Robust Trajectory Linearization Control of Hypersonic Entry Flight
Using Extended State Observer and Time-varying Bandwidth
Zhiqiang Pu* Guoliang Fan* Xiangmin Tan* Jianqiang Yi*
*Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China
(e-mail: zhiqiang.pu@ia.ac.cn)
Abstract: A robust trajectory linearization control (TLC) scheme is presented for a generic hypersonic
vehicle (GHV) entry flight. The basic TLC frame constructs a baseline controller for the GHV attitude
system, providing local closed-loop exponential stability along nominal trajectories. Then two strategies
are integrated with the basic TLC for robustness enhancement. For one thing, to cope with diverse
perturbations, extended state observer is designed to yield a compensation control law. For the other, an
adaptive time-varying bandwidth algorithm is developed, which can not only avoid actuator saturation
and integrator windup, but most importantly, also improve system robustness when huge dynamic
pressure variation occurs during entry flight. This integrated robust TLC scheme can guarantee a better
control performance and a larger stability domain. At last, the great advantages of the proposed robust
TLC scheme is demonstrated via three groups of simulation, including a three-DOF attitude tracking, a
BTT-180 maneuver simulation, and a six-DOF integrated guidance and control test.
Keywords: Hypersonic vehicle, Entry flight, Trajectory linearization, Extended state observer, Time-
varying bandwidth
1. INTRODUCTION
Reusable launch vehicles (RLVs) are viewed as a reliable and
cost-effective solution to access to space routine. In recent
years, one focus of RLVs that receives lots of attention is the
design of advanced and robust entry guidance and control
systems that meet safety, reliability, and cost requirements
(Jiang & Ordonez, 2009; Van Soest, Chu, & Mulder, 2006).
Entry flight, as the most complex flight phase for RLVs,
covers a large flight envelope during which the
environmental and aerodynamic characteristics feature rapid
and huge variations. Significant interactions also exist among
aerodynamics, propulsion, structures, and control (Bolender
& Doman, 2007; Wilcox, MacKunis, Bhat, Lind, & Dixon,
2010). In addition, diverse perturbations such as modelling
errors and parametric uncertainties must be accommodated.
All the difficulties described above pose huge challenges to
entry control design. As a conventional approach, gain
scheduling (GS) (Rugh & Shamma, 2000) has been applied
to trajectory tracking for systems with dynamics varying
sufficiently slowly. However, due to the large entry flight
envelope and complex plant features, GS is always time-
consuming and requires intuitive engineering skills based on
experience. It also involves costly controller redesigns due to
minor airframe alteration or mission reconfiguration. Hence,
improvements have been made for the last few decades by
using modern nonlinear control methods such as dynamic
inversion (Van Soest et al., 2006), back-stepping (Bialy,
Klotz, Curtis, & Dixon, 2012), and sliding mode control (Xu,
Mirmirani, & Ioannou, 2004). As one of the most popular
methods, dynamic inversion can cancel model nonlinearities
using nonlinear state transformations. However, accurate
cancellation cannot be achieved in practice because diverse
disturbances are inevitable during hypersonic entry flight.
Back-stepping can effectively handle such disturbances, but
two drawbacks have to be overcome, that is, the restriction to
nonlinear systems of lower triangular form and the tedious
analytic computation of virtual control signal derivatives.
Similarly, pure sliding mode control exhibits drawbacks that
include large control authority requirements and chattering.
As a novel alternative, trajectory linearization control (TLC)
(Huang, Liu, & Zhu, 2009; Liu & Zhu, 2007; Zhu, Banker, &
Hall, 2000) is a nonlinear control method which combines a
nonlinear pseudo inversion with a linear time-varying (LTV)
feedback stabilizer. It linearizes the system along a nominal
trajectory, and then casts nonlinear tracking into a regulation
problem for the tracking-error dynamics. TLC can be viewed
as an ideal GS controller without scheduling of controller
gains. With LTV PD-spectral theory, exponential stability of
the linearized system can be guaranteed. Moreover, TLC
provides a unique time-varying bandwidth (TVB) technique
to feasibly improve the control performance and system
robustness, which distinguishes it from other nonlinear
control methods. In a basic TLC frame, bandwidths are often
set as constants for simplicity.
As for inevitable disturbances, theoretical and practical
investigations show that a basic TLC frame may be degraded
by slightly large disturbances (Liu & Zhu, 2007). To enhance
system robustness, one natural idea is to design observers for
estimating and compensating the disturbances (Yang, Li, Sun,
& Guo, 2012). Such observers can be based on fuzzy logic or
neural network. However, online fuzzy or neural network
estimation is always time-consuming. Extended state
observer (ESO), as the centerpiece of the active disturbance
rejection control (ADRC) technique (Han, 2009; Zheng, Gao,