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This study presents a novel framework, namely, the fusion of a conventional controller and a linear model predictive controller, for the position control of a tilt-rotor tricopter. While the conventional controller in the outer loop is responsible for the position control, the inner-loop model predictive control-based controller handles the angular dynamics and vertical body velocity. Furthermore, a novel control allocation algorithm for the proposed controller is introduced. In addition, this study also covers mathematical modeling and trim analysis of the tilt-rotor tricopter dynam-ics. An evaluation of the designed control system is accomplished with a nonlinear 6-degree-of-freedom simulation model of the tilt-rotor tricopter in which realistic actuator limitations are considered. The efficiency of the proposed control algorithm is elaborated for a trajectory tracking problem where basic surveillance operation is considered. The simulation results show that the proposed model predictive controller is able to provide a satisfactory trajectory tracking performance under the realistic actuator limits.

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Feedback control of linear time-varying systems arises in numerous applications. In this paper we numerically investigate and compare the performance of two heuristic techniques. The first technique is the frozen-time Riccati equation, which is analogous to the state-dependent Riccati equation, where the instantaneous dynamics matrix is used within an algebraic Riccati equation solved at each time step. The second technique is the forward-propagating Riccati equation, which solves the differential algebraic Riccati equation forward in time rather than backward in time as in optimal control. Both techniques are heuristic and suboptimal in the sense that neither stability nor optimal performance is guaranteed. To assess the performance of these methods, we construct Pareto efficiency curves that illustrate the state and control cost tradeoffs. Three examples involving periodically time-varying dynamics are considered, including a second-order exponentially unstable Mathieu equation, a fourth-order rotating disk with rigid body unstable modes, and a 10th-order parametrically forced beam with exponentially unstable dynamics. The first two examples assume full-state feedback, while the last example uses a scalar displacement measurement with state estimation performed by a dual Riccati technique.

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