# Notes on a New Structure of Active Noise Control Systems
## 4 Simulation Case Studies
### Case Study 3  
The models of the reference signal measurement, disturbance, and secondary paths used in the previous two simulation case studies had similar amplitude frequency responses but different phase  
Figure 13: Differences between expressed in dB estimates of the mean square values of signals at the error microphone in the classical FxLMS and new FeFxLMS control system structures—the mixed spectrum noise with different variances of Gaussian white noise. characteristics implied by the corresponding time delays in the signal processing paths. To verify the research results in the third simulation case study, the models of the reference signal measurement path, acoustical disturbance path, secondary path control signal part, and error signal measurement path identified in a laboratory room were applied. These models (impulse responses) in the form of the corresponding FIR filters were identified offline with the LS method using multisine excitations [35]. For the purpose of simulations, they were cut to the first 100 elements. The active noise control system was used to create a local zone of quiet in the 70 m\({}^{3}\) reverberant room in the laboratory configuration shown in Figures 2 and 14. The room was disturbed by noises generated from a primary noise source being a loudspeaker driven from a computer by a forming filter and amplifier. Near the primary noises source (0.4 m), a reference microphone was placed. The error microphone was placed 1.8 m from the primary noise source. The control loudspeaker was placed 2.3 m from the primary noise source, and 1 m from the error microphone. It was driven from the dSPACE DS1104 R&D Controller Board by a forming filter and amplifier The signal picked up by the error microphone was further amplified and processed by an antialiasing Butterworth 4 th order filter with a cut off frequency equal to 120 Hz and fed to the control algorithm implemented in the controller board. The loudspeakers were Arton Audio Klasyk 70L Subwoofers with Alcone Acoustic AC10 HE cones and as the reference and error microphones Beyerdynamic MM1 measurement microphones were employed. The chosen laboratory configuration implies that the total time delay introduced by the error signal measurement path, controller, and secondary path (22 ms) was longer than the time delay introduced by the disturbance path model (14 ms). Dynamical properties of the laboratory plant are summarized in Figure 15 in which amplitude frequency responses of the reference signal measurement path, acoustical disturbance path, secondary path control signal part, and error signal measurement path (represented by the atialiasing filter) are shown. In the first step, the rate of convergence of the discrete-time signal \(e_{0}(i)\) is compared in the discussed active noise control system structures in simulations run to attenuate a noise with a mixed spectrum. The mixed spectrum noise is a sum of three random sines and a discrete-time Gaussian white noise with a given variance. The sine components frequencies were equal to 33, 70, and 80 Hz, amplitudes were equal to 1 and phase shifts that were random, equally distributed in the range \([0,2\pi)\). Such a random process is the input of the reference signal measurement and acoustical disturbance paths. For a given variance of the Gaussian white noise, 1000 realizations of this random process were generated, each realization of 50,000 samples and the classical FxLMS and new F  
Figure 14: The laboratory configuration. simulated. Parameter \(\mu\) was equal to \(5\times 10^{-6}\). Each realization of the discrete-time signal \(e_{0}(i)\) was processed in the same way as in the previous simulation case study. Differences between them are expressed in dB estimates of the mean square values of the discrete-time signals \(e_{0}(i)\) in classical FxLMS and new FeFxLMS control system structures are presented in Figure 16 for the variance of Gaussian white noise equal to 0, 0.0001, 0.001, 0.01, 1, and 2.