ABSTRACT

This report gives an overview of the aircraft control system, a graphical software environment for the design and analysis of the aircraft dynamics control system based upon MATLAB and SIMULINK. Its main goal is to simplify the fight control system design process. It determines the stability characteristics on the basis of time and frequency domain using Bode plots and root locus plots. Aircrafts adopt an eclectic approach for parameter identification method. Time- domain method for stability control parameters estimation is used alongside frequency –domain methods which are chiefly used for determining flying qualities parameters. Stability is an important factor for an aircraft and it is important for one should know about various stability factors before commenting on the aircraft stability.In this project we have considered a “fly-by-wire “aircraft i.e. a semi-automatic and typically computer-regulated system for controlling the flight of an aircraft or spacecraft. System identification methods compose a mathematical model or series of models, from measurements of inputs and outputs of dynamics system. These extracted models allow the characterizations of the response of the aircraft or the overall component behaviour and the constant values or the variations are noted. System identification is a procedure for accurately characterizing the dynamic response behaviour of completer aircraft and its control system response. This technology for modern fly-by-wire flight control system development and integration provides a unified flow of information regarding system performance. The obtained values form the mathematical models. Models can be defined by two approaches using time domain analysis i.e. root locus technique and frequency domain analysis using bode plot technique. Determining the stability of the aircraft using complex mathematical calculations is often time taking and approximate values are considered. In this project, the stability of aircrafts like – Boeing 767 aircraft is analysed. The stability factors are determined by using state space models in the software- MATLAB (Simulink). Using the software for determining the stability makes the work simple and it is less time consuming. It gives more accurate values and the results are more convincing.This report gives an overview of aircraft control and also GUI whose main aim is to bring stable controlled flight movement.

CONTENTS

Sl. No. Chapter Page No.

1 1. Introduction 12 2. History 2

3 3. Physics of Flight3.1 Equations of motion of flight3.2 Dimensions of flight

3-53-44-5

4 4. Basic Block Diagram of Aircraft Control System4.1 Description of block diagram4.2 Glossary of terms used in block diagram

6-96-78-9

5 5. Simulink Control of Aircraft Pitch5.1 Physical setup & System equation5.2 Building state space model5.3 Open loop response5.4 Generating close loop response5.5 Animation of Aircraft pitch

10-1710-111111-1313-1415-17

6 6. Aircraft Roll Control6.1 Modelling of PID Controller6.2 Result

18-2019-2020

7 7. Aircraft Yaw Control7.1 Yaw damper7.2 Design of Yaw Damper

21-252122-25

8 8. Simulink Block Diagram of aircraft 26

9 9. Flowchart of Pitch Control 27

10 10 Flowchart of Roll Control

28

11 11 Flowchart of Yaw Control 29

12 12. Aircraft Control Design Analysis12.1 Pitch Control Design and analysis12.2 Roll Control Design and analysis

12.3 Yaw Control Design and analysis

28-292828-2929

13 13. Future Aspects 30

14 14. Conclusion 31

15 15. Bibliography 32

Sl. No.

Figures Page No.

1 3.1 Motion of flight 3

2 3.2 Yaw, roll, pitch angle 4

3 4.0 Block Diagram of Aircraft Control System 6

4 5.1 Simulink control of Aircraft Pitch and output 12-13

5 5.3 Simulink model with output graph 14

6 5.4 Animation for Aircraft pitch 15-16

7 6.1 Block Diagram of roll control 19

8 6.1 Simulink diagram of PID controller 20

9 7.0 Yaw Control 21

10 7.2.1 Yaw Damper design in Pole-Zero Map 23

11 7.2.2 Impulse Response(fig 1,fig 2) 24

12 7.2.3 Bode Diagram and Root Locus 25

13 7.2.4 Impulse Response from rudder to yaw rate ,aileron ,bank angle

26

14 7.2.5 Root Locus and impulse response 27

15 8.0 Simulink block diagram of Aircraft Control System 28

LIST OF FIGURES

1 I ntroduction

A conventional fixed-wing aircraft flight control system consists of flight control surfaces. The respective cockpit controls, connecting linkages, and the necessary operating mechanisms to control an aircraft's direction in flight. Aircraft engine controls are also considered as flight controls as they change speed. The fundamentals of aircraft controls are explained in flight dynamics.

Flight dynamics is the science of air-vehicle orientation and control in three dimensions. The three critical flight dynamics parameters are the angles of rotation in three dimensions about the vehicle's center of mass, known as roll, pitch and yaw.

Aircraft engineers develop control systems for a vehicle's orientation (attitude) about its center of mass. The control systems include actuators, which exert forces in various directions, and generate rotational forces or moments about the center of gravity of the aircraft, and thus rotate the aircraft in pitch, roll, or yaw. For example, a pitching moment is a vertical force applied at a distance forward or aft from the center of gravity of the aircraft, causing the aircraft to pitch up or down.

Roll, pitch and yaw refer, in this context, to rotations about the respective axes starting from a defined equilibrium state. The equilibrium roll angle is known as wings level or zero bank angle, equivalent to a level heeling angle on a ship. Yaw is known as "heading".

