It is very difficult to obtain a linearizing feedback and a coordinate transformation map, even though the system is feedback linearizable. It is known that finding a desired transformation map and feedback is equivalent to finding an integrating factor for an annihilating one-form. In this paper we develop a numerical algorithm for an integrating factor involving a set of partial differential equations and corresponding zero-form using the C.I.R method. We employ a tensor product splines as an interpolation method to data which are resulted from the numerical algorithm in order to obtain an approximate integrating factor and a zero-form in closed forms. Next, we obtain a coordinate transformation map using the approximate integrating factor and zero-form. Finally, we construct a stabilizing controller based on a linearized system with the approximate coordinate transformation.

We propose a motor speed ripple elimination method using a state dependent disturbance observer (SDDOB). The SDDOB eliminates the state dependent disturbance in the system regardless of the operation frequency, input time delay and output time delay. The SDDOB and a main proportional integral (PI) controller constitute a robust motor speed controller. Experimental results show the effectiveness of the proposed method.

The main objective of vehicle suspensions is to improve ride comfort and road holding ability. Though passive suspensions consist of spring and damper, active suspensions adopt an actuator in addition to passive suspensions. In this paper, a quarter car model with an asymmetric hydraulic actuator is used. Moreover, the damping coefficient of the damper, which is changed according to the actuator velocity, is considered. The LPV (Linear Parameter Varying) model is obtained by applying feedback linearization technique. Next, a gain-scheduled controller, based on LQ regulator with different weighting factor, is designed according to the actuator velocity and the stability of the proposed controller is also proved. The effectiveness of the proposed controller is shown by numerical simulations.