Mathematical models of a pneumatic cascade and pneumatic membrane actuator described with a fractional calculus

The paper presents the analysis of dynamic properties of pneumatic systems such as: cascade connection of membrane pressure transmitters and a pneumatic membrane actuator by means of differential equations of integer and non-integer order. The analyzed systems were described from the time perspective by means of step response, and in terms of frequency with the help of the Bode plot, i.e. logarithmic magnitude and phase responses. Each response was determined using differential equations of non-integer order. To determine the responses, the interactive Simulink package was an irreplaceable programming tool built on the basis of the MATLAB program, which enables the analysis and synthesis of continuous dynamic systems.