On Guaranteeing Convergence of Discrete LQG/LTR When Augmenting It With Forward PI Controllers

Using the loop transfer recovery (LTR) method to recover the linear quadratic Gaussian (LQG) robustness properties is a well-established procedure, as well as augmenting the system with integrators at the plant input to deal with steady-state error. However, when using the discrete version of the LQG/LTR controller, simply using integrators discretized by the forward Euler method does not guarantee recovery convergence. This paper presents a solution: augmenting the system with a PI controller. A control moment gyroscope is used to apply this technique, and its modeling process is showed, along with its linearization and discretization. Particularly, it presents a resonance due to nutation frequency, which is damped in an inner loop prior to the robust control design by simple velocity feedback. Particle swarm optimization is applied aiming to shape the target open loop and to guarantee set point, disturbance and measurement noise robustness. At last, real experiments are conducted to corroborate the presented method.