This chapter introduced the novel dynamic inversion methodology. The first half of the chapter focused on exploring the effect of the additional dynamics, introduced by the novel dynamic inversion, on the closed loop system in an analytical manner. The aircraft equations of motion were simplified to include the longitudinal axis and one flexible mode. This simplification retained the crucial rigid/flexible mode dynamic interactions while making the problem mathematically tractable. The changes in dynamics attributed to the innovation in the inversion methodology have been traced for both linear and nonlinear systems. The modification alters the internal dynamics of the system and destroys the separation between internal dynamics and controlled dynamics that was present for the standard inversion case. However, when additional dynamics of W x( ) are present in one loop, the input-output dynamics reflect the modification in the altered loop and recover the standard integrator in the nominal one. This work has added to both analytical and physical insight regarding the nature of the novel dynamic inversion applied to an integrated flight/SMC control for a highly flexible aircraft.
The second half of the chapter focused on specific effects that the additional
dynamics associated with the novel dynamic inversion have on the response of the closed loop aircraft system. The additional dynamics have been analytically explored on
longitudinal and symmetric flexible dynamics of varying complexity. While the model used here is much simpler than the full model for which the controller introduced in next chapter was designed, the results are revealing nonetheless. This chapter provides some analytical basis and further insight into the workings of dynamic inversion methodology that has been modified to address the problem associated with these large, flexible aircraft.
There exists a large degree of freedom to control rigid body and flexible dynamics independently of one another in the novel dynamic inversion context. The apparent separation in controlling the short period and elastic mode dynamics through novel dynamic inversion is valuable when control of disturbances is as important as control of commanded variable. Specifically, the ability to alter the damping of elastic modes as
The increased complexity of system dynamics that included full longitudinal as well as multiple symmetric flexible mode dynamics showed that a certain degree of separation in controlling rigid body and flexible dynamics still exists. However, the introduction of parametric uncertainty into frequency and damping of the dominant flexible mode also showed the coupling between very low frequency rigid body and flexible dynamics. This coupling must be carefully considered during a controller design process since in the real world application there is always uncertainty present in the system.
Chapter 5 – Novel Dynamic Inversion Controller 5.1 Introduction
To provide an integrated flight/SMC controller for complex dynamics exemplified by the large, flexible transport aircraft whose model is described in detail in Chapter 3, the method of dynamic inversion is considered. Over the last decade, dynamic inversion methodology has gained considerable popularity in application to highly maneuverable fighter aircraft2, 3, 5 and might be of benefit to highly flexible aircraft. The attractiveness of this methodology lies in the fact that the inherent nonlinearities of the problem are explicitly considered. In other words, a nonlinear control law is designed that globally reduces the aircraft dynamics of interest into a set of integrators and thus, allows one linear controller to provide desired response throughout the flight envelope. This eliminates the need for extensive linearization of the aircraft model for different flight conditions, design of individual controllers for each of these conditions, and finally performing gain scheduling, which is typically an ad hoc and time consuming procedure, to link the individual controllers over the flight envelope.
The work presented in this chapter is a first step in determining whether dynamic inversion is a viable methodology to address the whole flight control problem of advanced flexible aircraft. The methodology is applied over a section of the flight envelope that includes the approach-to-land condition at the end of cruise, which makes for the worse case flight/flexible dynamics interaction. The problem is formulated to provide command following to pilot/autopilot inputs while minimizing elastic deflection at the pilot station. The aircraft has RCVs, all movable tail, and independently moving elevator. The controller is designed on a reduced longitudinal elastic model, which is open loop unstable, with 8 elastic modes considered, and then applied to the full
nonlinear longitudinal elastic model of 20 modes. As the first step, a standard dynamic inversion controller design was attempted, but failed to produce a stable closed loop system. This result is discussed in more detail in a later section. The results from the novel dynamic inversion controller, however, show substantially increased damping of the fuselage bending modes, which attenuates any excitation due to turbulence, and coordinated pitching of the entire vehicle thus minimizing the bending at the pilot station.
These results are compared to those of a controller designed for performance on a QSAE vehicle only, in order to provide a reference for low frequency flight performance as well as high frequency dynamic response.
As the vehicle models developed and matured, so has the dynamic inversion controller design. Initially, the vehicle did not have RCVs so the control had to be designed using the available surfaces. With development of RCV, the alternative control strategies did not have to be used; however, they produced some very interesting and useful results that are instructive for this class of vehicles. The results from these designs are described in detail in Appendix C.