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.
Describing Function Analysis of Mechanical Systems with Nonlinear Friction and Backlash Phenomena