Engine operation in the TPE-331 is maintained by the fuel control unit (FCU). In flight, the FCU's primary component, the fuel metering valve, is set by the pilot, using the power lever. During ground operation, the fuel metering valve is controlled by the underspeed governor (one of two governors which direct the function of the engine).
The TPE-331 uses two guiding control systems throughout it's operating range, depending on it's function at any given time. The minimum speed of the engine is set using an underspeed governor. This is a fuel metering valve which has direct control of the engine in beta and reverse, and protects from RPM decay beyond the minimum setting established by the operator in normal flight. The underspeed governor works much like a propeller governor, using spinning flyweights, a pilot valve under spring tension from the cockpit "condition lever" or "speed lever" (depending on the installation). The operator uses the condition leer to set the minimum engine speed in a similiar way that one sets the propeller governor with a propeller control...except that in the case of the TPE-331, it's the minimum engine fuel flow limit that's being set, as a function of RPM.
On the ground, the underspped governor will cause the TPE-331 to operate at 70% RPM at the LO RPM setting of the condition or speed lever. The HI RPM setting will cause the engine to operate at 97% (approx). During beta operation, which includes any engine operation with the propellers aft of the low pitch stops, the underspeed governor will maintain engine RPM and the pilot directly controls propeller blade angle by moving the power lever into the beta/reverse range. The farther the pilot retards the power lever into the reverse range, the greater the propeller blade angle in the reverse range, and the more fuel required of the FCU via the underspeed governor, to prevent the engine from decaying below it's minimum RPM.
In flight, the pilot controls the FCU fuel metering valve, and the propeller controls the engine speed. In beta and reverse operations, the pilot controls the propeller, and the FCU/fuel metering valve controls the engine. This is the fundamental difference between forward thrust or idle, and beta/reverse in the TPE=331.
Throughout the full range of operation, the various components of the engine "talk" to each other through feedback rods, valves, and preset limits in the engine, fuel controller, and propeller governor, as well as the underspeed and overspeed governors. The exact relationship of these components is variable according to the way in which a particular operator desires the engine to be set up. For example, one operator may establish the rigging such that at idle the engine is operating with substantial drag in flight, whereas another may have the engine operating with residual thrust at idle: both can be within the manufacturer's parameters.
The condition levers serve several functions. The chief function is to set the underspeed governor. These are comparable to setting high idle or low idle on the PT6A. In a two-lever airplane, however, the condition lever also serves the function of a propeller RPM control. It sets the operating RPM (within the 96% to 100% narrow operating range), and also sets the underspeed governor. The overspeed governor is independent, and always stays the same. (actual values vary depending on the unit, and whether it's a bendix or woodward governor or FCU).
I understand your question regards the specific relationship between the FCU and governor in the reverse range, but the function depends on which one is installed on that particular engine. With a woodward governor, for example, RPM increases as the power lever is advanced (or reversed), but with a bendix governor the RPM is maintained constant. The function and relationship depends on which components are installed on your specific airplane, and how they're rigged.
The condition lever thus sets the underspeed governor and the operating RPM just like a propeller lever on a piston airplane or on some PT6A installations. It also serves as the cutoff lever, and emergency feathering lever. To feather the propeller and fuel-chop the engine at the same time, the condition lever is retarded all the way to the rear stops.
It’s important to note that this function is specific to 2-lever installations. Some TPE-331’s use a power lever, propeller lever, and speed lever...just like many PT6A installations use three levers. Some PT6A installations just use two, however...and so also the TPE-331. Regardless of whether two or three levers are used, the engine function is the same; it's simply the cockpit controls in basic layout which vary.
Where three levers are used, a power lever, a propeller lever, and a speed lever, the speed function independently controls the underspeed governor, and the propeller lever controls the prop, except when in reverse...when the pilot turns control over the engine to the underspeed governor, and controls the propeller directly through the power lever (n the beta/reverse range. While this occurs, when the pilot is scheduling propeller blade angle in beta/reverse, the underspeed governor steps up speed to a predetermined setting in order to prevent RPM decay. To a minimal point, RPM is allowed to increase to a maximum value; this helps prevent a compressor stall and/or overtemperature.
[FONT="]Mechanically, the TPE-331 is one of the most complex aircraft engines built. From a pilot perspective it's operation is simple. From a mechanic's point of view, it's not.
[/FONT]
[FONT="]
[/FONT]