Robust Control System Design in UAV s a literature survey

Ch. Sunil Kumar M.E (Aerospace) IISc

Need for Robust Control In order to deal with the uncertainties in the aircraft model and also High frequency uncertainty eg: noise Methods of Robust control 1. LQG 2. Eigen Structure Assignment 3. Singular Value Based Loop shaping 1.LQG/LTR 2.Dynamic Inversion 4. H infinity 5. mu synthesis 6. Mixed h2/hinfinity

CONTROL OF AN UNMANNED AERIAL VEHICLE Hassan Noura Francois Bateman Proceeding of the 7th International Symposium on Mechatronics and its Applications (ISMA10), Sharjah, UAE, April 20-22, 2010

The Inertia values of the UAV model are obtained using Compound Pendulum Method. In Eigen structure assignment for MIMO systems, the Eigen vectors should be assigned as they are not unique. Longitudinal Control Law: uL = KL xL LLzL where xL is the state vector and zL is the integration of the error vector. x=[ v q Z0]T uL=[ x t ]T yL=[ v Z0]T

The eigen values of the Closed loop system are set and the Eigen vectors are found.

Lateral Control Law

Tracking Control Law similar to Longitudinal Control

The eigen values of the closed loop system are set and the eigen values are found. The state feedback gain Klat is calculated .

Results The control Law is implemented in MATLAB. The reference altitude, speed are changed and the corresponding change in throttle is rercorded. With a step change in reference roll angle, corresponding change in aileron and rudder inputs are recorded. The modeling uncertainties are not taken into account.

UAV CONTROLLER SYNTHESIS USING LQ BASED DESIGN METHODS Prof. Dr. SZABOLCSI, Rbert INTERNATIONAL CONFERENCE of SCIENTIFIC PAPER AFASES 2011 Brasov, 26-28 May 2011

LQR Full state feedback problem , LQG problem- allows internal and external disturbances In this paper, the theoritical background of these methods are given, that can be extended to UAV controller sythesis. LQR is an optimal control problem where a cost function is minimized. In this process we get the required solution. THE LQR DESIGN PROBLEM FORMULATION : Consider the system The optimal cost function to be minimized is

Where Q,R are the weighing matrices

The LQR problem is solved using Euler-Lagrange Equation, HamiltonJacobi-Bellman theory and Pontriagin s minimum principle To find a controller, find a positive definite solution for P of the Algebraic Riccati Equation Optimal Control vector can be derived as

This solution results in an asymtotically stable closed loop system. All the state variables should be available for measurement. Block diagram of the dynamic system

LQG Design Disturbed state space model w is the random plant disturbance and v is the sensor noise. The average cost function to be minimized Optimal state feedback gain matrix is and is obtained by solving the Algebraic Riccati equation. The Kalman Filter state Equation is The static gain L of the observer( kalman filter) is found from

Qo and Ro are weighting matrices for the observer. Block diagram of state observer is shown The structure of the LQG compensator is the series connection of the kalman filter and state feedback gain matrix

H-infinity State Feedback Control for UAV Maneuver Trajectory Tracking Yusong Jiao, Juan Du, Xinmin Wang, and Rong Xie International Conference on Intelligent Control and Information Processing August 13-15, 2010 - Dalian, China

In inner loop, robust H-infinity control theory is used to design the flight control system.

K(s) is the H-infinity problem solution. Altitude hold controller design

he=hg-h is chosen as the evaluation index. hg is the reference altitude

Standard H-infinity design question

w is the interference signal , here hg The state space realization designs the feedback control law to make the closed loop system stable. The controller K(s) is obtained. For the Lateral control, Yaw hold control design is used and w is the reference yaw angle. Results: Longitudinal , Lateral trajectory tracking and 3-D trajectory tracking results are simulated. The preset flight path and the output tracked path are shown.

Empirical Aerodynamic Modeling for Robust Control Design of An Oceanographic Uninhabited Aerial Vehicle Li Meng, Liu Li, S.M. Veres 2010 International Conference on Electronics and Information Engineering (ICEIE 2010)

A state space model of the UAV is provided from the existing formulae and the derivatives are estimated using UKF. UKF is used to estimate the aerodynamic parameters with uncertainty bounds A linearized model with parametric uncertainties is extracted from the nonlinear uncertain dynamics of the UAV using Linear Fractional Transformation. The LFT model and Non-linear model are compared. longitudinal controllers are synthesized by two different robust control methodologies, i.e. H-infinity and Mu-synthesis. Mu analysis for robust stability and robust performance

Monte-Carlo simulation is performed on the nonlinear model with aerodynamic parameter uncertainties in order to analyze robust performance of each controller. The Mu- controller performed better than the H-infinity controller. The H-infinity controller is designed on the system without considering the uncertainties while the Mu-synthesis design is done on the LFT model.

