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Unformatted text preview: Application of predictive control to a toy helicopter Jonas Balderud and David I. Wilson Department of Electrical Engineering Karlstad University, Sweden [email protected] Keywords: Matlab/Simulink, optimal control, heli- copter, MPC Abstract A toy helicopter makes for an impressive classroom control demonstration. However the challenge to ob- tain a robust, stable, multivariable controller is non- trivial given the nonlinear nature of the helicopter, the stochastic nature of the disturbances, and the perfor- mance limitations of PCs. This paper applies a model predictive controller using the Mathworks xPC tar- get to obtain significantly improved results over that achievable using classical control algorithms. 1 Predictive control in an education context In 1997, Karlstad University purchased, at not incon- siderable expense, a toy helicopter with two degrees of freedom and with three inputs as shown in Fig. 1. The intention was to use this bench-scale model in our au- tomatic control education to supplement our existing collection of laboratory equipment. Our wish was for a multi-input/multi-output (possibly non-square) inter- acting laboratory plant that exhibited both stable and unstable modes, possessing time constants in the or- der of seconds, and most importantly, to be visually arresting. This latter feature in particular is due to the simple fact that the helicopter is practically un- controllable under manual operation. The helicopter from Humusoft 1 satisfied most of these demands and we demonstrated it successfully in introductory control courses and during university open days. However some debilitating drawbacks for this labora- tory plant quickly became apparent such as severe stic- tion nonlinearities, and the difficulty in developing a white, or even grey-box model of the plant. These drawbacks are such that apart from the initial demon- stration, we found that we could not use the helicopter productively until late in our advanced control course. This is, of course, poor utilisation of an expensive re- 1 www.humusoft.cz Figure 1: The bench-scale 2DOF helicopter from Humu- soft. source. Some of these issues are independent of the helicopter and are further discussed in . The helicopter challenged us in the Mat- lab/Simulink environment using a modest 266MHz computer. While the Real-time Toolbox (also from Humusoft) performed adequately at modest sampling rates (0.1s and upwards), this was inadequate for the helicopter. The remainder of the paper is as follows. Section 2 reviews state-space model predictive control with con- straints and section 3 outlines the model development and identification of key parameters and the rational behind the implementation of MPC on a PC running a dedicated real-time operating system. Section 4 shows the performance of the MPC control scheme and sec- tion 5 finishes with some conclusions....
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This note was uploaded on 05/25/2011 for the course ECON 103 taught by Professor Poul during the Spring '11 term at American University of Central Asia.
- Spring '11