**José Ramírez Senent \*, Jaime H. García-Palacios and Iván M. Díaz**

Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, Calle del Profesor Aranguren, 3, 28040 Madrid, Spain; jaime.garcia.palacios@upm.es (J.H.G.-P.); ivan.munoz@upm.es (I.M.D.)

**\*** Correspondence: jose.ramirez.senent@alumnos.upm.es

Received: 29 September 2020; Accepted: 2 November 2020; Published: 3 November 2020

**Abstract:** Shake tables are one of the most widespread means to perform vibration testing due to their ability to capture structural dynamic behavior. The shake table acceleration control problem represents a challenging task due to the inherent non-linearities associated to hydraulic servoactuators, their low hydraulic resonance frequencies and the high frequency content of the target signals, among other factors. In this work, a new shake table control method is presented. The procedure relies on identifying the Frequency Response Function between the time derivative of pressure force exerted on the actuator's piston rod and the resultant acceleration at the control point. Then, the Impedance Function is calculated, and the required pressure force time variation is estimated by multiplying the impedance by the target acceleration profile in frequency domain. The pressure force time derivative profile can be directly imposed on an actuator's piston by means of a feedback linearization scheme, which approximately cancels out the actuator's non-linearities leaving only those related to structure under test present in the control loop. The previous architecture is completed with a parallel Three Variable Controller to deal with disturbances. The effectiveness of the proposed method is demonstrated via simulations carried over a non-linear model of a one degree of freedom shake table, both in electrical noise free and contaminated scenarios. Numerical experiments results show an accurate tracking of the target acceleration profile and better performance than traditional control approaches, thus confirming the potential of the proposed method for its implementation in actual systems.

**Keywords:** shake table control; vibration testing; system identification; inverse dynamics; feedback linearization; servohydraulics
