Parametric model of servo-hydraulic actuator coupled with a nonlinear system: Experimental validation

A Self‐tuning Robust Control System for nonlinear real‐time hybrid simulation

“…13 To model the dynamics of a typical hydraulic transfer system, the fluid flow rate is often linearized about the origin. In this model by Dyke et al 2 and Maghareh et al, 11,12 the interaction between the hydraulic actuator and the physical specimen is captured as shown in Figure 3, where s ∈ C denotes the Laplace variable. The equations describing the fluid flow rate q in an actuator can be linearized about the origin to obtain the following equations: where F a , , V, A a , K q , i, K c , x, and x 1 indicate actuator force, bulk modulus of the fluid, half the volume of the actuator, piston area, valve flow gain, valve input, leakage coefficient, and actuator displacement and velocity, respectively.…”

“…The equations describing the fluid flow rate q in an actuator can be linearized about the origin to obtain the following equations: where F a , , V, A a , K q , i, K c , x, and x 1 indicate actuator force, bulk modulus of the fluid, half the volume of the actuator, piston area, valve flow gain, valve input, leakage coefficient, and actuator displacement and velocity, respectively. 2,4,[11][12][13][14][15] By combining Equations (1) and (2), and solving for . F a , the following expression is obtained:…”

“…In a previous study and based on Equations (1) to (5), a physics-based nonlinear model for a servo-hydraulic actuator coupled with a nonlinear physical specimen was developed, validated, and transformed into a controllable canonical form. 11,12 This controllable canonical model captures the nonlinear dynamics in Figure 3. In this dynamical model, the physical specimen-here, physical substructure-is described with a general mathematical form of…”

“…11 Hereafter, x n indicates the nth derivative of actuator displacement with respect to time, and nonlinear function h is a continuous, twice-differentiable function. Maghareh et al 11,12 showed that the block diagram provided in Figure 3 can be mathematically described as…”

A simplified model of a fueldraulic actuation system with application to load estimation

“…In summary, the dynamics of the VSV actuation system in the Trent 1000 RSS is described by a nonlinear dynamical system (equations (1)-(12)) with three states (velocityẋ VSVA , head-end pressure P H and rod-end pressure P R ), one input (the control input TMC) and three exogenous variables (high-pressure H p and low-pressure Lp, entering in (6) and 7, and the actuator's loading F L in (1)). Note that the nonlinearity of the system is due to the flow equations (6-10).…”