Describing function analysis of reset systems

Sandwiched deadbands can be seen in a wide variety of systems, such as electro-hydraulic systems controlled by closed-center valves. In such a system, the deadband is between the plant and actuator dynamics and therefore can not be compensated directly like an input deadband. Though this sandwiched deadband problem may be attenuated to certain degree through sophisticated advanced control techniques, the increased cost and the necessity of actuator state feedback prohibit their widespread application in the industry. An economical and popular method is to add an inverse deadband function in the controller to cancel or compensate the highly nonlinear behavior of the deadband. However, such a solution requires that the dynamics before the deadband (eg. the valve dynamics) is fast enough to be neglected — a requirement that can not be met in reality unless the closed loop bandwidth of the overall system is limited very low. To raise the achievable closed loop bandwidth for a much improved control performance, it is essential to be able to precisely characterize the effect of this sandwiched deadband on the stability and performance of the overall closed-loop system, which is the main focus of the paper. Specifically, a describing function based nonlinear analysis will be conducted to predict when the instability will occur and how the resulting limit cycle depends on the actuator dynamics and the targeted closed-loop bandwidth. Based on the analysis, the optimal closed-loop bandwidth can be determined to maximize the achievable overall system performance. The technique is applied to an electro-hydraulic system controlled by closed-center valves to optimize the controller design.

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Modelling and performance of a pneumatic brake actuator

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406211430882 ◽

2011 ◽

Vol 226 (8) ◽

pp. 2077-2092 ◽

Cited By ~ 10

Author(s):

Jonathan I Miller ◽

David Cebon

Keyword(s):

Time Delays ◽

Function Analysis ◽

The Novel ◽

Performance Limits ◽

Heavy Vehicles ◽

Describing Function ◽

One Dimensional ◽

High Bandwidth ◽

And Performance ◽

Actuator Design

Heavy vehicles have sluggish pneumatic brake actuators that limit the control bandwidth of their anti-lock braking systems. In order to implement more effective braking controllers, it is proposed that high-bandwidth, binary-actuated valves are directly placed on the brake chambers. This article details investigations made into modelling and controlling heavy-vehicle pneumatic brake actuators with a view towards implementing the novel brake actuator design. One-dimensional flow theory is combined with simple thermodynamic arguments for polytropic systems to describe the charging and discharging of a brake chamber. Particular attention is paid to the simulation of perceptible vibrations caused by the piston’s motion at relatively low charging pressures, using a hysteresis model. The resulting equations are linearized and used to design a closed-loop pressure controller for the actuator. Finally, the non-linear performance limits of the valves, caused by dead-zones and time delays, are investigated using a describing function analysis.

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