A fixed-wing aircraft increases or decreases the lift generated by the wings when it pitches nose up or down by increasing or decreasing the angle of attack (AOA). The roll angle is also known as bank angle on a fixed-wing aircraft, which usually "banks" to change the horizontal direction of flight. An aircraft is usually streamlined from nose to tail to reduce drag making it typically advantageous to keep the sideslip angle near zero, though there are instances when an aircraft may be deliberately "sideslipped" for example a slip in a fixed-wing aircraft.

Actually, because of the high cost of building and flight testing a real aircraft the importance of the mathematical model goes far beyond design. The mathematical model is used, in conjunction with computer simulation (like MATLAB Simulink is used here) to evaluate the performance of the prototype aircraft and hence improve the design.

2 Review

Mechanical or manually operated flight control systems are the most basic method of controlling an aircraft. The complexity and weight of mechanical flight control systems increase considerably with the size and performance of the aircraft. Hydraulically powered control surfaces help to overcome these limitations. With hydraulic flight control systems, the aircraft's size and performance are limited by economics rather than a pilot's muscular strength. A stick shaker is a device (available in some hydraulic aircraft) that is attached to the control column, which shakes the control column when the aircraft is about to stall. A fly-by-wire (FBW) system replaces manual flight control of an aircraft with an electronic interface. The movements of flight controls are converted to electronic signals transmitted by wires (hence the fly-by-wire term), and flight control computers determine how to move the actuators at each control surface to provide the expected response.

An autopilot is a system used to control the trajectory of a vehicle without constant 'hands-on' control by a human operator being required. Autopilots do not replace a human operator, but assist them in controlling the vehicle, allowing them to focus on broader aspects of operation, such as monitoring the trajectory, weather and systems.

Autopilots have evolved significantly over time, from early autopilots that merely held an attitude to modern autopilots capable of performing automated landings under the supervision of a pilot.

Modern autopilots use computer software to control the aircraft. The software reads the aircraft's current position, and then controls a Flight Control System to guide the aircraft. In such a system, besides classic flight controls, many autopilots incorporate thrust control capabilities that can control throttles to optimize the air speed.

In order to save the high cost of building and flight testing a real aircraft ,computer simulation (Using software like MATLAB Simulink ) the control design of aircrafts are being tested in recent times.

3. Physics of Flight

3.1 Equations of motion of flight

Figure a

There are four forces that act on an aircraft in flight: lift, weight, thrust, and drag. The motion of the aircraft through the air depends on the relative size of the various forces and the orientation of the aircraft. For an aircraft in cruise, the four forces are balanced, and the aircraft moves at a constant velocity and altitude. Here, we consider the relations of the forces during a gradual climb. We have drawn a vertical and horizontal axis on our aircraft through the center of gravity. The flight path is shown as a red line inclined to the horizontal at angle c. The lift and drag are aerodynamic forces that are defined relative to the flight path. The lift is perpendicular to the flight path and the drag is along the flight path. The thrust of the aircraft is also usually aligned with the flight path. Some modern fighter aircraft can change the angle of the thrust, but we are going to assume that the thrust is along the flight path direction. The weight of an airplane is always directed towards the center of the earth and is, therefore, along the vertical axis.

Forces are vector quantities. We can write two component equations for the motion of the aircraft based on Newton's second law of motion and the rules of vector algebra. One equation gives the vertical acceleration av, and the other gives the horizontal acceleration ah in terms of the components of the forces and the mass m of the aircraft. If we denote the thrust by the symbol F, the lift by L, the drag by D, and the weight by W, the vertical component equation is:

F * sin(c) - D * sin(c) + L * cos(c) - W = m * av

where sin and cos are the trigonometric sine and cosine functions. Similarly, the horizontal component equation is:

F * cos(c) - D * cos(c) - L * sin(c) = m * ah

We can simplify the equations a little by using the definition of excess thrust Fex:

Fex = F - D

The resulting equations of motion are:

Vertical: Fex * sin(c) + L * cos(c) - W = m * av

Horizontal: Fex * cos(c) - L * sin(c) = m * ah

For small climb angles, the cos(c) is nearly 1.0 and the sin(c) is nearly zero. The equations then reduce to:

Vertical: L - W = m * av

Horizontal: F - D = m * ah

3.2 Dimensions of Flight plane

To roll the plane to the right or left, the ailerons are raised on one wing and lowered on the other. The wing with the lowered aileron rises while the wing with the raised aileron drops.

Pitch makes a plane descend or climb. The pilot adjusts the elevators on the tail to make a plane descend or climb. Lowering the elevators caused the airplane's nose to drop, sending the plane into a down. Raising the elevators causes the airplane to climb.

Yaw is the turning of a plane. When the rudder is turned to one side, the airplane moves left or right. The airplane's nose is pointed in the same direction as the direction of the rudder. The rudder and the ailerons are used together to make a turn

The pilot controls the engine power using the throttle. Pushing the throttle increases power, and pulling it decreases power.

The ailerons raise and lower the wings. The pilot controls the roll of the plane by raising one aileron or the other with a control wheel. Turning the control wheel clockwise raises the right aileron and lowers the left aileron, which rolls the aircraft to the right.

