Long short-term memory (LSTM) neural network-based system identication and augmented predictive control of piezoelectric actuators
Atomic force microscope (AFM), scanning tunnel microscope (STM), precision robotic manipulator, etc. have been used widely for various applications. These systems undoubtedly perform the task with micro-level accuracy of operations. Note that in these applications, the use of piezoelectric actuators (PEA) is ubiquitous. The desired high-resolution and better accuracy by such instruments/ systems can be easily achieved by the use of PEA owing to its desired properties such as high precision, quick response, better stability, high stiffness, etc. These properties make PEA the best choice in the applications which demand a micro-nano level of accuracy in the operations. Though PEA is suitable in critical applications and systems requiring high accuracy, PEA exhibits undesirable nonlinearities due to its hysteresis and creep behavior. These nonlinearities significantly bound the accuracy of operation by PEA and, consequently, the use of PEA. To tackle the effect of hysteresis, creep and other nonlinearities exhibited by PEA, modeling and control of PEA are essential. The model based control approaches are, specifically, effective in achieving the desired level of performance, especially in tracking applications. However, modeling accuracy and linearization losses are the factors responsible for the compromise in the desired performance.
To overcome this, in this work, we developed a novice LSTM neural network-based system identification and predictive control approach to compensate for PEA nonlinearities and achieve better accuracy in the tracking applications.
In the first work, to model the complete dynamics of PEA, an LSTM neural network was built and trained on input-output data of commercial PEA. The input signal required for the training the LSTM model was designed using the k-means clustering method in such a way that it covers most of the working frequencies. The use of LSTM network benefits by confirming the long-term dependencies and temporal connection of time series data and hence modeling the dynamics of PEA for a broader range of frequency. Additionally, the use of LSTM ensures the model generalization and reduces the gradient vanishing or exploding problem due to its inherent architecture. Further, to validate the accuracy of the LSTM model, the output of the model was compared with the actual commercial PEA outputs. Moreover, to evaluate the effectiveness of the LSTM model in tracking control applications, it was used with nonlinear model predictive control (NLMPC) as its internal system dynamics model. To estimate the states of the system, an unscented Kalman filter was designed and used along with NLMPC. The results have demonstrated the efficacy of the proposed modeling approach for both low and high-frequency input excitations as well as in tracking control when used with NLMPC.
Next, in the second work, understanding the capability of LSTM in modeling nonlinear dynamics of PEA effectively, an inversion LSTM based predictive control approach was devised. To improve the accuracy of the LSTM in identifying the system dynamics, a multilayered LSTM model was built and trained on the PEA data to obtain the inversion dynamics model of PEA. This LSTM model was further concatenated with a physical PEA resulting in a mostly linear combined system. The advantage of such an approach is that it allows the use of linear control approaches without sacrificing accuracy. Additionally, this approach significantly reduces the computational burden on the controller and hence improving the speed of operation. Further, this combined system (LSTM+ PEA) was controlled with a linear model predictive controller (MPC). A steady-state Kalman filter was designed in the Matlab to estimate the states of this system. Furthermore, similar to the previous approach, the effectiveness of the proposed method was evaluated in tracking control of complex reference trajectories. The results have demonstrated improvement in modeling accuracy, better tracking control with reduced computational load in real-time.
Altogether, in this work, we present a new LSTM neural network-based system identification and augmented predictive control of PEA, which outperforms traditional PID in trajectory tracking application.