Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying

This work deals with the development of a decentralized optimal control algorithm, along with a robust observer,for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements.A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains,which will give enough flexibility in the choice of initial estimates.Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.

Stability Analysis of q-axis Rotor Flux Based Model Reference Adaptive System Updating Rotor Time Constant in Induction Motor Drives

q-axis rotor flux can be chosen to form a model reference adaptive system(MRAS)updating rotor time constant online in induction motor drives.This paper presents a stability analysis of such a system with Popov’s hyperstability concept and small-signal linearization technique.At first,the stability of q-axis rotor flux based MRAS is proven with Popov’s Hyperstability theory.Then,to find out the guidelines for optimally designing the coefficients in the PI controller,acting as the adaption mechanism in the MRAS,small-signal model of the estimation system is developed.The obtained linearization model not only allows the stability to be verified further through Routh criterion,but also reveals the distribution of the characteristic roots,which leads to the clue to optimal PI gains.The theoretical analysis and the resultant design guidelines of the adaptation PI gains are verified through simulation and experiments.