The rudder works to control the yaw of the plane. The pilot moves rudder left and right, with left and right pedals. Pressing the right rudder pedal moves the rudder to the right. This yaws the aircraft to the right. Used together, the rudder and the ailerons are used to turn the plane.The elevators which are on the tail section are used to control the pitch of the plane. A pilot uses a control wheel to raise and lower the elevators, by moving it forward to back ward. Lowering the elevators makes the plane nose go down and allows the plane to go down. By raising the elevators the pilot can make the plane go up.

The pilot of the plane pushes the top of the rudder pedals to use the brakes. The brakes are used when the plane is on the ground to slow down the plane and get ready for stopping it. The top of the left rudder controls the left brake and the top of the right pedal controls the right brake.

If you look at these motions together you can see that each type of motion helps control the direction and level of the plane when it is flying.

4. Basic Block Diagram of Aircraft Control System

Block Diagram of Aircraft Control System

4.1 DESCRIPTION OF THE BLOCK DIAGRAM OF AIRCRAFT CONTROL SYSTEM

The description of the block diagram of the digital autopilot in aircraft control system is as follows:

The elevator deflection angle is fed to our pitch controller as an input to the pitch controller. The elevator deflection angle may be measured by using sensors like gyro sensors attached to the aircraft. The output of the pitch controller designed by us gives a proper controlled pitch angle (θ )which is used to control the pitch of the aircraft along the lateral axis.

The aileron deflection angle (∂a) is fed to the PID controller designed by us for roll control. The aileron deflection angle may be measured by using sensors like gyro sensors attached to the aircraft. The output of the PID controller i.e., the roll angle is fed to the ailerons to achieve stable controlled movement of ailerons along the longitudinal axis.

The rudder deflection angle and aileron deflection angle are fed to the yaw damper designed by us for yaw control. The rudder deflection angle and aileron deflection angle may be measured by sensors like gyro sensor attached to the aircraft.

The yaw damper output consisting of yaw rate and bank angle is fed to a washout circuit so that the spiral mode of operation of aircraft persists even after damping the Dutch roll mode oscillations. From the washout circuit the yaw rate and bank angle can be amplified and finally fed to the rudder and aileron of the aircraft to achieve stabilized yaw movement of aircraft along the vertical axis.

In this way pitch, roll and yaw can be controlled in a modular approach so that even if there is malfunctioning of one of the controllers along any of the axis the whole system would not suffer from complete failure.

4.2 GLOSSARY OF TERMS USED IN THE BLOCK DIAGRAM:

i) Rudder: The rudder is the small moving section at the rear of the stabilizer that is attached to the fixed sections by hinges. The rudder controls the yaw.

ii) Aileron: Ailerons are small hinged sections on the outboard portion of a wing. Ailerons can be used to generate a rolling motion for an aircraft. The ailerons controls the roll.

iii) Elevator: Elevators are flight control surfaces usually at the rear of an aircraft, which controls aircraft pitch and therefore angle of attack and the lift of the wing.

iv) Pitch Angle: Pitch angle is the angle between the longitudinal axis (where the plane is pointed) and the horizon. This angle is displayed on the attitude indicator or artificial horizon.

v) Gyro sensor: Gyro sensor senses the rotational motion and also senses the changes in orientation.

vi) Elevator Deflection Angle: It is the angle made by the elevator axis of the aircraft with the lateral axis of the plane of the aircraft.

vii) Aileron Deflection Angle: It is the angle made by the aileron axis of the aircraft with the vertical axis of the plane of the aircraft considered.

viii) Roll Angle: The roll angle is known as bank angle on a fixed wing aircraft which usually banks to change the horizontal direction of the flight.

ix) PID controller: A proportional–integral–derivative controller(PID controller) is a control loop feedback mechanism (controller) commonly used in industrial control systems. A PID controller continuously calculates an error value as the difference between a desired set point and a measured process variable. The PID controller is used here to design the roll control. The PID controller has a dynamic response compared to the other normal controllers hence it is chosen to design the roll control.

x) Yaw Damper:  Yaw Damper is an independent subsystem compatible with any autopilot or semi-autopilot system. It enhances directional stability by eliminating short-term yaw oscillations.

xi) Washout circuit: A washout circuit is a filter that makes a transition caused by changes in the input source more smooth. An example of this transition is the change in the modes of a signal. The general form of this filter is: H(s) = s/(s+a). Washout circuit is used in the yaw control so that the spiral mode of operation of aircraft persists even after damping the Dutch roll mode oscillations.

xii) Yaw Rate: Yaw rate refers to the rate of change of yaw,i.e., time derivative of yaw. Denoted by symbol: psi.

xiii) Bank Angle: The angle between the horizontal plane and the right wing in the lateral plane.

5. Simulink control of Aircraft Pitch

5.1. Physical setup and system equations

The equations governing the motion of an aircraft are a very complicated set of six nonlinear coupled

differential equations. However, under certain assumptions, they can be decoupled and linearized into

longitudinal and lateral equations. Aircraft pitch is governed by the longitudinal dynamics. Here we

will design an autopilot that controls the pitch of an aircraft.

For this system, the input will be the elevator deflection angle   and the output will be the pitch angle   of the aircraft.

Before finding the transfer function and state-space models, following are some numerical values to simplify the modelling equations.

The above equation is the longitudinal equations of motion for the aircraft.

Putting the values in equation we get

These values are taken from the data from Boeing's commercial aircraft (Boeing 747 Jet Airways).

