Flight control - root location, time constant , Other Engineering

In a continuous time linear system whenever any of the characteristic roots, say λ, has a positive realpart, ie Re(λ) = λR > 0, then the system is unstable. Stability is ensured i 3 each root λ has a negative real part, ie λR > 0. Typical time responses for stable systems are shown in figure 4.1 and unstable systems in figure 4.2. Note the unstable response is the reverse time plot of the stable plot with the initial and final values interchanged ; clearly this is because reversing the sign of the roots is equivalent to reversing the time variable ie (-λ)(+t) = (+λ)(-t).

In a discrete time, sampled data, systems the stability criterion is that the characteristic roots have magnitude less than 1, ie lie in the unit circle in the complex plane. However this course only considers continuous systems. 

Real Roots

Modes of purely real roots are non-oscillatory. When a C.E. such as p(s) = 0 (where p(s) is a polynomial of order n) has a real root it can be factored p(s) = (s-λR)q(s) = 0 where q(s) is a polynomial of orderone less than p(s). Then s = λR clearly satisfies the equation. The variable s is a complex frequency expressible in units of [s-1]. The inverse of -λR is termed the time-constant of the root τ that is τ = -1/λexpressible in units of [s]. 

91_real root.png

Posted Date: 8/27/2012 3:55:51 AM | Location : United States







Related Discussions:- Flight control - root location, time constant , Assignment Help, Ask Question on Flight control - root location, time constant , Get Answer, Expert's Help, Flight control - root location, time constant Discussions

Write discussion on Flight control - root location, time constant
Your posts are moderated
Related Questions
Q.  There is no end centered tetragonal lattice in the bravis list, but there is an end centered orthorhombic lattice. Explain why this is so? Ans.  A tetragonal system is

External cooling Cooling of the external skin of an aero-engine is achieved by suitable design of the aircraft airframe; the layout will depend upon where the engine is fitted



2. Differentiate between stream oriented and data gram oriented socket in java?

THE IDEAL OPERATIONAL AMPLIFIER Although the characteristics of an ideal operational amplifier are unattainable, modern integrated circuit types can provide an extremely close

I need help in engineering mechanics questions? Do you provide homework help, Please let us know how do i get it quich time...

would you help with Evans diagram( draw and explain) for Iron in seawater,and how variability of Oxygen concentration affect the electrode potential vs.current?

what do you mean by diffraction of light? what is the diffrence between interference and diffraction of light?distinuish between Fresnel''s and Fraunhofer''s diffraction.

find voltage gain of junction field effect transistor