Here our main focus is to monitor and maneuver the flight for a particular distance in a time-scale with absolute control. For this a rigorous formulation of flight mechanics and theories associated with advanced control systems are simplified and analyzed to obtain a feasible & optimized solution. It is also important to remember that this idea basically involves handling problems of maneuvering control and other pilot-issues of an inner-loop flight-control system and does not dwell on outer loop control systems . The operational significance of this maneuver is that it allows the pilot to slew quickly without increasing the normal acceleration and turning.

1. Presented By :- Ansuman Mishra
Ashutosh Pradhan
Dhiroj Kumar Sahoo
Dibya Jyoti Mohanta
TRACKING AND CONTROL PROBLEMs OF
AN AIRCRAFT
Guided By :- Monalisha Samal
(Asst. Professe Ece Dept.)

2. Abstract
 Modern flight dynamics and its applications to monitoring & trafficking aircraft continue to be among the
most fascinating ideas of the modern era of advanced engineering.
 Here our main focus is to monitor and maneuver the flight for a particular distance in a time-scale with
absolute control. For this a rigorous formulation of flight mechanics and theories associated with advanced
control systems are simplified and analyzed to obtain a feasible & optimized solution.
 It is also important to remember that this idea basically involves handling problems of maneuvering control
and other pilot-issues of an inner-loop flight-control system and does not dwell on outer loop control systems
.
 The operational significance of this maneuver is that it allows the pilot to slew quickly without increasing the
normal acceleration and turning.

3. CONTENTS
Introduction
Problem Definition
Mathematical Calculation
Aircraft Dynamics
State Space Equation & Augmented States

4. Introduction
 The essence of designing and maneuvering a dynamic aircraft system revolves around setting up the flight control
problem from its inception. It involves a series of well-defined procedures followed by rigorous algebraic
formulations of the non-linear dynamic model of the controlled “plant”. Secondly, the linearization of the above
non-linearity is obtained via a controller (LQR) yielding a Linear-time-invariant model which is routinely used for
controller design.
 To account for the various aspects affecting the control design, we need to have a detailed study of the flight
mechanics. The aircraft balance parameters which includes the lift yawing movement, the pitching slide force and
the rolling drag forces play a very critical role in modifying flight characteristics. For this, the nine state equations
are derived from the Euler’s equation of motion followed by their transformation into the state-space form. Once
the state-space variables are defined we now construct a stabilizing linear state-feedback controller that
minimizes the performing index. For this, it is assumed that the optimal-closed loop system is asymptotically stable.
The Algebric-Riccati-equation which forms the central basis for the above system is solved using a controller.
Now, the choice of a controller plays a very critical role in determining the degree or extent of stability of a control
system. Henceforth, a detailed study of the respective controller is absolutely essential for success of the designing
the aircraft model.

5.  One of the greatest difficulties to apply new and classical control methods is the effort to learn, to implement and
to apply the method, and the problematical that is to re-design with a non-familiar method. The Linear Quadratic
method is considered to be relatively easy to use, but requires a good understanding of optimal control theory.
Obtaining the desired results by selection of weighting functions will probably provide the greatest difficulty for a
new user. In general, optimality with respect to some criterion is not the only desirable property for a controller.
One would also like stability of the closed-loop system, good gain and phase margins, robustness with respect to
un-modeled dynamics, etc. Taking these parameters into considerations, the LQR forms the ideal controlling device
for designing a Flight control system (FCS).
 It is also very important to remember that during solving of the ARE equation a set of augmented state-vectors are
added resulting in the formation of an augmented model. Finally, using the MATLAB M-file, we obtain the
feedback coefficients of the tracking controller, and model the flight dynamics. The corresponding waveforms
indicating the lateral, longitudinal dynamics and various Euler angles provide a detailed account of the LQR
control of aircraft dynamics and maneuvering of the Flight control system.
Introduction Continue

6. Aircraft Maneuver

7. ProblemDefinition
 The aim of this project is to build a tracking controller which would basically help us in maneuvering the flight
control system(FCS) for a period of five seconds with respective Euler angles(pitch, yaw and roll angles)
maintained at 1 radians with the help of a linear quadratic regulator(LQR).
 We are also looking into the various control parameters affecting the flight-in-loop issues like Angle-of-attack
and side-slip angle.

8. Mathematical Calculation
 Here we are going to use following Mathematical Calculation :-
LINEAR QUADRATIC
REGULATOR
ALGEBRIC RICCATI’S
EQUATION
 We use LINEAR QUADRATIC REGULATOR to calculate State-Space Models, Input-Output Relations and Linear
quadratic regulation (LQR) feedback configuration.
 Our goal is to construct a stabilizing linear state-feedback controller but from LQR only we can get linear
quadratic equation.
 So For getting a stable linear state-feedback we should use ALGEBRIC RICCATI’S EQUATION.

9. LINEARQUADRATICREGULATOR
 In this section we study controllers that are optimal with respect to energy-like criteria.
 These are particularly interesting because the minimization procedure automatically produces controllers that are
stable and somewhat robust. In fact, the controllers obtained through this procedure are generally so good that we
often use them even when we do not necessarily care about optimizing for energy.
 Moreover, this procedure is applicable to multiple-input/multiple-output processes for which classical designs are
difficult to apply.
State-Space Models
System with m inputs and k outputs
 A state-space model for this system relates the input and output of a system using the following
1st-order vector ordinary differential equation

10. LINEARQUADRATICREGULATOR
 From State Space model we get
Input-Output Relations
 The transfer function of this system can be found by taking the Laplace transform of the above equations:
 where X(s), U(s) and Y(s) denote the Laplace transform of x(t), u(t) and y(t) respectively. Solving X(s),
we get,
 and therefore
 defining,
 we conclude that,
 when x(0) = 0. The general solution to the system
in the time-domain is given by,

11. LINEARQUADRATICREGULATOR
Feedback Configurations
Linear quadratic regulation (LQR) feedback configuration
 In this configuration, the state-space model is of the form

12. ALGEBRICRICCATI’SEQUATION
 Our goal is to construct a stabilizing linear state-feedback controller of the form u = -Kx that minimizes the
performance index J. We denote such a linear control law by u*.
 Theorem: if the state-feedback controller u* = -Kx is such that
 For some, , then the controller is optimal
 Hence the candidate for an optimal control law has the form
 u* = -R-1BTPx = -Kx,
 where K = -R-1BTP. Note that
 ( dV/dt + xT Qx + uT Ru) = (2xTPAx + 2xTPBu + xT Qx+ uT Ru)
= (2xT PB + 2uT R)
= 2R
> 0
 Thus the second order sufficiency condition for u* to minimize the above equation is satisfied.
0)(  RuuQxx
dt
dV
Min TT

13. AIRCRAFTDYNAMICS
 Modern flight control systems (FCS) consist of:
 • Aerodynamic control surfaces and/or engine’s nozzles
 • actuators
 • sensors
 • a sampler and ZOH device
 • compensators

14. FlightControl Requirements
 The flight control system constitutes the pilot/aircraft interface and its primary mission is to enable the
pilot/aircraft to accomplish a prespecified task. This entails the following:
 1. Accommodate a high α (velocity vector roll) maneuvers.
 2. Meet handling/flying qualities specifications over the entire flight envelope and for all aircraft
configurations, including tight tracking and accurate pointing for Fire Control.
 3. Above and beyond item 1, obtain optimal performance.
 4. Minimize number of placards, the number of limitations and restrictions the pilot must adhere to: - pilot
can fly his aircraft in “abandon”.