Feedback linearization and backstepping: an equivalence in control design of strict-feedback form

2019 ◽  
Vol 37 (4) ◽  
pp. 1049-1069 ◽  
Author(s):  
Thanh T Tran
Keyword(s):  
Flight Control ◽  
Feedback Linearization ◽  
High Performance ◽  
Control Design ◽  
Backstepping Control ◽  
Analytical Models ◽  
Linear Feedback ◽  
Specific Class ◽  
Feedback Form ◽  
Non Linear

Abstract This paper investigates an equivalence between feedback linearization and backstepping control. Implications from equivalence are that stability and performance properties of one method are the same for another method. Thus, a property known to exist only for one method could be used to prove property also holds for another. Also, a suspected advantage of one method over the other could be proven to be a false conjecture. Control laws in both approaches are achieved by coordinate transformations and non-linear feedbacks. Further, resulting non-linear feedback control law achieved by feedback linearization method matches exactly with non-linear controller achieved by the backstepping control design. This equivalence is a general analytical match within the specific class of non-linear dynamic systems under investigation. Demonstrations are considered and validated via flight control of longitudinal dynamics of a high performance aircraft simulation model. Algorithms are tested and evaluated with analytical models and non-linear closed-loop simulation.

Flight control design using non-linear inverse dynamics

Automatica ◽  
1988 ◽  
Vol 24 (4) ◽  
pp. 471-483 ◽  
Author(s):  
Stephen H. Lane ◽  
Robert F. Stengel
Keyword(s):  
Flight Control ◽  
Inverse Dynamics ◽  
Control Design ◽  
Non Linear

scholarly journals High Speed Microactuators for Low Aspect Ratio High Speed Micro Aircraft Surfaces

Actuators ◽  
2021 ◽  
Vol 10 (10) ◽  
pp. 265
Author(s):  
Ronald Barrett-Gonzalez ◽  
Nathan Wolf
Keyword(s):  
Aspect Ratio ◽  
Flight Control ◽  
High Speed ◽  
High Performance ◽  
Dynamic Range ◽  
Feedback System ◽  
Analytical Models ◽  
Control Surface ◽  
Operational Environment ◽  
Low Aspect Ratio

This paper covers a class of actuators for modern high speed, high performance subscale aircraft. The paper starts with an explanation of the challenges faced by micro aircraft, including low power, extremely tight volume constraints, and high actuator bandwidth requirements. A survey of suitable actuators and actuator materials demonstrates that several classes of piezoceramic actuators are ideally matched to the operational environment. While conventional, linear actuation of piezoelectric actuators can achieve some results, dramatic improvements via reverse-biased spring mechanisms can boost performance and actuator envelopes by nearly an order of magnitude. Among the highest performance, low weight configurations are post-buckled precompressed (PBP) actuator arrangements. Analytical models display large deflections at bandwidths compatible with micro aircraft flight control speed requirements. Bench testing of an example PBP micro actuator powered low aspect ratio flight control surface displays +/−11° deflections through 40 Hz, with no occupation of volume within the aircraft fuselage and good correlation between theory and experiment. A wind tunnel model of an example high speed micro aircraft was fabricated along with low aspect ratio PBP flight control surfaces, demonstrating stable deflection characteristics with increasing speed and actuator bandwidths so high that all major aeromechanical modes could be easily controlled. A new way to control such a PBP stabilator with a Limit Dynamic Driver is found to greatly expand the dynamic range of the stabilator, boosting the dynamic response of the stabilator by more than a factor of four with position feedback system engaged.

scholarly journals Dynamic backstepping control for pure-feedback non-linear systems

2019 ◽  
Vol 37 (2) ◽  
pp. 674-697
Author(s):  
Sheng Zhang ◽  
En-Mi Yong ◽  
Yu Zhou ◽  
Wei-Qi Qian
Keyword(s):  
Linear Systems ◽  
Algebraic Equation ◽  
Control Method ◽  
Backstepping Control ◽  
Free Form ◽  
Control Law ◽  
Backstepping Method ◽  
Feedback Form ◽  
Non Linear ◽  
Non Linear Systems

Abstract A dynamic backstepping control method is proposed for non-linear systems in the pure-feedback form, for which the traditional backstepping method suffers from solving the implicit non-linear algebraic equation. This method treats the implicit algebraic equation directly via a dynamic way, by augmenting the (virtual) controls as states during each recursive step. Compared with the traditional backstepping method, one more Lyapunov design is executed in each step. As new dynamics are included in the design, the resulting control law is in the dynamic feedback form. Under appropriate assumptions, the proposed control scheme achieves the uniformly asymptotic stability and the closed-loop system is local input-to-state stable for various disturbance. Moreover, the control law may be simplified to the inverse-free form by setting large gains, which will alleviate the problem of `explosion of terms’. The effectiveness of this method is illustrated by the stabilization and tracking numerical examples.

scholarly journals Dynamic Feedback Backstepping Control for a Class of MIMO Nonaffine Block Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Hai-Yan Li ◽  
Yun-An Hu ◽  
Jian-Cun Ren ◽  
Min Zhu
Keyword(s):  
Nonlinear Systems ◽  
Feedback Linearization ◽  
Closed Loop ◽  
Sliding Mode ◽  
Design Method ◽  
Control Design ◽  
Backstepping Control ◽  
Dynamic Feedback ◽  
Closed Loop System ◽  
Linearization Techniques

For a class of MIMO nonaffine block nonlinear systems, a neural network- (NN-) based dynamic feedback backstepping control design method is proposed to solve the tracking problem. This problem is difficult to be dealt with in the control literature, mainly because the inverse controls of block nonaffine systems are not easy to resolve. To overcome this difficulty, dynamic feedback, backstepping design, sliding mode-like technique, NN, and feedback linearization techniques are incorporated to deal with this problem, in which the NNs are used to approximate and adaptively cancel the uncertainties. It is proved that the whole closed-loop system is stable in the sense of Lyapunov. Finally, simulations verify the effectiveness of the proposed scheme.

scholarly journals Non-Linear Dynamic Inversion Control Design for Rotorcraft

Aerospace ◽  
2019 ◽  
Vol 6 (3) ◽  
pp. 38 ◽  
Author(s):  
Joseph Horn
Keyword(s):  
Flight Control ◽  
State Feedback ◽  
Control Design ◽  
Linear Analysis ◽  
Order System ◽  
Dynamic Inversion ◽  
Order Linear ◽  
Full State ◽  
Non Linear ◽  
Full State Feedback

Flight control design for rotorcraft is challenging due to high-order dynamics, cross-coupling effects, and inherent instability of the flight dynamics. Dynamic inversion design offers a desirable solution to rotorcraft flight control as it effectively decouples the plant model and effectively handles non-linearity. However, the method has limitations for rotorcraft due to the requirement for full-state feedback and issues with non-minimum phase zeros. A control design study is performed using dynamic inversion with reduced order models of the rotorcraft dynamics, which alleviates the full-state feedback requirement. The design is analyzed using full order linear analysis and non-linear simulations of a utility helicopter. Simulation results show desired command tracking when the controller is applied to the full-order system. Classical stability margin analysis is used to achieve desired tradeoffs in robust stability and disturbance rejection. Results indicate the feasibility of applying dynamic inversion to rotorcraft control design, as long as full order linear analysis is applied to ensure stability and adequate modelling of low-frequency dynamics.

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