18 Towards the Development of a Digital Twin for Structural Dynamics Applications 177 10-1 100 101 f [Hz] -60 -50 -40 -30 -20 -10 0 10 20 T [dB] KE passive KE VFC 10.77dB reduction KE LQR 12.77dB reduction Fig. 18.12 Time-averaged kinetic energy of the 3-storey building with and without a control action on the third floor. The control gains of the Velocity Feedback Controller and the Linear Quadratic Regulator are designed in terms of equal control effort. The kinetic energy reduction is calculated as the integral of the frequency dependent kinetic energy A linear quadratic regulator (LQR) [14] has been chosen as a full state control method that is model based. The LQR solves the linear quadratic Gaussian problem that minimises a cost function that is a trade off between the performance of the controller and the control effort required to achieve that performance. The control action, in this case, is still applied only on the third floor of the structure, but the matrix of feedback gains is calculated to achieve a global performance of vibration reduction, hence considering all the states of the system. This method can give a better performance than the previous one, however, if the dynamics of the structure changes during the operation, the control performance could degrade, or worse, the controller could become unstable. Figure 18.12 shows a comparison among these control strategies for the data set one (bumper not in contact) in terms of kinetic energy for the same control effort requirements. The LQR strategy performs slightly better than the VFC in this scenario, giving a better reduction of the kinetic energy. If the plant dynamics changes, however, the LQR feedback gains are not designed to adapt to these changes and could lead to a worse than expected performance. The design parameters of the LQR controller, are computed for the nominal system and usually stay the same throughout the asset operation even though the plant dynamics could change. Instead of using a LQR controller, one could use another model based control method, such as model predictive control (MPC). MPC would still be liable to the same problems faced by the LQR, however, the internal model of MPC can be made adaptive and it could be updated by the data-augmented model. Adaptive MPC can be implemented to achieve an optimal performance, however, its robustness against uncertainties and potential faults needs to be compared against the robustness and performance of the non-model based control methods, such as VFC. 18.7 Decisions in a Digital Twin Decision-making is a key process required for digital twins. In order to remain a useful tool for the end-user, digital twins must continuously adapt so that they are representative of the physical twins. In the three-storey building structure case study, data-augmented modelling allows the digital twin to identify when a decision may be required as an inflation in the prediction variance is observed. Upon seeing this trigger caused by the previously unseen nonlinear condition, the digital twin should decide whether to perform one of the following actions:
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