In this chapter, the flow inside a novel high-speed rotary on/off valve has been analyzed using CFD. CFD validated and aided the development of analytical equations which predict the valve pressure drop and the valve turbine torque as a function of geomet- rical design parameters. The analytical equations can be further utilized in the valve parameter optimization. Compared with the current prototype valve, the optimized valve can reduce the fully open loss by 62.5%. An improved optimized design of the inlet pressure rail with nozzles was established via CFD. The fluid volume inside the valve inlet pressure rail and the nozzles was reduced by 66%, while the pressure drop was only slightly larger (6.7%). The analysis can be extended to the design of any high-speed digital valves, where compressible loss counts for a large portion of the valve operational losses, and the balancing between compressible loss and throttling loss is important. The approach of developing a semi-empirical formula to predict the pressure drop for the center PWM section of the valve spool can also be extended to the analysis of similar valves in developing a reduced order model to predict the valve pressure drop analytically.
Chapter 3
Event based Kalman filter for
valve spool rotary states
estimation
3.1
Introduction
In this chapter, the valve spool angular states (angular position and velocity) sensing and estimation problem will be addressed. The self-spinning feature of the rotary valve prefers non-contact sensing to measure the valve spool rotary position. Non-contact sensors can simplify the valve sealing structure, and they can avoid the interference between the sensor and the valve spool motion (in both rotary and axial directions). The valve spool angular position is measured using a non-contact optical sensor, which consists of a laser module, a photodiode and a rotary encoder, as shown in Fig. 3.1. The light emitted from the laser is reflected from a code wheel attached to the spool end. The photodiode outputs a high-low alternating signal, depending on whether the laser light is reflected off of a black or reflective (metal) sector on the code wheel. Changes in the photodiode response are used to sense the spool angular position. Due to the small spool diameter (25.4mm) and the relatively large laser beam spot size (5mm in diameter), the encoder resolution is relatively poor (8 sectors per revolution). Improving the quality of the laser source can permit the usage of a high resolution code
wheel, therefore improving the sensing resolution. However, it is expensive to realize this improvement.
Photodiode
Laser
module
Code wheel
Figure 3.1: PWM valve rotary sensing mechanism
Two approaches have been frequently used to estimate the angular velocity from encoder measurements, depending on whether the angular velocity is high or low: finite difference method [80] and inverse-time method [81][82]. If the angular velocity is high, the finite difference method is preferred, where the angular velocity is calculated by counting the number of pulses within a fixed time interval, converting the counts to angle, and dividing the angle by the time interval. If the angular velocity is low, the inverse-time method is preferred, where the angular velocity is calculated by dividing the sector angle by the time between successive pulses.
If the sampling frequency is relatively slow, and the encoder resolution is low, the measurement of pulses will be obtained at irregular time instants. Both approaches will produce noisy estimations of the angular states. The performance of both finite difference estimators and inverse-time estimators can be improved by adding additional low pass filters to either pre-process the position signal (integration of the encoder), or to further filter the estimated velocity. Depending on the assumption of the noise model that is corrupting the position measurement, optimal estimators can be achieved
to estimate the velocity from the position measurement. Glad and Ljung [83] presented a Kalman filter to estimate the angular velocity, and the measurements of the angular positions are obtained at irregular time instants. The measurement, as presented in [83], can be obtained from light response changes when holes on a disc mounted on the axis pass through light source. The uncertainty of the occurrence time was converted to measurement noise, and a linear time-invariant (LTI) system with a zero mean measure- ment noise is derived. The corresponding estimator design can follow a typical Kalman filter design procedure. Simulation results show that the Kalman filter approach is superior to both the finite difference method and the inverse-time method.
In our problem, because the encoder resolution is very low, it is beneficial to also estimate the angular position and velocity between transitions of the encoder counts. Since the measurement of black-white transition events can occur at irregular times, we propose an event based Kalman filter observer for this purpose. When the sampling intervals are large, the uncertainty in when the transition occurs becomes more uncer- tain. The transition events are subject to uncertainty due to finite sampling interval, the fact that the optical signal changes gradually and the threshold for distinguishing a white or black sector is uncertain. Continuous time, time-varying Kalman filter theory is adopted to accommodate the uncertain event based measurements. The resulting al- gorithm is such that between events, the Kalman filter operates in an open loop manner; when a transition is detected, both the Kalman filter gain and the state estimate are updated discretely. Compared with Glad and Ljung’s work in [83], our work provides the additional data estimation in between the sampling times.
In the next section, the rotary sensing working principle will be introduced. In section 3.3, the two sources of noise which corrupt the encoder measurement on event detection time will be described. The system modeling will be presented, focusing on formulating the time uncertainty to a measurement noise on position. This formulation is important to derive an LTI system model. The proposed event based Kalman filter will be introduced in section 3.4 to estimate the states of the LTI system. Finally, the simulation validation and the experimental validation of the event based Kalman filter will be presented in section 3.5 and section 3.6.