CONTROL SYSTEM ANALYSIS

Control System Analysis



[Name of the Institute]

Control System Analysis

Assignment 01

The given perubed equations for the longitudinal dynamics of aircraft are

?u? (t) = Xu ?u + Xw ?w - g (?0??) + XdEdE +Xuu0(t)

?w?(t) = Zuu0(t) + U0q - g (?0 ?? ) + ZdE dE + Zu ?u + Zw ?w

?q?(t) = (Mu + Mw? Zu )u0(t) + (Mu + Mw? Zu )?u(t)+ (Mu + Mw? Zw )?w(t) + ( Mq + Mw? U0)?q(t) - gMw?(?0??) + ( MdE + Mw? ZdE ) dE

??. = ?q.

State Space Representation

= +

Assignment 02

Common Terms Used

Eigen value

“Complex numbers, ? that satisfy Ax = ?x where A is a n*n matrix and x is some vector.

In this case, x is called an eigenvector.” (LBM)

Static error

Difference between the input and the output values when t?8 and the temporal evolution of these signals is almost null.

PID Controller

“A PID controller attempts to correct the error between a measured process variable and a desired set point by calculating and then outputting a corrective action that can adjust the process accordingly and rapidly, to keep the error minimal.” (Wikipedia 2009)

Dirac impulse

“I t is defined as the function which is representing an infinitely sharp peak bounding unit area. This function d(x) has the value zero everywhere except at x = 0 where its value is infinitely large in such a way that its total integral is 1.” (Wikipedia 2009)

Step function

Discontinuous function whose value is zero before the step time and A after, where A is a constant different from zero.

Introduction

Aircrafts are never stable by themselves, they need to control. Otherwise they would fly in a constant turn. In order to make this aircraft fly in the direction we want, we have to make corrections at any time. There are two ways of making these corrections: the first one is a correction by the pilot, and the other is by the automatic flight control system (AFCS). This

AFCS uses a feedback control which is much more accurate and faster, and which can eliminate some disturbances. (Mc Lean 1990)

But sometimes and under some conditions these feedback control systems tend to oscillate.

That is why the AFCS system is not really stable. If we use a high amplification, the response will be more accurate and faster but the system will be less stable. Then we have to find a compromise between stability and accuracy when we design a system like the AFCS.

As we want to study aircraft stability, we have to make a model of the aircraft. The first step for this modeling is to know which equations are used for the flight dynamics. Then we will integrate them in the aircraft model. Most of these equations are non-linear but we will see that we can get a linear model which is really close from the non-linear model but much easier and faster for the simulations.

In order to understand the stability phenomenon we will first study the flight dynamics of the aircraft without trying to control it. Then we will see ...