Dynamic analysis of pneumatic actuators M. Sorli a,1 , L. Gastaldi a, * , E. Codina b , S. de las Heras b,2 a Dipartimento di Meccanica, Politecnico di Torino, c.so Duca degli Abruzzi 24, 10129 Torino, Italy b Departement de Mec  anica de Fluids, Universitat Polit  ecnica de Catalunya, c/Colon 7-11, 08222 Terrassa, Spain Received 28 October 1998; received in revised form 7 April 1999 Abstract The paper deals with the dynamic analysis of double acting actuators, both linear and ro- tary ones. Two dierent formulations to model a pneumatic circuit, composed of an actuator and a digital valve, are presented. In the ®rst one an air thermodynamic transformation is as- sumed and the simulation is carried out in the MATLAB-Simulink environment, while in the second one also the energy equation is introduced, so that the thermic exchange between the chambers and the external ambient is considered. Furthermore models of actuators, both lin- ear and rotary, using the bondgraph method are presented; the energy and continuity equa- tions are implement by using two C-®elds. Finally simulations results, obtained in the two dierent environments, are compared and discussed. Ó 1999 Elsevier Science B.V. All rights reserved. Keywords: Pneumatic actuator; Dynamic analysis; Bondgraph; Non-linear model www.elsevier.nl/locate/simpra Simulation Practice and Theory 7 (1999) 589±602 Notations A piston area b critical pressure ratio c v gas speci®c heat at constant volume c p gas speci®c heat at constant pressure C valve conductance C e external torque * Corresponding author. Fax: +39-011 564 69 99; e-mail: gastaldi@polito.it 1 Fax: +39-011 564 69 99; e-mail: sorli@polito.it 2 Fax: +34-93 7398101; e-mail: delasheras@mf.upc.es 0928-4869/99/$ - see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 8 - 4 8 6 9 ( 9 9 ) 0 0 0 1 2 - 9