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Nonlinear $$L_{2}$$ control of a laboratory helicopter with variable speed rotors. (English) Zbl 1114.93024
Summary: This paper considers the problem of a nonlinear $$L_{2}$$-disturbance rejection design for a laboratory twin-rotor system. Since the rotor blades present fixed angle of attack, control is achieved by using the rotor speeds as control variables. This mechanical device features highly nonlinear strongly coupled dynamics. The control is developed considering a reduced order model of the rotors obtained by application of a time-scale separation principle, including integral terms on the tracking error to cope with persistent disturbances. An explicit suboptimal solution to the associated partial differential (HJBI) equation is applied. This yields global asymptotical stability for the reduced system. The controller exhibits the structure of a partial feedback linearization with an external nonlinear PID. The paper proposes systematic tuning procedure allowing independent weights for each degree of freedom. The methodology has been tested by experimental results using a laboratory helicopter.

##### MSC:
 93B11 System structure simplification 93B20 Minimal systems representations 93D20 Asymptotic stability in control theory 93C95 Application models in control theory 93C15 Control/observation systems governed by ordinary differential equations 34H05 Control problems involving ordinary differential equations 93C10 Nonlinear systems in control theory
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