Mathematical models of the pneumatic cascade and a mem-brane pneumatic actuator described by the fractional calculus

Abstract

The paper presents the analysis of dynamic properties of pneumatic systems such aa pneumatic cascade and a membrane pneumatic actuator using differential equations of integer orders and differential equations with derivatives of non-integer orders. The analyzed systems were described in the domain of time by means of step characteristics and in terms of frequency with the help of Bode characteristics, i.e. logarithmic amplitude and phase characteristics. Each characteristic was determined on the basis of a differential equation with derivatives of non-integer order. To determine the characteristics, an irreplaceable programming tool was the interactive Simulink package built on the basis of the MATLAB programme, which allows the analysis and synthesis of continuous dynamic systems.