ADRC for statically unstable longitudinal flight dynamics

PD attitude control is widely used for the flight vehicles, especially in boost phase, where the dynamics are often statically unstable. An enhanced PD control scheme based on state observer compensation is presented to cope with the situation. By utilizing the measurable data, the observer allows treating the entire response of the system, with the exception of the control term as a disturbance, and to use the estimation of the disturbance to cancel-out this response and thereby to effectively simplify the control channel. The control algorithm is derived based on the linear perturbation dynamics of flight vehicles. To reduce the phase lag, a reduced-order observer is employed to simplify the proposed approach. With reasonable assumptions, a sufficient condition on selecting of key control parameters is established to guarantee closed-loop stability, which provides a guideline for control tuning. According to stability margin tester philosophy, an interactive graphical tuning methodology is explicitly presented, where both the 67.5deg phase margin law and the fixed ratio between the critical frequency and the rising time play the essential roles. Some illustrative examples are provided to validate the results.