Transfer function

To find the transfer function of the above system, we need to take the Laplace transform of the above modelling equations. When finding a transfer function, zero initial conditions must be assumed. The Laplace transform of the above equations are shown below. 

After few steps of algebra, we obtained the following transfer function.

State space model of the pitch control equations:

Recognizing the fact that the modelling equations above are already in the state-variable form, we can rewrite them as matrices as shown below.

Since our output is pitch angle, the output equation is the following.

The next step is to choose some design criteria. In this we will simulate the linearized aircraft model with the state feedback controller design. In this we will specifically use the linearized state- space model obtained in aircraft pitch.

The above equations match the general linear state –space form:

dx/dt=Ax+Bu

y=Cx+Du

5.2 Building the state –space model

Then we come to building a Simulink model of the above equations. We use the state -space block made available in Simulink to model the open-loop plant.

For a step reference, the design criteria are the following.

Overshoot less than 10%

Rise time less than 2 seconds

Settling time less than 10 seconds

Steady-state error less than 2%

Open-loop response

With the equation that is the general linear state –

space form i.e.

dx/dt=Ax+Bu

y=Cx+Du

We will now build a Simulink model of the above

equations. We will employ the State-Space block

made available in Simulink to model the open-loop

plant. Specfically, we will follow the steps given

below.

We have opened a new model window in Simulink.

There we have inserted a Step block from the

Simulink/Sources library.

To provide a appropriate step input at t=0, we

set the Step time to "0" in Step block and Final value to "0.2" to represent the 0.2-radian

reference we are assuming.

Then we inserted a Demux block from the

Simulink/Signal Routing library and entered "3" for the Number of outputs; one output for

each of the three state variables. Figure a

Then we have inserted a

Scope from the Simulink/ Sinks

library and connected the third output of the

Demux block to the scope. We will only plot

the third state variable which corresponds to

system's output which is the aircraft’s pitch

theta

Then we add Terminator blocks from the

Simulink/Sinks library to the two signals of

the Demux block that we are not

plotting.

After this we insert a State-Space block from

the Simulink/Continuous library and connect

the input to the Step block and the output to

the Demux block.

We enter parameters in state space block as shown in Figure. a Figure b.

Note, that in the above figure1 the C matrix is

entered as a 3x3 identity matrix using

the eye command rather than [0 0 1] as given in

the original state-space equations. The reason for

this is because in state-feedback control it is

assumed that all of the state variables are

measured, not just the output. If this is not the

case, then an observer needs to be designed to

estimate any state variables that are not

measured

.

When finished, the completed model in Figure.b gives the output in the scope shown in Figure.c.

figure c.

5.3 Generating the closed-loop response

The open loop response is unstable. In order to view a stable response, we will now quickly add the

state-feedback control gain K. This gain was designed using the Linear Quadratic Regulator method

and resulted in a calculation of K = [-0.6435 169.6950 7.0711].

In order to add the state-feedback control to our

model, we followed the steps given below.

Insert the sum block from the Simulink/Math

Operations library which is "|+-" between

the Step

reference and the State-Space block.

Figure.d

Insert a Gain block from the Simulink/Math

Operations library whose output is given to

the "-" sign of the Sum figure d.

block and the input to the output of the

State-Space block

by branching off the output signal by right-

clicking on the existing line. Figure d.

Next we enter the information in the Gain block as shown. Specifically, we enter the value for the

matrix gain K and change the Multiplication setting to Matrix(K*u) as shown in Figure.d.

Adding the appropriate labels will then leave us with the Simulink model as shown in Figure. e.

Figure.e

Next running the simulation by pressing Ctrl-T or selecting Start from the Simulation menu. When

the simulation is finished, we got the output from scope as shown in Figure f.

Figure f

5.4 Animation for the Aircraft Pitch

Purpose

The purpose of this Graphical User Interface (GUI) is to allow the user to view an animation of the

Bus Suspension system with the step disturbance response plot. This allows the user to see the

correlation between the plot and the systems physical response.

The animation and GUI are based on the Aircraft Pitch: State-Space Controller Design.

Running the GUI

To run the GUI you will need 2 files. Copy each of them to the directory in which you are running

MATLAB.

pitchgui.fig - contains the graphical interface.

pitchgui.m - contains the GUI callback function.

Once these files are copied into your MATLAB

directory, simply enter the following command:

pitchgui

The other file need not be run from the

command window, it will be called separately

by the GUI. The following figure 1. should

appear on your screen after the command has

been executed:

Fig 1Using the GUI

Below are descriptions of each of the controls found in the GUI. These descriptions are intended to

give the user a better understanding of what each control actually does. However, feel free to

experiment with the controls and use this section as a reference for any questions you might have.

The first group of controls contains the Run, Reset and Exit buttons. These controls perform most of

the work in the GUI.

Run - This button performs the simulation, plots the response in the upper-right portion of the

window and runs the animation in the lower-right portion of the window.

Reset - This button clears the upper-right step response plot and sets the ball position and beam angle

to zero in the lower-right plot. If a plot is not cleared, the next run will be graphed on the same plot.

This is useful if you want to graphically see the effect of varying a parameter.

Exit - This button closes the GUI.

An example of the animation and response plot are shown below. The red line in the animation

represents the plane's elevator control surface.

