the model error is correct is studied. It is demonstrated that in many cases the approach makes the learning particularly sensitive to relatively small parameter errors in the model, but sensitivity is sometimes limited to parameter errors of a specific sign

Inversion-based feedforward-feedback control: theory and implementation to high-speed atomic force microscope imaging

In this dissertation, a suite of inversion-based feedforward-feedback control techniques are developed and applied to achieve high speed AFM imaging. In the last decade, great efforts have been made in developing the inversion-based feedforward control as an effective approach for precision output tracking. Such efforts are facilitated by the fruitful results obtained in the stable-inversion theory, including, mainly, the bounded inverse of nonminimum-phase systems, the preview-based inversion method that quantified the effect of the future desired trajectory on the inverse input, the consideration of the model uncertainties in the system inverse, and the integration of inversion with feedback and iterative control. However, challenges still exist in those inversion-based approaches. For example, although it has been shown that the inversion-based iterative control (IIC) technique can effectively compensate for the vibrational dynamics during the output tracking in the repetitive applications, however, compensating for both the hysteresis effect and the dynamics effect simultaneously using the IIC approach has not been established yet. Moreover, the current design of the inversion-based feedforward feedback two-degree-of-freedom (2DOF) controller is ad-hoc, and the minimization of the model uncertainty effects on the feedforward control has not been addressed. Furthermore, although it is possible to combine system inversion with both iterative learning and feedback control in the so-called current cycle feedback iterative learning control (CCF-ILC) approach, the current controller design is limited to be casual and the use of such CCF-ILC approach for rejecting slowly varying periodic disturbance has not been explored. These challenges, as magnified in applications such as high-speed AFM imaging, motivate the research of this dissertation. Particularly, it is shown that the IIC approach can effectively compensate for both the hysteresis and vibrational dynamics effects of smart actuators. The convergence of the IIC algorithm is investigated by capturing the input-output behavior of piezo actuators with a cascade model consisting of a rate-independent hysteresis at the input followed by the dynamics part of the system. The size of the hysteresis and the vibrational dynamics variations that can be compensated for (by using the IIC method) has been quantified. Secondly, a novel robust-inversion has been developed for single-input-single-output (SISO) LTI systems, which minimized the dynamics uncertainty effect and obtained a guaranteed tracking performance for bounded dynamics uncertainties. Based on the robust-inversion approach, a systematic design of inversion-based two-degree-of-freedom (2DOF)-control was developed. Finally, the robust inversion- based current cycle feedback iterative learning control approach was developed for the rejection of slow varying periodic disturbances. The proposed CCF-ILC controller design utilizes the recently-developed robust-inversion technique to minimize the model uncertainty effect on the feedforward control, as well as to remove the causality constraints in other CCFILC approaches. It is shown that the iterative law converges, and attains a bounded tracking error upon noise and disturbances. In this dissertation, these techniques have been successfully implemented to achieve high-speed AFM imaging of large-size samples. Specifically, it is shown that precision positioning of the probe in the AFM lateral (x-y) scanning can be successfully achieved by using the inversion-based iterative-control (IIC) techniques and robust-inversion based 2DOF control design approach. The AFM imaging speed as well as the sample estimation can be substantially improved by using the CCF-ILC approach for the precision positioning of the probe in the vertical direction