Iterative feedback and feedforward controller tuning for repetitive processes
Authors
Gao, Xuemei
ORCID
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Other Contributors
Mishra, Sandipan
Bevilacqua, Riccardo
Maniatty, Antoinette M.
Julius, Anak Agung
Bevilacqua, Riccardo
Maniatty, Antoinette M.
Julius, Anak Agung
Issue Date
2014-08
Keywords
Mechanical engineering
Degree
PhD
Terms of Use
Attribution-NonCommercial-NoDerivs 3.0 United States
This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.
This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.
Full Citation
Abstract
Portable ILC addresses the portability problem between different trajectories on the same system, i.e. how can a feedforward control signal be generated from learning from a training trajectory. Portable ILC learns a model of the impulse response of an inverse plant in the process of iteratively tuning the feedforward input for a given (training) trajectory. It then transfers the learned model to initialize the feedforward input for a different (testing) trajectory without re-learning. Due to the model carrying system dynamics-related information, the proposed portable ILC imposes no restriction on the lengths of the training and testing trajectories. These algorithms are demonstrated on a high precision motion control stage.
Reference position tracking in motion control is of significant importance in manufacturing, especially when a part of high precision is being manufactured. Typically, many manufacturing tasks are repetitive since the same parts are made in mass scale. For these repetitive processes/tasks, two qualities of motion control are desirable: (1) high precision reference tracking for each repetitive task; and (2) smooth transition from one repetitive task to another. The first quality requires continuous improvement of tracking performance for each repetitive task, while the second demands a short transition period when switching from one repetitive task to another. To address these two needs, a controller needs to be well-tuned to extract the greatest amount of performance while requiring minimum transition time for re-tuning of the controller when switching from one task to another.
This thesis addresses the controller tuning problem for high precision tracking in repetitive processes in the framework of a two degree-of-freedom control loop. In this control structure, both the feedback controller and the feedforward input are designed and tuned iteratively to extract high performance in terms of tracking error. The tuning algorithm for the feedback controller is designed so as to guarantee closed-loop stability while delivering the smallest tracking error in the root means square (RMS) sense. The feedforward control input is tuned using iterative learning control (ILC). For tuning the feedforward control input using ILC, two methods are designed, namely, non-repetitive analysis-based ILC and portable ILC. The former improves tracking performance within one repetitive process by separating repetitive error and non-repetitive error, while the latter extends to learning between different repetitive processes.
For the feedback controller, the proposed model and data synthesized auto-tuning method uses experimental data collected in conjunction with a model of the plant to automatically tune the feedback controller iteratively. A key challenge in automated feedback tuning is guaranteeing stability of the closed-loop system during the tuning process. In order to achieve this, the traditional feedback controller tuning problem is reformulated into the tuning of the Youla parameterized version of the controller. Thus at each iteration of the tuning process, the Youla parameter is iteratively tuned to minimize a given cost function, which is typically a quadratic cost consisting of control effort 2-norm and tracking error 2-norm. This makes the optimization problem quadratic in the parameters and at the same time, eliminates the need for checking stability at each iteration. The proposed auto-tuning algorithm can be used for (1) optimizing a given controller, or (2) generating an optimal controller.
Typically, after the feedback controller has been tuned, the feedforward controller is tuned for a better transient performance. For reference tracking in repetitive processes, the feedforward control input is typically designed using ILC, where the feedforward control input is tuned by learning from previous iterations to minimize a cost function. A basic assumption in ILC is that both the disturbance is repetitive; in practice though, the disturbance contains both repetitive and non-repetitive parts. Furthermore, the feedforward signal obtained by using ILC is limited to the same reference and changing the reference requires a complete re-learning. To address these issues, two algorithms are designed in this thesis: the non-repetitive analysis-based ILC and portable ILC.
