A new controller based on desired compensation adaptation law (DCAL) is proposed in this paper. The original DCAL control input can be split up into three main separate terms; an adaptive feedforward term, a proportional-derivative (PD) feedback term and a compensation term. Inspired from the fact that nonlinear time-varying feedback gains lead to improved performance, we propose in this work to revisit DCAL control scheme by replacing the constant feedback gains in the PD feedback term by nonlinear time-varying ones. The proposed nonlinear gains are automatically adjusted according to the variation of the tracking error yielding improved tracking performance. Besides, to cope with the internal forces issue that appears in the case of redundantly actuated parallel kinematic manipulators (RA-PKMs), we propose to use a projection operator to reduce these forces. The projection operator, which is based on the kinematics of the manipulator, reduces the part of the control inputs responsible for internal forces. To demonstrate the relevance of the proposed control strategy, both standard DCAL and the proposed extended DCAL controller are experimentally implemented on a three degree of freedom (3-DOF) RA-PKM called Dual-V. Based on the obtained results, it is shown that the proposed controller outperforms the original one in terms of tracking performance while reducing the control effort.