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This paper proposes a Lyapunov based model reference adaptive PD/PID controller for Satellite Launch Vehicle (SLV) systems. SLV is an open loop unstable plant with time varying characteristics and in general it is handled with the help of gain scheduling controllers. To improve the tracking performance, Lyapunov based adaptive PD and PID controllers are designed for model reference adaptive control structure and the performances are compared with existing gain scheduling PD/PID controller. In particular, we show that an adaptive PID controller outperforms in the presence of unmodelled dynamics and wind disturbance conditions.