Non-repetitive analysis-based ILC separates the tracking error into repetitive and non-repetitive parts explicitly and designs a learning law based on the minimization of the expected value of a cost function (such as control effort and error norm) at each iteration. The derived update law is iteration-varying and depends on the ratio of the covariance of the non-repetitive component of the tracking error to the covariance of the residual total tracking error. This implies that in earlier iterations the learning is rapid (large learning gains) and as iterations go by, the algorithm is conservative and learns slowly. The proposed algorithm is also extended to the case where the learning filter is fixed and the optimal (iteration-varying) scalar learning rate needs to be determined.
Reference position tracking in motion control is of significant importance in manufacturing, especially when a part of high precision is being manufactured. Typically, many manufacturing tasks are repetitive since the same parts are made in mass scale. For these repetitive processes/tasks, two qualities of motion control are desirable: (1) high precision reference tracking for each repetitive task; and (2) smooth transition from one repetitive task to another. The first quality requires continuous improvement of tracking performance for each repetitive task, while the second demands a short transition period when switching from one repetitive task to another. To address these two needs, a controller needs to be well-tuned to extract the greatest amount of performance while requiring minimum transition time for re-tuning of the controller when switching from one task to another.
This thesis addresses the controller tuning problem for high precision tracking in repetitive processes in the framework of a two degree-of-freedom control loop. In this control structure, both the feedback controller and the feedforward input are designed and tuned iteratively to extract high performance in terms of tracking error. The tuning algorithm for the feedback controller is designed so as to guarantee closed-loop stability while delivering the smallest tracking error in the root means square (RMS) sense. The feedforward control input is tuned using iterative learning control (ILC). For tuning the feedforward control input using ILC, two methods are designed, namely, non-repetitive analysis-based ILC and portable ILC. The former improves tracking performance within one repetitive process by separating repetitive error and non-repetitive error, while the latter extends to learning between different repetitive processes.
For the feedback controller, the proposed model and data synthesized auto-tuning method uses experimental data collected in conjunction with a model of the plant to automatically tune the feedback controller iteratively. A key challenge in automated feedback tuning is guaranteeing stability of the closed-loop system during the tuning process. In order to achieve this, the traditional feedback controller tuning problem is reformulated into the tuning of the Youla parameterized version of the controller. Thus at each iteration of the tuning process, the Youla parameter is iteratively tuned to minimize a given cost function, which is typically a quadratic cost consisting of control effort 2-norm and tracking error 2-norm. This makes the optimization problem quadratic in the parameters and at the same time, eliminates the need for checking stability at each iteration. The proposed auto-tuning algorithm can be used for (1) optimizing a given controller, or (2) generating an optimal controller.
Typically, after the feedback controller has been tuned, the feedforward controller is tuned for a better transient performance. For reference tracking in repetitive processes, the feedforward control input is typically designed using ILC, where the feedforward control input is tuned by learning from previous iterations to minimize a cost function. A basic assumption in ILC is that both the disturbance is repetitive; in practice though, the disturbance contains both repetitive and non-repetitive parts. Furthermore, the feedforward signal obtained by using ILC is limited to the same reference and changing the reference requires a complete re-learning. To address these issues, two algorithms are designed in this thesis: the non-repetitive analysis-based ILC and portable ILC.
Non-repetitive analysis-based ILC separates the tracking error into repetitive and non-repetitive parts explicitly and designs a learning law based on the minimization of the expected value of a cost function (such as control effort and error norm) at each iteration. The derived update law is iteration-varying and depends on the ratio of the covariance of the non-repetitive component of the tracking error to the covariance of the residual total tracking error. This implies that in earlier iterations the learning is rapid (large learning gains) and as iterations go by, the algorithm is conservative and learns slowly. The proposed algorithm is also extended to the case where the learning filter is fixed and the optimal (iteration-varying) scalar learning rate needs to be determined.
Description
August 2014
School of Engineering
School of Engineering
Department
Dept. of Mechanical, Aerospace, and Nuclear Engineering
Publisher
Rensselaer Polytechnic Institute, Troy, NY
Relationships
Rensselaer Theses and Dissertations Online Collection
Access
CC BY-NC-ND. Users may download and share copies with attribution in accordance with a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License. No commercial use or derivatives are permitted without the explicit approval of the author.