Thesis title: Inertial and kinematic control of mechanisms by semi-active dampers
The present work is framed in the field of the inertial and kinematic control of mechanisms by semi-active dampers. The proposed investigation explores a new possibility with respect to the classic usage of damping which can be found in literature, based on purely dissipation purposes. In fact, stiffness and damping are the main impedance parameters which could be modified through active and semi-active control strategies to achieve different tasks, mostly to face vibration attenuation problems. The remaining parameter, i.e. the inertia, is something difficult to be directly controlled. Thus, the present thesis aims to show how the inertial properties of a system can be indirectly modified by acting semi-actively on the viscosity of the dampers characterizing the linkages of a mechanism.
The influence of the inertial properties based on the modification of the damping coefficients of the actuators characterizing the constraints of the system can be achieved in two ways: by acting on the equivalent mass of the system or by acting on the geometry of the constraints. In both the two scenarios, the hidden relationship between damping and inertial characteristics of a rigid system is shown firstly through elemental examples, to present the fundamental concepts, and then through the development of a more general theory. Successively, the Optimal Control Theory (OCT) is utilized to attack the dynamics of a system in presence of actuators equipped with tunable dampers. In particular, depending on the application, the optimal damping coefficients laws are determined by two control strategies: an iterative Linear Quadratic Regulator (LQR) scheme and the Nonlinear Model Predictive Controller (NMPC).
The change in the equivalent mass of a system can be achieved by attaching small mass-damper devices to a primary structure. Depending on the external excitation, the controller can vary the damping coefficients of the mass-damper devices to modify the equivalent mass of the system and so its natural frequencies, in particular to avoid resonant conditions. This possibility is investigated by considering a simple architecture, defined as Toy model, consisting of a main mass constrained to the frame with a spring and to which a small mass-damper device is attached. The iterative LQR scheme is adopted to reduce its vibrational repsonse in presence of harmonic excitations whose frequency could move within or cross the frequency band of the system, it is shown how the controller, to reduce the amplitude response of the main mass, tunes opportunely the damping coefficient of the damper to change its natural frequency to avoid the resonant condition. Finally, a slightly different architecture is considered to let the modification of the LQR scheme by introducing the concept of the Instantaneous Frequency (IF) of the system response.
The change in the geometry of the constraints through damping control permits the kinematic guidance of a rigid body and, fundamentally, the indirect control of the corresponding polodes, equivalent inertia tensor and natural frequencies of the system. This possibility is explored in three main applications: (i) the LQR scheme is used to solve the trajectory-tracking problems of a planar rigid body constrained by 4/8 tunable dampers and, successively, of a Stewart hexapod platform constrained by six tunable dampers; (ii) the LQR scheme is adopted to modify the damping coefficients of the dampers of the suspension system of a vehicle to mitigate the roll angle in roll resonant conditions; (iii) the NMPC is adopted to control the damping coefficients of two rotary dampers within a planetary gearbox to achieve speed and torque control of a Continuously Variable Transmission (CVT) system powered by a DC Motor in different target-load combinations imposed for the output shaft.