The article considers the step and impulse response of second-order linear systems with a positive zero. A particular parameterization of the system equations is proposed which enables good assessment of the influence of its parameters on transients. Expressions missing in the literature are derived for step response parameters such as the values of undershoot, overshoot, time of inverse response, rise time and settling time, as well as of impulse response. Based on them, a precise time-domain approach to design feedforward, feedback and mixed feedback– feedforward control structures for nonminimum phase objects is presented that considers both setpoint tracking and disturbance rejection.

There are many industrial environments which are exposed to a high-level noise. It is necessary to protect people from the noise. Most of the time, the consumer requires a miniature version of a noise canceller to satisfy the internal working place requirements. Very important thing is to select the most appropriate personal hearing protection device, for example an earplug. It should guarantee high passive noise attenuation and allow for secondary sound generation in case of active control. In many cases the noise is nonstationary. For instance, some of the noisy devices are switched on and off, speed of some rotors or fans changes, etc. To avoid any severe transient acoustic effects due to potential convergence problems of adaptive systems, a fixed-parameter approach to control is appreciated. If the noise were stationary, it would be possible to design an optimal control filter minimising variance of the signal being the effect of the acoustic noise and the secondary sound interference. Because of noise nonstationarity for most applications, the idea of generalised disturbance defined by a frequency window of different types has been developed by the authors and announced in previous publications. The aim of this paper is to apply such an approach to different earplugs and verify its noise reduction properties. Simulation experiments are conducted based on real world measurements performed using the G. R. A. S. artificial head equipped with an artificial mechanical ear, and the noise recorded in a power plant.