The equivalent mobile robot system open loop transfer function with load and gears attached, in terms of the input voltage, [V.sub.in] (s) and angular velocity, ([[omega].sub.robot](s), is given as
Based on the equations that describe the DC motor, system dynamics and sensor modelling, the next open loop transfer function, relating the armature input terminal voltage, [V.sub.in](s) to the output terminal voltage of the tachometer [V.sub.ach](s), with most corresponding load torques applied, is
This was also noted that the first tuning method was only suitable for simple systems without any integrator or dominant complex conjugate poles in open loop transfer function .
The closed loop system depicted in Fig.7 was designed incorporating open loop transfer function (OLTF) obtained from previous section.
For this system, the open loop transfer function (OLTF) was calculated as: