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Surface control design of rocket using MIMO PID robust integral backstepping

Rocket is a system with multiple inputs and multiple outputs that has unstable dynamics, non-linear, high order, and sensitive to external disturbances. The mathematical model which represents the dynamics of the rocket has parameters that are usually an approximation, this leads to uncertainty of empirical representations. In addition, wind disturbances can destabilize the movement of the rocket. In this paper, it is proposed the robust MIMO PID controller obtained by using the robust H∞ synthesis via integral backstepping method for rocket control problems. Synthesis of PID controllers using robust H8 methods in the form of state feedback results in integral backstepping structure and new parameter ρ. PID controller parameters are obtained via the algebraic Riccati equation solution to determine the optimum value of ρ and γ. The controller is tested through a simulation model of a rocket in flight conditions at altitudes of 1.000 meters to 10.000 meters with a wind disturbance and model uncertainties. Simulation results show that the wind disturbance attenuation reaches −46 dB at a frequency of disturbances and μ-analysis in the frequency domain shows that the system is stable robust.