This paper explores a strategy of model-referenced trajectory tracking for a rigid-link cylindrical robot by employing an Adaptive Computed Torque Control Scheme (ACTCS) in conjunction with a Linear Optimal Controller (LOC). The adaptive control scheme is based on a version of Narendra's Direct Model-referenced Adaptive Control algorithm and includes adaptive sampling. The results presented here represents an extention of previous work whereby the formulation of the ACTCS and its experimental evaluation for a 3-DOF cylindrical robot was developed. This paper investigates the addition of a linear optimal tracking controller in the scheme. Experimental results show that the adaptive controller brings the end-effector of the robot manipulator onto the model-referenced differential manifold swiftly and robustly.