The next control allows you to set the weighting factor of the Q matrix for the LQR design method

utilized in the animation.

Pitch Angle Factor - This editable text field weights the plane's pitch angle in the LQR controller.

Increasing the weighting factor improves the plane's response, making it reach it's commanded

position faster.

Feel free to change the weighting factor to see what happens!

The control shown below allows you to change the step input command.

Step Slider - The slider allows you to change the magnitude of the step input command. You can

click on the arrows to move the slider, grab the slider bar and move it, or click on the slider to change

the step input. The current value of the step input is displayed in the upper portion of the box.

This next group of controls contains checkboxes that allow the user to change various features of the

GUI.

Manual Advance - If this control is checked, the user is able to advance the animation and plot one

frame at a time. The frames are advanced by pressing any key on the keyboard. This function is useful

if the animation moves too fast for the user and will allow the user to better visualize the entirety of

the system's motion.

Plot Separately - By checking this box the step response plot is graphed in its entirety before the

animation is run.

Reference Input - This box is automatically checked when the GUI is run. By un-checking it the user

removes the reference input term, Nbar, from the simulation. The reference input is used to correct

steady-state errors common to full-state feedback systems.

Remember, this GUI is intended to be an interactive learning tool that will allow the user to get a

feeling for how some basic control techniques and ideas are represented in the real world. Therefore,

the user is encouraged to play around with this tool to enhance their understanding of controls.

6 Aircraft roll

Considering the following states and output matrix equations describing the lateral directional

equations of motion of an aircraft.

dx/dt=Ax(t)+Bu(t)……………………….(1)

y(t)=Cx(t)+Du(t)………………………….(2)

ALL the four states of ‘x’ are available for the controller. When the parameter in the plants have non

–linearities and time –varying dynamics, the control system should posses a mechanism for

automatically adjusting them. By using a fixed controller we cannot achieve a satisfactory

compromise between robust stability and performance. Then we have to use adaptive control. The

adaptive control use is justified on complex and mission critical systems exihibiting time varying

dynamics.

The roll angle motion of an aircraft is controlled by adjusting roll angle signal. In this study, an auto-

pilot controller is modeled to control the roll angle of an aircraft. The roll motion depends upon many

parameters like side slip angle, rolling rate, yawing rate, aileron deflection and so on.

By applying Newton’s law and making relevant assumptions for simplification and finding the transfer function,

the transfer function from aileron deflection angle to roll angle is given by the following equation (3)

.........................................(3)

All these parameters are time dependent and time-varying dynamics.

In most of the research literature, different control algorithms and methods are discussed for reconfigurable control . There are different control approaches. Among them adaptive control is widely used because the controller has the ability to analyze nonlinearities and time-varying dynamics that are found in most of the processes. Several control strategies have been proposed such as PID , fuzzy logic , neural networks , LQR . Among all, PID is very simple and easy to control nonlinearities and time-varying parameters. A fixed controller cannot be implemented to achieve satisfactory results. So, continuous adaption to these parameters is required for controlling of roll motion. An adaptive control is modelled for the roll motion i.e., dependent on different dynamic parameters.

For the design of PID (Proportional-Integral-Derivative) controller, we require the specification of three parameters: proportional gain, integral time constant and derivative time constant. The following transfer function describes the PID controller:

Gc (s) = Kp + Kp/Ti.s + Kp.Td.s ------- (2)

It can also be re-written as

Gc (s) = Kp + Ki/s + Kd. s ------- (3)

Where Kp is the proportional gain

Ki = Kp/Ti is the integral gain

Kd = Kp /Td is the derivative gain of the controller.

The discrete time equivalent expression can be given as

u(k) = Kpe(k)+Ki Ts Σe(i) + Kd /Ts ∆e(k) ----- (4)

Where u(k) is the control signal ‘i’ is considered from 1 to n.

e(k) is the error signal between reference input and the plant output.

Ts is the sampling period

and ∆ e(k) = e(k)- e(k-1).

The PID parameters Kp, Ki , Kd are manipulated to produce various response curves for a given plant. The parameters of PID controller can be changed in two types. Firstly, by using Zeigler-Nichols tuning formula. In second way, adaptively the parameters are estimated and hence they are called adaptive controllers.

6.1 MODELLING OF PID CONTROLLER

The general structure of a auto-pilot control system will be as shown in . Specifically, the aileron deflection is controlled by the roll control loop. The roll control block diagram is as shown in fig. (i). The deflection of ailerons is achieved from the force initiated by actuators. The amount of force, direction and angle how much the deflection must be, all these parameters are obtained by the control system. The input to the control system is the data from different sensors. The data obtained from the sensors is mixed in data fusion and filtering unit and if any error occurs it is minimized by the controller.

Figure.(i)

In this study, the controller here in the block diagram is PID controller i.e., implemented by MATLAB simulink. The MATLAB simulink diagram of PID controller is as shown in fig.(ii).

Figure.(ii)

The input to the PID controller is the error signal i.e., obtained by the difference between input and feedback from the plant. In this study, as we are considering the roll angle motion of an aircraft, we limit ourselves for acceptable stability and medium fastness. We modeled a MATLAB simulink model as shown in fig.(ii) considering the plant as roll motion control.

