A High Performance Pneumatic Force Actuator System: Part I—Nonlinear Mathematical Model

Model this paper, we developed a detailed mathematical model of dual action pneumatic actuators controlled with proportional spool valves. Effects of nonlinear flow through the valve, air compressibility in cylinder chambers, leakage between chambers, end of stroke inactive volume, and time delay and attenuation in the pneumatic lines were carefully considered. We performed system identification, numerical simulation, and model validation experiments for two types of air cylinders and different connecting tubes length. The mathematical model of the present article is used in a sequel article to develop high performance nonlinear pneumatic force controllers.@S0022-0434~00!00503-7# Modern force-reflecting teleoperation, haptic interfaces, and other applications in robotics require high performance force actuators, with high force output per unit weight. It is also important to have linear, fast and accurate response, as well as low friction and mechanical impedance. Traditional geared electrical motors cannot provide these characteristics. Few newly designed motors have special direct-drive actuators, with no intermediate mechanisms. Yet, applications such as teleoperation master arms with gravitational compensation, require long duration, static high force output. In these cases, direct drive electrical actuators necessitate special cooling systems to dissipate the excessive heat. We believe that pneumatic cylinders can offer a better alternative to electrical or hydraulic actuators for certain types of applications. Pneumatic actuators provide the previously enumerated qualities at low cost. They are also suitable for clean environments and safer and easier to work with. However, position and force control of these actuators in applications that require high bandwidth is somehow difficult. This is mainly due to compressibility of air and highly nonlinear flow through pneumatic system components. In addition, design and space considerations in many applications force the command valve to be positioned at relatively large distance from the pneumatic cylinder. Thus, the effects of time delay and attenuation caused by the connecting tubes becomes significant. These difficulties limited the early use of pneumatic actuators to simple applications that required only positioning at the two ends of the stroke. Subsequently, more complete mathematical models for the thermodynamic and flow equations in the charging-discharging processes were developed ~Shearer @1#!. As a result, more complex position controllers, based on the linearization around the mid stroke position were developed ~Burrows @2#, Liu and Bobrow @3#!. These simplified models provided only modest performance improvements. During the last decade, nonlinear control techniques were implemented using digital computers. Bobrow and Jabbari @4# and McDonell and Bobrow @5# used adaptive control for force actuation and trajectory tracking, applied to an air powered robot. Improved results were presented, but they were confined mainly for low frequencies ~approx. 1 Hz!. Sliding mode position controllers were also tested ~Arun et al. @6#, Tang and Walker @7#!, again with improved results at low frequencies. As a general characteristic, the mathematical models used in these controllers assumed no piston seals friction, linear flow through the valve, and neglected the valve dynamics. Ben-Dov and Salcudean @8# developed a forced-controlled pneumatic actuator that provided a force with an amplitude o f2Na t 16 Hz.Their model included the valve dynamics and the nonlinear characteristics of the compressible flow through the valve. A comparison between linear and nonlinear controllers applied to a rotary pneumatic actuator is presented by Richard and Scavarda @9#. The mathematical model accounted for the leakage between actuator’s chambers and the nonlinear variation of the valve effective area with the applied voltage. Their model depends heavily on curve fitting using experimental values, making it difficult to apply to even slightly different systems. The goal of this article is to provide an accurate model of a pneumatic actuator system controlled by a proportional spool valve. This model is targeted to develop force controllers that perform at significantly more demanding operating conditions. For this purpose, the model takes into consideration the friction in the piston seals, the difference in active areas of the piston due to the rod, inactive volume at the ends of the piston stroke, leakage between chambers, valve dynamics and flow nonlinearities through the valve orifice, and time delay and flow amplitude attenuation in valve-cylinder connecting tubes. Since the ultimate purpose of the modeling effort is for control applications, the proposed equations should be suitable for on-line implementation. We designed special experiments in order to identify the unknown characteristics of the pneumatic system, such as: valve discharge coefficient, valve spool viscous friction coefficient, and piston friction forces. The model was finally tested using two experiments that allowed the measurement of the actuator force output and piston displacement. The experimental results were compared with the results obtained by numerical simulation.