Pitch Attitude Controller Design and Simulation for a Small Unmanned Aerial Vehicle Chenggong Huang Qiongling Shao, Pengfei Jin, Zhen Zhu, Bihui Zhang 2009 International Conference on Intelligent Human-Machine Systems and Cybernetics

This paper compares the classical PID-controller, Integral separated PID controller and Adaptive proportion PID controller. Classic PID control: The control output is of the form

The integral module plays an important role to eliminate static error and to enhance control precision in PID control system. An overstepping error occurs in case of this type of system. The Control output of integral PID controller

is a control threshold which is set under consideration of performance demand of control system.

Adaptive proportion PID controller With a larger proportion parameter of PID, UAV has an excellent dynamic performance while stability reduces and vice versa.

The simulation results compares classic PID control with the integral module PID control and the Adaptive Proportion PID control. The adaptive proportion PID controller is good in both stability and dynamic performance of pitch attitude control.

Robust and Randomized Control Design of Mini-UAVs: The MH1000 Platform Laura Lorefice, Barbara Pralio and Roberto Tempo Proceedings of the 2007 American Control Conference Marriott Marquis Hotel at Times Square New York City, USA, July 11-13, 2007

This paper deals with a hybrid scheme of inner loop and outer loop controller. The Inner-loop controller realizes linearization and decoupling of flight systems by employing feedback linearization. The outer-loop controller is designed to realize the robustness of flight systems by using mu- synthesis approach. It takes into account the unmodeled dynamics and disturbances.

Design of Robust Backstepping Controller for Unmanned Aerial Vehicle Using Analytical Redundancy and Extended State Observer Liwei Qiu, Jianqiang Yi, GuoliangFan, Wensheng Yu and Ruyi Yuan

Analytical redundance of attitude angle rates could be realized by using reduced order nonlinear state observer method. Information of attitude angles measured by gyroscopes is used to obtain attitude angle rates. Linearization and decoupling of flight states are realized by employing backstepping method, which ensures the stability of nominal UAV dynamics throughout the flight envelope via twice step back . An ESO compensator is adopted to estimate the unmodeled dynamics in real time, which is realized via the appropriate parameter adjusting. Numerical simulation shows that UAV equipped with the hybrid control scheme has good maneuverability, strong self-learning ability of compensating the unmodeled dynamics and enough robust stability against constraints of actuators.

References CONTROL OF AN UNMANNED AERIAL VEHICLE Hassan Noura Francois Bateman Proceeding of the 7th International Symposium on Mechatronics and its Applications (ISMA10), Sharjah, UAE, April 20-22, 2010 UAV CONTROLLER SYNTHESIS USING LQBASED DESIGN METHODS Prof. Dr. SZABOLCSI, Rbert INTERNATIONAL CONFERENCE of SCIENTIFIC PAPER AFASES 2011 Brasov, 26-28 May 2011 H-infinity State Feedback Control for UAV Maneuver Trajectory Tracking Yusong Jiao, Juan Du, Xinmin Wang, and Rong Xie International Conference on Intelligent Control and Information Processing August 13-15, 2010 - Dalian, China Empirical Aerodynamic Modeling for Robust Control Design of An Oceanographic Uninhabited Aerial Vehicle Li Meng, Liu Li, S.M. Veres 2010 International Conference on Electronics and Information Engineering (ICEIE 2010) Pitch Attitude Controller Design and Simulation for a Small Unmanned Aerial Vehicle Chenggong Huang Qiongling Shao, Pengfei Jin, Zhen Zhu, Bihui Zhang 2009 International Conference on Intelligent HumanMachine Systems and Cybernetics Design of Robust Backstepping Controller for Unmanned Aerial Vehicle Using Analytical Redundancy and Extended State Observer Liwei Qiu, Jianqiang Yi, Guoliang Fan, Wensheng Yu and Ruyi Yuan Robust and Randomized Control Design of Mini-UAVs: The MH1000 Platform Laura Lorefice, Barbara Pralio and Roberto Tempo Proceedings of the 2007 American Control Conference Marriott Marquis Hotel at Times Square New York City, USA, July 11-13, 2007 Dr. M. Seetharama Bhat Modern Control for Aerospace Vehicles Department of Aerospace Engineering Indian Institute of Science Bangalore 560012, INDIA Raymond T.Stefani, Bahram Shahian, Clement J.Savant, Gene H.Hostetter Design of Feedback Control Systems Oxford University Press 2002 John J.DAzzo, Constantine H.Houpis Linear Control System Analysis and Design Conventional and Modern Second Edition International Student Edition McGraw-hill International Book Company