Generalized Predictive Control: ARIX vs. ARIMAX-Based Designs for a Floating Spacecraft Emulator Using a Quadcopter

In this work, the Generalized Predictive Control (GPC) is revisited in order to assess a novel design procedure that avoids the Diophantine equations to simplify the GPC design in the colored noise case. The proposed method is investigated in a simulated case study of a double-integrator system to emulate a floating spacecraft simulator in a ludic and motivational form. Such emulation is proposed by combining a network-controlled quadcopter and a set of computer-based control algorithms to impose the double-integrator dynamics being representative of the behavior of the aerial system. The GPC design based on auto-regressive integrated moving average with exogenous inputs (ARIMAX) is compared to the more common ARIX-based design, assuming the presence of colored noise disturbances. These designs were also compared to the Linear Quadratic Gaussian method to establish a baseline result with a well-known control technology. The ARIMAX models obtained for the quadcopter were estimated using least-squares methods based on registered flight data. The amplitude spectrum of the estimated colored noise disturbances was analyzed to justify the feasibility of the study between the considered GPC designs. The main finding of this study was that no enhancement could be observed in the ARIMAX-based GPC that could justify the increased complexity of modeling the plant and designing the controller for the colored noise case.