Flight control - root location, time constant , Other Engineering

Assignment Help:

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


Related Discussions:- Flight control - root location, time constant

Aeroengine - velocity trinagle, If radial velocity is neglected, for a stat...

If radial velocity is neglected, for a stat or there is no change from the cascade analysis. For a rotor this vectorial For a rotor this vectorial addition gives rise to graphical

Finance, Let C(K) denote a European vanilla Call option with strike price K...

Let C(K) denote a European vanilla Call option with strike price K. Assume that all options are identical except for strike price, and strike prices satisfy (K1) What are the no-

Detection and removal of shadow from an image, plz give an exact method for...

plz give an exact method for the detection and removal of shadow from an image

Class a amplifier operation, Expertsmind.com brings you unique solution in...

Expertsmind.com brings you unique solution in electrical engineering Class A Amplifier Operation Class A amplifiers are biased so that variations in input signal polarit

Flight control - root location, In a continuous time linear system whenever...

In a continuous time linear system whenever any of the characteristic roots, say λ, has a positive realpart, ie R e (λ) = λ R > 0, then the system is unstable. Stability is ensure

Inhibit gate, Inhibit Gate Occasionally it is required to 'hold' one in...

Inhibit Gate Occasionally it is required to 'hold' one input to an AND gate at a particular logic level in order to disable the entire gate. One method of representing this sy

Difference amplifier, Difference amplifier: Figure shows how two inputs...

Difference amplifier: Figure shows how two inputs can be subtracted. This circuit differs from previous types with negative feedback in that the non-inverting terminal is not

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd