This chapter presents a brief overview of the general equations of unsteady motion for an aircraft. It then proceeded to development of coupled quasi-steady/dynamic
validly represented as quasi-static states. Continuing this development the dynamics associated with the specific vehicle under study are presented and discussed in detail at a flight condition that makes the flexible mode interaction with the rigid flight dynamics most pronounced. The specific dynamics description prepares the background and highlights some issues that arise in controller design for the HSCT vehicle under study that is presented in Chapter 5.
Chapter 4 – Introduction to Novel Dynamic Inversion 4.1 Introduction
An innovation has been added to the standard methodology of dynamic inversion in the manner described in this work to accommodate the highly flexible nature of the advanced aircraft and fulfill the dual objectives of integrated flight/SMC control. The novel approach to the nonlinear dynamic inversion allows the methodology to more intelligently handle flexible dynamics (or any dynamics with pole-zero pairs very close to the jω-axis). In the standard dynamic inversion, the controlled variable’s dynamics are cancelled by the controller, which may or may not be an appropriate approach. This new approach to standard dynamic inversion still maintains control of CVs while the
innovation allows a change to the dynamics of the controlled variable without cancellation of its dynamics. This is accomplished by introducing dynamics into the inversion loop itself. What this novel approach enables is altering flexible mode damping without cancellation, thus improving disturbance response and avoiding the potentially destabilizing effect of pole cancellation close to the jω-axis in case of modeling
uncertainty.
This chapter introduces the novel dynamic inversion and explores the effects on the closed loop dynamics the innovation has both analytically and numerically. In order to make the problem mathematically tractable and to gain better understanding of dynamic interactions in a closed loop system under novel dynamic inversion, the aircraft model has been simplified from the very complicated one described in Chapter 3 while retaining the essential characteristics. These essential characteristics are the interaction of flexible modes on rigid body dynamics and vice versa. What is not retained is the interaction of flexible modes among themselves, but based on experience it is not a critical element of the dynamic behavior. The simplification involved considers longitudinal dynamics with a single elastic mode and a control law based on novel dynamic inversion only. In addition, throughout this chapter the analysis considers the inner loop of the dynamic inversion only, i.e., the ydes to y portion. It is important to note that the nature of ydes
The influence that novel dynamic inversion has on the closed loop dynamics is studied analytically for both linear and nonlinear systems as well as different cases of dynamics for the new methodology. In addition, the affects the dynamics of the
innovative dynamic inversion have on the closed loop system response is studied through pole movement as a function of the innovation’s dynamics. The model involved
considers a linearized version of the aircraft dynamics while still retaining essential characteristics such as rigid body/flexible mode coupling. The initial linear system considered is short period longitudinal dynamics with a single elastic mode to which dynamic inversion, both original and novel concept, is applied to show the affects on aircraft dynamics due to the introduced modifications. The complexity of the model is then gradually increased to include more dynamics.
This chapter is organized as follows. Following the introduction, section 2 introduces the novel dynamic inversion followed by a section discussing model selection for use in the symbolic analysis. Section 4 explores the linear system case. Three different
variations in the novel dynamic inversion dynamics are explored in this section. Section 5 discusses the same three variations for a nonlinear system. Following this, the second major portion of this chapter considers the influence of novel dynamic inversion on system response. To provide context for the results that follow it, section 6 discusses the standard dynamic inversion results as applied to the short period plus one elastic mode linear equations of motion. The following section then deals with the innovation introduced into the dynamic inversion that is the primary focus of this chapter. The subsequent sections address the increasing complexity of the model by introducing full longitudinal dynamics and additional flexible modes, respectively. The final section explores how uncertainty introduced into elastic mode frequency and damping influences closed loop dynamics that are found in the traditional rigid body frequency range. The conclusions that are drawn from this analysis then follow.
Throughout this chapter, the analysis considers the inner loop of the dynamic inversion only, i.e., the y to ydes portion. It is important to note that the nature of ydes