After extensive simulation study on various values for parameters of PID controller for roll transfer function implementation, we determined values for Kp, Ki , Kd as a good compromise between stability and performance. The Ku value is tuned and chosen, the point of sustained oscillations. By using Ku and relationship equations , Kp, Ki , Kd values are determined and the response for the particular values are shown in the results. The Kp, Ki , Kd values are manipulated for different values and final appropriate response is considered for the better error reduction of the sensed input data. The resultant signal with minimum error will be given to analog to ARINC 429 converter and then to actuators followed by ailerons for the smooth and stable aileron deflection of an aircraft for roll. Always roll motion should be performed in cruise state only.

6.2 RESULTS

The open loop response of the system is not considered because of its exponentially rising output, as it does not use feedback for necessary corrective measure. The closed loop structure with feedback mechanism provides a better response with ringing and longer settling time. To achieve a better response, a PID controller has been modelled with the plant. The response of the system with the plant is more stable with less ringing and settling time, with some considerable overshoot. The transient characteristics of the PID controller are

7. Yaw Control

In flight, any aircraft will rotate about its center of gravity, a point which is the average location of the mass of the aircraft. We can define a three dimensional coordinate system through the center of gravity with each axis of this coordinate system perpendicular to the other two axes. We can then define the orientation of the aircraft by the amount of rotation of the parts of the aircraft along these principal axes. The yaw axis is perpendicular to the wings and lies in the plane of the aircraft centerline. A yaw motion is a side to side movement of the nose of the aircraft as shown in the animation.The yawing motion is being caused by the deflection of the rudder of this aircraft.

On all aircraft, the vertical stabilizer and rudder create a symmetric airfoil. This produces no side force when the rudder is aligned with the stabilizer and allows the combination to produce either positive or negative side force, depending on the deflection of the rudder. Some fighter planes have two vertical stabilizers and rudders because of the need to control the plane with multiple, very powerful engines.

7.1 Yaw damper

In order to control the yaw motion of the aircraft yaw damper is used. A yaw damper is a device used on many aircraft (usually jets ) to damp (reduce) the rolling and yawing oscillations known as the Dutch roll mode. It requires yaw rate sensors and a processor that provides a signal to an actuator connected to the rudder. The use of a yaw damper helps to provide a better ride for passengers, and on some aircraft the yaw damper is a required piece of equipment to ensure that the aircraft stability remains within certification values.

Dutch roll mode:

A Dutch Roll is a combination of rolling and yawing (coupled lateral/directional) oscillations that normally occurs when the dihedral effects of an aircraft are more powerful than the directional stabilityDutch roll is a type of aircraft motion, consisting of an out-of-phase combination of "tail-wagging" and rocking from side to side. This yaw-roll coupling is one of the basic flight dynamic modes.  Dutch roll stability can be artificially increased by the installation of a yaw damper

7.2 Yaw Damper design

The design of a YAW DAMPER for a 747® aircraft using the classical control design features in Control System Toolbox™.

A simplified trim model of the aircraft during cruise flight

has four states:

beta (sideslip angle), phi (bank angle), yaw rate, roll rate

and two inputs: the rudder and aileron deflections.

All angles and angular velocities are in radians and radians/sec.

Given the matrices A,B,C,D of the trim model, use the SS command to create the state-space model in MATLAB®:

A=[-.0558 -.9968 .0802 .0415; .598 -.115 -.0318 0; -3.05 .388 -.4650 0; 0 0.0805 1 0];

B=[ .00729 0; -0.475 0.00775; 0.153 0.143; 0 0];

C=[0 1 0 0; 0 0 0 1];

D=[0 0; 0 0];

sys = ss(A,B,C,D);and label the inputs, outputs, and states: figure 1

set(sys, 'inputname', {'rudder' 'aileron'},... 'outputname', {'yaw rate' 'bank angle'},... 'statename', {'beta' 'yaw' 'roll' 'phi'});This model has a pair of lightly damped poles. They correspond to what is called the Dutch roll mode. To see these modes, type

axis(gca,'normal')h = pzplot(sys);setoptions(h,'FreqUnits','rad/s','Grid','off');The pole zero plot is shown in fig. 1

"Grid" is selected to plot the damping and natural frequency values. In order to design a compensator that increases the damping of these two poles.

Start with some open loop analysis to determine possible control' strategies. The presence of lightly damped modes is confirmed by ' looking at the impulse response:'

impulseplot(sys)The plot is shown in figure 2

Figure 2

To inspect the response over a smaller time frame of 20 seconds, you could also type

impulseplot(sys,20)

The plot is shown in figure 3.

Figure 3.

Look at the plot from aileron to bank angle phi. To show only this plot, right-click and choose "I/O Selector", then click on the (2,2) entry.

This plot shows the aircraft oscillating around a non-zero bank angle. Thus the aircraft turns in response to an aileron impulse. This behavior will be important later.

Typically yaw dampers are designed using yaw rate as the sensed output and rudder as the input. In order to inspect the frequency response for this I/O pair we use the bode plot.

sys11 = sys('yaw','rudder'); % select I/O pairh = bodeplot(sys11);setoptions(h, 'FreqUnits','rad/s','MagUnits','dB','PhaseUnits','deg');The plot is shown in figure 4.

