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

Caselet- 2, suggestion regarding credit limit. should it be approved or not...

suggestion regarding credit limit. should it be approved or not what should be the amount of

Case study, Which type of financing is appropriate to each firm?

Which type of financing is appropriate to each firm?

Laser beam welding, In laser beam welding coalescence is produced by the he...

In laser beam welding coalescence is produced by the heat obtained from the application of a concentrated coherent light beam impining upon the surface to be joined .   It con

Drilling assignment, I need help in doing a project in excel that has ever...

I need help in doing a project in excel that has everything about drilling like mud pump etc ..

Process control, sir how can I find the transfer function of control valve

sir how can I find the transfer function of control valve

#title: Signal Processing, how to load a large file consisting hex bytes wi...

how to load a large file consisting hex bytes without spaces and plot the required bytes

Accounting rate of return method, Accounting rate of return method ARR met...

Accounting rate of return method ARR method is also known as ‘Return on Investment Method’. Here accounting information as shown in the financial statement is the basis for measu

Double acting feathering system, Double acting feathering system: To pr...

Double acting feathering system: To prevent excessive drag in the event of a propeller on engine failure, the double acting propeller as with the single acting propeller requir

Diod, i donot under stand about diod and transistor

i donot under stand about diod and transistor

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