Actuator Models

A typical actuator comprises electric, hydraulic, and mechanical elements. A comprehensive mathematical model of an actuator is required for the design of flight-control laws and nonlinear flight simulation. For control-law design, a small – amplitude linear model is sufficient. The large-amplitude behavior is also very important for nonlinear simulation. This behavior is characterized by a first-order system dynamics with limits of position, rate, and accelerations of the actuator (and the control surfaces). The typical actuator model constants for a transport aircraft are given in Table 6.1 [9].

The actuators used on aircraft are of two types: direct drive valve (DDV) and electro-hydraulic servo-valve (EHSV) [10]. DDV is designed to produce a large force to overcome forces due to flow, stiction, and acceleration or vibration, and the force motor is directly attached to and positions a spool valve (the force motor directly couples to the main control valve). A position feedback from the spool position to the input voltage is present. In the EHSV the first stage of a hydraulic preamplifier multiplies the force output of the torque motor to a sufficient level for overcoming the opposing forces. A direct position feedback through a flapper and nozzle arrangement is obtained in EHSV. The actuator consists of an electric force motor driving a main control valve, which in turn drives the main ram piston against the load. This is achieved by the flow of hydraulic fluid across it. The actuators themselves have two position feedback loops. DDV and EHSV can be modeled as a first-order transfer function (TF):

x_ K /T e _ s + 1/T

Here, x is the valve position and e is the input voltage to the valve. If necessary a second-order model can be used. The model of the valve flow can be obtained as described here. The load flow can be expressed as a function of the valve position

TABLE 6.1 Control Surface Actuator Model Parameters Elevator Aileron Rudder DC gain 0.89 0.73 0.795 Time constant (s) 0.06 0.07 0.07 Position limits (0) -19 to 16 —21 to 21 — 30 to 30 Rate limits (0/s) —30 to 30 —79 to 79 —50 to 50

and the load pressure, neglecting the return pressure and for a constant supply pressure:

Q = f (x, P)

The expression in terms of small changes can be obtained as

df df

DQ=Dx+@PDP (6-5)

since f is essentially a function of Q variable

@Q @Q

DQ = – Q Dx + @Q DP (6.6)

Next, we define the sensitivities as Kx = @Q as the flow gain and Kp = as the flow

pressure coefficient to obtain

DQ = KxDx + Kp DP (6.7)

We can also define the pressure sensitivity as Kpx = @Q = K- Kx = K, and insert­

ing this into linearized expression we obtain

Kx

DQ = KxDx + KL dp (6.8)

Kpx

DQ = Kx ^ Dx + ^ (6.9)

Finally, in the form of perturbation variables (using the same symbols) for small amplitude variation, we get

Q = Kx[x + K^) (6.10)

The main rotor ram assembly model can be found in Refs. [10,11]. The hydraulic subsystems are hydraulic pumps, accumulators, and hydraulic lines. The pump can be modeled as first-order lag dynamics. The lines’ dynamics can be approximated as lumped parameter coefficient.