A Method for the Frequency Domain Design of Pwm-controlled Pneumatic Systems

This paper presents a rigorous analysis and design method for PWM-based control of pneumatic systems. An equivalent analytical model incorporating the effects of a finite PWM switching period is formulated. This equivalent model was motivated by a lack of control design and analysis techniques needed to treat the inherently non-analytical switching models associated with PWM-based systems. The equivalent model enables the design of a loop compensator that rigorously addresses control design issues of stability robustness, disturbance rejection, insensitivity to sensor noise, performance bandwidth and actuator saturation. Simulation of this compensator with both the equivalent design model and a full nonlinear switching model for a particular pneumatic robot application is presented which demonstrates and validates the proposed method. INTRODUCTION Pneumatic actuators can offer significantly higher massspecific power densities than can DC motors, especially given the fact that a pneumatic actuator can be appropriately loadmatched for most robotic applications without the use of a mechanical transmission (e.g., they do not require a gearhead). Unlike hydraulic actuation systems, pneumatic systems do not require a return path for the working fluid, and therefore the actuation system can be simpler, lighter, and more compact than hydraulic counterparts. Unlike DC motors, the control of pneumatic systems is more complex and more difficult, due in part to the fact that the fluid transmission is typified by fluid mechanics that are nonlinear and generally difficult to characterize accurately, and in part to the fact that the supply and control components (i.e., servovalves) are not as readily available or well-packaged as their electrical counterparts. Control of pneumatic systems is generally implemented via the proportional control of servovalves, in which pneumatic fluid flow is generally proportionally constricted (i.e., throttled) by electrically-controlled valves. This proportional control approach has been studied by several researchers, including Shearer [1], Liu and Bobrow [2], Kunt and Singh [3], Ye et al. [4], and Bobrow and McDonell [5]. The control of such systems is complicated by the need to accurately describe the flow characteristics of a proportional servovalve, which is typically accomplished empirically with a set of pressure/flow relationships. Like a linear servoamplifier for DC motors, the servovalve control approach for pneumatic systems controls the power delivered to the actuator by power dissipation. Such an approach is particularly undesirable in systems for which efficiency is paramount. Pulse-width modulated (PWM) control offers an alternative to the servovalve control approach that both circumvents the accurate dynamic characterization of throttling a fluid flow, and more significantly, offers appreciably higher control efficiency. The primary problem with the control of PWM pneumatic systems is that the introduction of switching results in a non-analytic system model, and thus excludes the direct application of welldeveloped analytic control approaches. This paper provides a method to transform the non-analytic, nonlinear description of PWM-based control of a pneumatic system into an analytic, linear model, which in turn enables the application of frequency domain methods to address issues of performance and stability robustness. PWM-BASED CONTROL In a continuously-controlled pneumatic system, the power delivered to an actuator is metered by varying flow resistance continuously through a proportional valve. As a result, the