This plot shows that the rudder has a lot of authority around the lightly damped Dutch roll mode (1 rad/s).

A reasonable design objective is to provide a damping figure 4

ratio zeta > 0.35, with natural frequency

Wn < 1.0 rad/s. The simplest compensator is a gain.

We use the root locus technique to select an adequate feedback gain value:

h = rlocusplot(sys11);setoptions(h,'FreqUnits','rad/s')The figure is shown in figure 5.

Hence, we need positive feedback!

Figure 5.

So after giving the positive feedback

h = rlocusplot(-sys11);setoptions(h,'FreqUnits','rad/s')The plot is given in figure 6.

This gives better results. When we click on the blue curve and move the black square to track the gain and damping values. The best achievable closed-loop damping is about 0.45 for a gain of K=2.85.

Figure 6.

The SISO feedback loop is closed and the impulse response is observed.k = 2.85;cl11 = feedback(sys11,-k);Note: feedback assumes negative feedback by default

impulseplot(sys11,'b--',cl11,'r') legend('open loop','closed loop','Location','SouthEast')The response is shown in figure 7.

The response looks pretty good.

Figure 7

The loop was closed around the full MIMO model and the response from the aileron was observed.. The feedback loop involved input 1 and output 1 of the plant:

cloop = feedback(sys,-k,1,1); impulseplot(sys,'b--',cloop,'r',20) % MIMO impulse responseThe response is shown in figure 8.

The yaw rate response is now well damped.

Figure 8.

Figure 8

When moving the aileron, however, the system no longer continues to bank like a normal aircraft, as seen from

impulseplot(cloop('bank angle','aileron'),'r',18)

You have over-stabilized the spiral mode. The spiral mode is typically a very slow mode that allows the aircraft to bank and turn without constant aileron input. Pilots are used to this behavior and will not like a design that does not fly normally.

In order to make sure that the spiral mode doesn't move farther into the left-half plane when we close the loop. One way flight control designers have fixed this problem is by using a washout filter.

In signal processing, a washout filter is a filter that makes a transition caused by changes in the input source more smooth. An example of this transition is the change in the modes of a signal. The general form of this filter is: H(s) = s/(s+a)

Washout Filter:

Using the SISO Design Tool (help sisotool), you can graphically tune the parameters k and a to find the best combination. In this example we choose a = 0.2 or a time constant of 5 seconds.

Form the washout filter for a=0.2 and k=1

H = zpk(0,-0.2,1);the washout is connected in series with the design figure 9

model, and root locus is used to

determine the filter gain k: figure 9

oloop = H * (-sys11); % open loop'h = rlocusplot(oloop);setoptions(h, 'FreqUnits','rad/s')sgridThe plot is shown in figure .9 Figure 10The best damping is now about zeta = 0.305 for k=2.34.

The loop was closed with the MIMO model and the impulse response was checked. Figure 10

k = 2.34;wof = -k * H; % washout compensatorcloop = feedback(sys,wof,1,1); impulseplot(sys,'b--',cloop,'r',20)The impulse response is shown in figure 10.The washout filter has also restored the normal bank-and-turnbehavior . figure 10

The impulse response from aileron to bank angle shows

that the washout filter had restored the normal bank-and-turn behaviour.

impulseplot(sys(2,2),'b--',cloop(2,2),'r',20)

legend('open loop','closed loop','Location','SouthEast')

The response is shown in the figure 11

This design substantially increases the damping while allowing the pilot to fly the aircraft normally.

8. Simulink block diagram of Aircraft Control System.

9. Flow chart of pitch control

10. FLOWCHART OF ROLL CONTROL :

SELECTION OF MATRIX EQUATION FOR ROLL CONTROL OF AIRCRAFT

DEVELOPMENT OF APPROPRIATE TRANSFER FUNCTION

MODELLING OF PID CONTROLLER FOR ROLL CONTROL

AILERON DEFLECTIONCONTROLLED ROLL MOTION

11.FLOWCHART OF YAW CONTROL

12 Aircraft Control Design Analysis

12.1) Pitch control design and result analysis:

We have built a physical setup and used system equations to build the state space model for pitch control of the aircraft. At first we implemented the open loop model by using state space block in Simulink. We find the open loop response of the created model in the scope. The response is found to be unstable with very high settling time. Hence we intended to stabilize the response by implementing a closed loop model. The closed loop model is similar to our open loop model except of the fact that we added a state feedback control gain block to it. Again we see the closed loop response of our newly created model in the scope. Now we find the response is stabilized with minimum settling time and less oscillations. Thus we achieve our intended model of pitch control system for our aircraft.

12.2) Roll control design and result analysis:

Having noted the limitations of the open loop system in our pitch control design we introduced a closed loop system with efficient characteristics using PID controller in our roll control design. The PID controller has dynamic response compared to other normal controllers and hence is chosen for our roll control design. This design controller possesses response time in milliseconds with very good settling time but with considerable overshoot as seen in the response generated in the scope due to the simulation of the roll control model designed by us. Continuous adaption to parameters like sideslip angle, rolling rate, aileron deflection etc is required for controlling of roll motion. Hence, a fixed controller cannot be implemented to achieve the satisfactory results. So a PID controller is used to control non-linarites and time varying parameters. The Kp, Ki and Kd values are chosen so that we can have a good compromise between stability and performance.

