Incremental Nonlinear Dynamic Inversion Control for Hydraulic Hexapod Flight Simulator Motion Systems

Abstract

Hydraulic driven manipulators face serious control problems due to the nonlinear system dynamics and model and parametric uncertainties of hydraulic actuators. In this paper, a novel sensor-based Incremental Nonlinear Dynamic Inversion controller is applied to force tracking control of hydraulic actuators of a hexapod flight simulator motion system, which together with an outer-loop motion tracking controller forms a motion control system. Due to the use of feedback of pressure difference derivatives, the proposed technique is not dependent on accurate model and parameters, which makes the controller inherently robust to model uncertainties. Furthermore, The sensor-based control approach is particularly suitable for hydraulic force tracking in existence of an outer-loop controller decoupling hydraulic-mechanic interaction term from the inner-loop dynamics. Simulation results indicate that the novel approach yields better tracking performance and confirm the greater robustness to model and parametric uncertainties compared with a traditional nonlinear dynamic invention approach.

Stability Analysis for Incremental Nonlinear Dynamic Inversion Control

“…(10) or the term δ(ξ, ∆t) in Eq. (22) are often directly omitted in literature [9][10][11][12][13][14][15][16][17] by claiming that the ∆ξ related term is smaller than the ∆u related term when the sampling frequency is high, which is referred to as the time scale separation principle. This statement is not mathematically rigorous and is especially deficient for unstable nonlinear plants because the plant simplifications are made before designing the INDI control inputs.…”

“…The sampling frequency used by quad-rotor UAV is f s = 512 Hz [13,14]. For the applications on hydraulic systems, f s = 5000 Hz is desirable for controlling the hydraulic forces [16,17]. 2) Disturbance intensity: This can be seen from the expressions for Γ ξ , Γ η and definitions ofd,d ε , that stronger disturbances result into larger ultimate bounds.…”

“…Regarding the applications of INDI to aerospace system angular rate control problems, the sensing of angular accelerations is needed. The angular accelerometer is already available in market, and a commonly used alternative way to obtain the angular accelerations is by differentiating the filtered angular rate signals [10][11][12][13][14][15][16][17]. There have been legitimate concerns about the stability issue of this approach, and based on the above discussions, the system is able to sustain sufficiently small lags caused by filtering and actuator dynamics.…”

“…The concept of this method originated from the late nineties and was previously referred to as the Simplified NDI [7] and Modified NDI [8]. INDI control has been elaborately applied on various aerospace systems [9][10][11][12][13][14][15][16][17].…”

“…It is neither physically meaningful nor practical to separate the higher-order elastic dynamics into cascaded loops. In view of these reasons, the INDI control will be broadened into not necessarily relative-degree-one problems in this paper with consideration of the internal dynamics.The existing derivations of the INDI control law are based on the so-called time scale separation principle, which claims that when the sampling frequency is high, the controls can change significantly faster than the states [9][10][11][12][13][14][15][16][17]. The nonlinear plants are then simplified into linear incremental dynamic equations by omitting state variation related nonlinear terms and higher-order terms in their Taylor series expansion, based on which the incremental control inputs are designed.…”