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1. Identification of Self-Excited Systems Using Discrete-Time, Time-Delayed Lur’e Models

   Paredes, Juan ; Bernstein, Dennis S. ( May 2021 , Proceedings of the American Control Conference)

   null (Ed.)

   This paper considers system identification for systems whose output is asymptotically periodic under constant inputs. The model used for system identification is a discretetime Lur’e model consisting of asymptotically stable linear dynamics, a time delay, a washout filter, and a static nonlinear feedback mapping. For sufficiently large scaling of the loop transfer function, these components cause divergence under small signal levels and decay under large signal amplitudes, thus producing an asymptotically oscillatory output. A leastsquares technique is used to estimate the coefficients of the linear model as well as the parameters of a piecewise-linear approximation of the feedback mapping. 

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2. NARMAX Identification Based Closed-Loop Control of Flow Separation over NACA 0015 Airfoil

   https://doi.org/10.3390/fluids5030100  

   Obeid, Sohaib ; Ahmadi, Goodarz ; Jha, Ratneshwar ( September 2020 , Fluids)

   null (Ed.)

   A closed-loop control algorithm for the reduction of turbulent flow separation over NACA 0015 airfoil equipped with leading-edge synthetic jet actuators (SJAs) is presented. A system identification approach based on Nonlinear Auto-Regressive Moving Average with eXogenous inputs (NARMAX) technique was used to predict nonlinear dynamics of the fluid flow and for the design of the controller system. Numerical simulations based on URANS equations are performed at Reynolds number of 106 for various airfoil incidences with and without closed-loop control. The NARMAX model for flow over an airfoil is based on the static pressure data, and the synthetic jet actuator is developed using an incompressible flow model. The corresponding NARMAX identification model developed for the pressure data is nonlinear; therefore, the describing function technique is used to linearize the system within its frequency range. Low-pass filtering is used to obtain quasi-linear state values, which assist in the application of linear control techniques. The reference signal signifies the condition of a fully re-attached flow, and it is determined based on the linearization of the original signal during open-loop control. The controller design follows the standard proportional-integral (PI) technique for the single-input single-output system. The resulting closed-loop response tracks the reference value and leads to significant improvements in the transient response over the open-loop system. The NARMAX controller enhances the lift coefficient from 0.787 for the uncontrolled case to 1.315 for the controlled case with an increase of 67.1%. 

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3. Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertainty

   https://doi.org/10.23919/ACC53348.2022.9867457  

   Sinha, Rohan ; Harrison, James ; Richards, Spencer M. ; Pavone, Marco ( June 2022 , American Control Conference)

   We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems commonly model the nonlinear effects of an unknown environment on a nominal system. We optimize over a class of nonlinear feedback policies inspired by certainty equivalent "estimate-and-cancel" control laws pioneered in classical adaptive control to achieve significant performance improvements in the presence of uncertainties of large magnitude, a setting in which existing learning-based predictive control algorithms often struggle to guarantee safety. In contrast to previous work in robust adaptive MPC, our approach allows us to take advantage of structure (i.e., the numerical predictions) in the a priori unknown dynamics learned online through function approximation. Our approach also extends typical nonlinear adaptive control methods to systems with state and input constraints even when we cannot directly cancel the additive uncertain function from the dynamics. Moreover, we apply contemporary statistical estimation techniques to certify the system’s safety through persistent constraint satisfaction with high probability. Finally, we show in simulation that our method can accommodate more significant unknown dynamics terms than existing methods. 

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4. Feedback control design using model predictive control formulation and Carleman approximation method

   https://doi.org/10.1002/aic.16666  

   Hashemian, Negar ; Armaou, Antonios ( June 2019 , AIChE Journal)

   Model predictive control (MPC) for nonlinear systems involves a nonlinear dynamic optimization (NDO) step, which is required to be solved repeatedly. This step is computationally demanding, specially in dealing with constrained and/or nonlinear large‐scale systems. This paper presents a method for accelerating the NDO in state‐feedback regulation problems. Exploiting Carleman approximation, this method represents the nonlinear dynamics in a bilinear form and discretizes the resulting system in the time domain. The gradient and Hessian of the cost function with respect to the feedback gains are also analytically derived. The Carleman approximation of the nonlinear system may introduce errors in the prediction and sensitivity analysis. The manuscript derives a criterion under which the input‐to‐state stability of the new design is guaranteed. The proposed MPC is implemented in a chemical reactor example. Simulation results show that replacing conventional MPC schemes by the presented method reduces the computation time by an order of magnitude.

    

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5. Self-sensing active artificial hair cells inspired by the cochlear amplifier, Part II: Experimental validation

   https://doi.org/10.1177/1045389X231164514  

   Davaria, Sheyda ; Malladi, Vijaya V. N. Sriram ; Tarazaga, Pablo A. ( April 2023 , Journal of Intelligent Material Systems and Structures)

   Mimicking the nonlinear compressive behavior of the mammalian cochlear amplifier that results in the compression of high-intensity sounds and amplification of faint stimuli can lead to transformative improvements in the dynamic range, sharpness of the response, and threshold of sound detection in cochlear implants to aid individuals with hearing loss. Furthermore, it can enhance the dynamic properties of sensors. This research on developing self-sensing artificial hair cells (AHCs) validates the phenomenological control algorithm established in Part I of the paper to achieve a cochlea-like response from the quadmorph AHCs. As the beam is excited, the voltage of the piezoelectric layers is measured and used to generate a control voltage. Consequently, the controller applies cubic damping to the AHC, while reducing linear damping near its first natural frequency to replicate the biological cochlea’s function. Experimental results validate the model built in Part I of the paper and the work is extended to implement a multi-channel AHC. The system works independent of external sensors and offers significant advantages over previous generations of AHCs such as the ability to embed AHCs in a limited space and to combine several AHCs in an array without the need for external feedback measurement devices.

    

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