12.3) Yaw control design and result analysis:

In this yaw control design we have designed a yaw damper for a 747 jet aircraft using the classical control design features in control system toolbox in MATLAB (Simulink). A simplified trim model of the aircraft during cruise flight is considered. A state space model is created in MATLAB to create the yaw damper. The two inputs to our yaw damper model are the rudder and aileron deflections. The outputs of the yaw damper model designed by us are yaw-rate and bank angle. We have considered a Dutch roll mode for our analysis and so this model has a pair of lightly damped poles as seen in our pole zero map and also the impulse responses. Typically yaw dampers are designed using yaw rate as the sensed output and the rudder as the output. So we inspect the frequency response for this I/O pair using bode diagram. This plot shows that the rudder has a lot of authority around the lightly damped Dutch roll mode. So we have to provide a damping ratio zeta>0.35 with natural frequency Wn<1.0 rad/sec. The simplest compensator is a gain. Within use the root locus technique to select an adequate feedback gain value. The root locus plot shows we need positive feedback. Finally we find the best achievable closed loop damping is about 0.45 for a gain of K=2.85. With this SISO feedback loop the impulse response looks pretty good. Now we close the loop around the full MIMO model and see how

the response from the aileron looks. The yaw rate response is now well damped. But we find that we have over stabilized the spiral mode as the system no longer continues to bank like a normal aircraft as seen from the impulse plot of bank angle and aileron. Pilots are used to spiral mode and so we have to make sure that the spiral mode does not move farther into the left-half plane when we closed the loop. We have fixed this problem by using a washout filter with proper tuned parameters (as found by us). Finally the best damping is found to be zeta=0.305 for K=2.34. Next we close the loop with the MIMO model and check the impulse response. We find that the washout filter was also restored the normal bank-and-turn behavior as seen by looking at the impulse response from aileron to bank angle. Thus the yaw damper designed by us meets our predefined requirements.

13 Future aspects of this project

The use of simulation in the development of aircraft and aircraft systems has become prevalent throughout the domain of the aircraft product development process. Rapid advances in aircraft technology and growth in the sophistication of this technology is requiring more sophisticated methods of developing, integrating, testing, and certifying systems be employed. Luckily, when done well, the investment in simulation based aircraft testing software, systems, and IT infrastructure has offered significant returns and has resulted in risk mitigation, reduced loss of life, less flight testing, and brings new technologies into the products much quicker than previous processes . Real-time, hardware-in-the-loop, pilot-in-the-loop simulation, and real-time open-loop testing have become the go-to approaches to help bring down to size an ever-increasingly challenging set of tasks. These methods are found in iron bird simulators, aviation integration labs, cockpit development and verification labs, and in the system verification departments at the typical aircraft subsystem supplier.In the decade from 2000 to 2010, a tremendous amount of technology advancement was seen using Simulink models to design a system, and use Simulink-interfaced code generators to output C code providing the behavioral capability associated with any intelligent subsystems within the designed system.The Flight Test Program represents the final system integration testing effort. Model based verification involves testing one or more systems interfaced with simulation in order to put the system(s) through normal and failure mode conditions that are highly representative of the complete aircraft behaviour.

Design of aircraft control system using MATLAB (Simulink) will help to perform model based system verification in a timely and cost-effective manner today and in years to come.

14. Conclusion

Model building is a fundamental process . An aircraft designer has a mental model of the type of the aircraft that is needed, uses physical models together wind tunnel data , and designers with mathematical models that incorporate the experimental data. The modelling process is often iterative ; a mathematical model based on the laws of physics will suggest what experimental data should be taken and the model may then undergo considerable refinement in order to feed the data. In building the mathematical model we recognise the onset of the law of diminishing returns and build a model that is good enough for our purposes but has known limitations. Some of these limitations involve uncertainty in the values of parameters. Later we attempt to characterize this uncertainty mathematically and allow for it in control system design.

Actually, because of the high cost of building and flight testing a real aircraft , the importance of the mathematical model goes far beyond design. The mathematical model is used in conjunction with computer simulation ( like MATLAB Simulation) to evaluate the performance of the prototype aircraft and hence improve the design. It can also be used to derive training simulator , to reconstruct the flight conditions involved in accidents, and to study the effects of modifications to the design.

Hence it can be concluded that in our project the motion of the aircraft is stabilized by controlling the motion of the aircraft along the three axis that is pitch, roll and yaw. The pitch motion is stabilized by using a state feedback control gain block. The roll motion is stabilized by using a PID controller. And the yaw motion is stabilized by using a yaw damper.

15. Bibliography

I. Editors- v.Sridhar, Holalu Seenappa Sheshadri, M .C Padma, ‘Emerging research in Electronics , Computer science &technology’ (Proceedings of International Conference , ICERECT 2012).

II. Modelling of Closed Loop PID Controller for an Autopilot Aircraft Roll Control sited in International Conference on Recent Advances in Communication VLSI & Embedded Systems(2014).

III. By Ashish Tewari,Departmet of Aerospace Engineering,IIT Kanpur ‘Automatic Control of Atmospheric & Space Flight Vehicals: Design &Analysis with MATLAB and Simulink ‘( 4th August,2011)