Modeling and design of tape transport mechanism

The proposed tape transport mechanism consists of three servos: the capstan servo which controls the speed required by the tape transport system, the take-up reel servo and supply reel servo, which will rotate at a slightly different speed from the capstan servo to provide the necessary tape tension control. The mathematical model of the system is derived. Since the proposed system is a multi-input/multi-output (MIMO) system, the mathematical model is arranged into a state-space representation of the system. The controller designed for the tape transport system is the linear quadratic regulator (LQR). Since steady-state error is present, and intended design specification is not fully met, an input gain matrix N¯ is implemented. Simulation is carried out using MATLAB to investigate the step responses of the uncompensated tape transport system, with the linear quadratic regulator and with the linear quadratic regulator with the implementation of N¯.