Linear quadratic optimal control of a high-performance loudspeaker

Due to the nonlinearity of loudspeaker systems, the sound produced by these systems is riddled with harmonic and intermodulation distortions. To control/reduce these distortions, this paper proposes the use of two Linear Quadratic Optimal Control techniques - the Linear Quadratic Regulator (LQR) and the Linear Quadratic Gaussian (LQG) controller that combines the Linear Quadratic Regulator (LQR) controller with the Kalman filter. The LQR controller is used for computing the control signals of the loudspeaker system, while the Kalman filter acts as an estimator. Firstly, the state space model of the system and the mathematical model of the control strategies are derived. The control strategies are then tested under various conditions using MATLAB/Simulink. The results obtained show the competence of the proposed control strategies in maintaining the system’s stability while reducing the harmonic distortions produced by loudspeaker systems.