Identification of viscous friction coefficients for a pneumatic system model using optimization methods

Pneumatic actuators are often used in industrial automation for reasons related to their good power/weight ratio, easy maintenance and assembly operations, clean operating conditions and low cost. This set of advantages, is, however, made up for by the difficulties met during the design. Indeed, the presence of the air along with its natural compressibility introduces further complexities to those already existing: friction forces, losses and time delays in the cylinder and transmission lines. In particular friction is very difficult to estimate using specially designed experiments [E. Richer, Y. Urmuzlu, A high performance pneumatic force actuator system part 1-nonlinear mathematical model, ASME J. Dyn. Syst. Meas. Control 122 (3) (2000) 416-425], and equivalent parameters are used in modelling pneumatic systems [K. Hamiti, A. Voda-Besancon, H. Roux-Buisson, Position control of a pneumatic actuator under the influence of stiction, Control Eng. Pract. 4 (8) (1996) 1079-1088]. It is commonly described [K. Hamiti, A. Voda-Besancon, H. Roux-Buisson, Position control of a pneumatic actuator under the influence of stiction, Control Eng. Pract. 4 (8) (1996) 1079-1088] as linear viscous damping, coulomb friction, stiction [D. Karnopp, Computer simulation of stick-slip friction in mechanical dynamic system, J. Dyn. Syst. Meas. Control, 107 (1986) 100-103] or some combination of these. In linear control theory, it is assumed that the friction is linear viscous. Unfortunately attempts to ignore significant coulomb friction or stiction may lead to erroneous predictions of a system's behaviour [K. Hamiti, A. Voda-Besancon, H. Roux-Buisson, Position control of a pneumatic actuator under the influence of stiction, Control Eng. Pract. 4 (8) (1996) 1079-1088]. As a result, the analytical models, describing the dynamics of the pneumatic system, are not only non-linear but several tuning parameters can also be involved. In this paper a complete mathematical model [D. Ben-Dov, S.E. Salcudan, A force controlled pneumatic actuator, J. Dyn. Syst. Meas. Control 113 (1991) 267-272; D. Karnopp, Computer simulation of stick-slip friction in mechanical dynamic system, J. Dyn. Syst. Meas. Control, 107 (1986) 100-103; A. Messina, N.I. Giannoccaro, A. Gentile, Experimenting and modelling PWM-based pneumatic actuators, Mechatronics 15 (7) (2005) 859-881; E. Richer, Y. Urmuzlu, A high performance pneumatic force actuator system part 1-nonlinear mathematical model, ASME J. Dyn. Syst. Meas. Control 122 (3) (2000) 416-425] of a pneumatic actuator driven by two on/off two ways valves (with Pulse Width Modulation technique) is validated by tuning a number of geometric and functional characteristics and parameters by means of non-linear optimization algorithms. The experimental data were obtained driving the on/off valves with five different duty cycles: 10, 25, 50, 75 and 90% over a period of 20ms and measuring the actuator position with a potentiometer. In particular experimental apparatus [J.L. Shearer, Study of pneumatic processes in the continuous control of motion with compressed air-I, Trans. ASME 78 (2) (1956) 233-249] was realised in order to measure valve coefficients in all operative conditions. The viscous coefficients of the system are identified using non-linear optimization methods that consider, for each iteration, the differential equations' system of the model.