State-variable control of a loudspeaker system using digital signal processing
Griesbach, Linden M.
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A loudspeaker system in which velocity feedback is used to control the frequency response is designed and tested. The control is based on state-variable feedback with loudspeaker velocity and force acting on the loudspeaker compliance being the two state variables of interest. Loudspeaker velocity is sensed via a voice-coil sensor which is developed as part of this project. Since only the loudspeaker velocity is sensed, a statevariable estimator (or observer) is used to derive the other state variable. The control system is implemented via a digital signal processor (DSP). The first step in the development of this system is the derivation of an electrical circuit that models the electrical, mechanical, and acoustic behavior of the loudspeaker system. Based on this model, state equations and transfer functions are derived. Actual parameters for the loudspeaker are then determined from the manufacturer's published data and by experimentation. Once the system parameters are known, well-known methods are used to determine the feedback gains required to achieve the desired performance. In this case, it is arbitrarily decided to lower the natural frequency and increase the damping compared to the openloop system. These same methods are also used to determine the estimator gains. The entire system including the loudspeaker, state-variable feedback, and estimator are digitally simulated to verify the design values. Finally, DSP software is written and the system is tested. Results show that the desired response is to within 1.53 dB.