Online Optimization of Adaptive Vibration Control System of Dynamically Loaded Flexible Structures

Author: Guangyang Chen

Chen, Guangyang, 2018 Online Optimization of Adaptive Vibration Control System of Dynamically Loaded Flexible Structures , Flinders University, College of Science and Engineering

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Many physical systems to be controlled are time-varying in nature, i.e., the system parameters will change according to different operating conditions. This is certainly true for a dynamically loaded flexible structure in which system parameters, such as natural frequencies, are functions of the structure loading conditions. In this circumstance, an adaptive control system will be needed to provide a consistent system performance over a wide range of operating conditions. Different from a non-adaptive control system, an adaptive control system must be able to work with unknown structural parameters and must provide a satisfactory control effect with a fast time response.

In this project, a multi-input multi-output (MIMO) vibration cancellation control system is developed for a dynamically loaded plate structure to remove its single and multiple modes of vibrations caused by unwanted disturbances. The adaptive MIMO control system is constituted by an online parameter estimator and an adaptive controller. With appropriately estimated parameters supplied by the online parameter estimator, the adaptive controller will be able to control the system successfully. Positive position feedback (PPF) that offers a fast roll-off at high frequencies is chosen to construct the adaptive controller. The stability of the resulting closed-loop system is guaranteed with high robustness.

Since the design of the controller depends on a validated mathematical model of the system, a MIMO system identification is conducted via experiment. Only the first three modes of the system are considered to be within the frequency range of concern. The experimental setup is constituted by a top plate supported by three pairs of sensors and actuators that are connected to a base plate. The base plate is shaking consistently by a disturbance transducer that introduces a disturbance signal into the system. By using curve fitting techniques, a transfer function matrix of the MIMO plate structure is obtained.

A most recognized challenge in an adaptive controller design lies in the optimization of the controller parameters. For online control of a time-varying system, the controller parameters need to be updated whenever a change in the system operating condition occurs. Online controller parameter optimization thus presents the biggest challenge in fulfilling the required control goal with unknown operating conditions. Computation of real-time optimization of controller parameters requires a large amount of computational time with high computation power and is often considered as unachievable in real-time implementations.

In this project, a sub-optimization method is proposed, in which two optimized PPF controllers are designed off-line for two different working conditions (unloaded and fully-loaded). When an unknown working condition is observed and estimated by the online parameter estimator, one of the two pre-designed PPF controllers will be applied to the system temporarily to control the unknown condition, while a new PPF controller will be optimized online within a required period of time to replace the pre-designed controller.

To achieve this, a mathematical model of the current working condition is first generated by online parameter estimation. The vibration frequency is estimated by a frequency estimator. A linear relation is assumed for mode shape prediction purpose. For each one mode, the mode shape is changing linearly subject to the change of the natural frequency. The damping ratios of the unknown working condition are selected to be the same as either the unloaded or the fully-loaded condition based on which frequency is closer to the unknown working condition. Secondly, according to the structure of the MIMO PPF controller, the compensator frequency matrix, damping matrix, and gain matrix are the compensator parameters that need to be designed. For the purpose of active damping, the frequency matrix is set to be equal to the natural frequency matrix of the structure. The damping ratio matrix of the pre-designed PPF controller is used as the damping matrix for the unknown working condition due to high robustness of the PPF controller. Thus, the only compensator parameter that needs to be optimized is the gain matrix. Subsequently, an H∞ norm of the closed loop frequency response function is defined for the optimization purpose. Then, two optimization methods are proposed, the Genetic Algorithm (GA) method and the Simulated Annealing (SA) method. For the GA method, the computational time is mainly related to the size of population and the number of generations. To ensure the population diversity, the size of population cannot be largely deducted. However, by setting different Probability of Performing Crosser and Probability of Mutation for two fitness levels (under average and over average), the number of generations can be reduced. For the SA method, normally, the initial value of the optimization parameter is chosen randomly. However, for saving time purpose, the initial value is selected to be the value of the chosen pre-designed PPF controller. In principle, although the GA method can provide a very accurate optimization result, it costs more time. On the contrary, the SA method requires less time, but possesses a limited ability to find the most accurate optimization result.

To propose the sub-optimization step, two optimized MIMO PPF controllers are designed off-line for the unloaded and fully-loaded conditions, respectively, and the simulation results validate the effectiveness of both scenarios. Compared with the open-loop frequency response, the closed-loop frequency response can achieve up to 10.347dB attenuation. Then, the simulation of an unknown working condition is carried out in which one of the pre-designed MIMO PPF controllers is used to temporarily control the unknown condition. Simultaneously, the GA and SA methods are used to calculate the optimized parameters of the PPF controller for the unknown working condition online. The frequency matrix and the damping matrix of the adaptive controller are designed in advance, while the gain matrix of the controller is optimized online. To take into account the possible spill-over effect that high frequencies may introduce to low frequencies, the controller gain for the highest mode of concern is optimized first, followed by the gains of the subsequent lower modes of concern. As soon as an optimized gain is generated, the corresponding gain and designed frequency of the adaptive controller are updated. The other parameters of the adaptive controller remain pending, until the whole gain matrix is optimized. Simulation results reveal that a further 5.20 dB attenuation can be achieved by using the SA optimization method in 28.158 seconds, while a further 5.43 dB attenuation is achievable by using the GA optimization method, the total computation time is 428.472 seconds

In conclusion, compared to the traditional GA and SA methods, the proposed modifications, as applied to the online optimization of the underlying MIMO PPF adaptive controller gain matrix, can save a significant amount of computational time. Even though the time consumption is still considered to be high for an effective real-time operation of the MIMO adaptive controller, the proposed method provides a foundation upon which possible means of achieving further reduction of the computational time can be investigated. Nevertheless, this thesis sets up an example of combining an online optimization scheme with an online parameter estimation capability to produce an adaptive control system that is capable of dealing with unknown working conditions of a MIMO time-varying dynamic structure satisfactorily.

Keywords: Online Optimization, Time-varying sysem, GA,SA

Subject: Engineering thesis

Thesis type: Masters
Completed: 2018
School: College of Science and Engineering
Supervisor: Fangpo He