Parallel Distributed Compensation Based Stabilization of A 3-DOF RC Helicopter: A Tensor Product Transformation Based Approach

This paper presents a control solution for the stabilization of the 3-DOF RC helicopter via the combination of the TP (Tensor Product) model transformation and the PDC (Parallel Distributed Compensation) control design framework. First we recall the nonlinear model of the RC helicopter and its simplified version, in order, to facilitate control design. Then we execute the TP model transformation on the simplified model to yield its TP model representation, that is a kind of polytopic model with specific characteristics, whereupon the PDC framework can immediately be applied. The control design considers practical control specifications such as: good speed of response and physical constrain on the control effort to avoid actuator saturations. We guarantee these specifications by LMI (Linear Matrix Inequality) conditions developed under the PDC frameworks. Further, we avoid the discrepancies, introduced via the simplification of the model, by applying LMI conditions specialized for robust control. By simultaneously solving these LMI conditions, we render a stabilizing nonlinear controller that achieves good speed of response with small control effort without actuator saturations. Simulation results are included to validate the control design. It will be pointed out that the resulting controller is equivalent with the controller successfully applied in the real control experiment of the helicopter presented in a recent paper. The main conclusion of this paper is, that the proposed design process is systematic, non-heuristic and straightforward, the stability proof of the resulting controller is tractable via the feasibility test of LMIs and, hence, exact. The whole design procedure is automatically computed via commercialized mathematical tools (MATLAB LMI Toolbox) without analytical interaction. The computational time is about minutes on a regular PC.