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Impulse response For

or characterize a linear system can be applied to some type of input test signals and observing its output. The most common test signals are the unit impulse, unit step and sinusoidal signals. The system's response to a test signal is a property description or mathematical model thereof. The characterization used in systems analysis is that when the input is a Dirac Delta unit impulse applied at time t = τ anyone. Excitation by a unit impulse is equivalent to applying the system input an infinite number of frequencies with equal amplitude, and the output of the system will reply to each and every one of the infinite present in the input frequency. In this case the output is called "impulse response", "impulse response" or "IR" system "and is represented by h (t, τ). Therefore, in a linear system characterized by transformation of the impulse response is from (2.1)





An RLC circuit RLC circuit is one which has as components a resistor, a capacitor and an inductor connected in series in a time equal to zero, the capacitor has a maximum load (Qmax). After a time equal to zero, the total energy of the system is given by the equation presented in this section oscillations in LC circuits U = [Q2 / (2C)] + (LI2 / 2) The oscillations in LC circuits had mentioned that the oscillations were not damped since the total energy remained constant. RLC circuits, since there is resistance, there are damped oscillations because there is a part of the energy converted into heat in the resistance. The total energy change depending on the weather system is given by the energy dissipation in a resistor: dU / dt = - 2R Then we derive the total energy equation with respect to time and replaced the one given: LQ "+ RQ '+ (Q / C) = 0 You can see that the RCL circuit is a damped oscillatory behavior: m (d2x/dt2) + b (dx / dt) + kx = 0 If we take a small resistance, the equation would change : Q = Q max e - (Rt/2L) Cos wt, w = [(1/LC) - (R/2L) 2] 1 / 2 The higher the resistance value, the swing buffer will set faster would absorb more energy from the system. If R is equal to (4L / C) ½ the system is overdamped.




Routh stability test-Hurtwitz.

Stability.
In studying the stability of a system must distinguish between absolute and relative stability. Absolute stability

:
If a linear time invariant stable return to its equilibrium condition after being subjected to a disturbance in one of its entries. Mathematically, it is known that a system is stable when all roots of its characteristic equation are located in the left half-plane s-plane Stability
Relative
refers to the degree of stability of response and is measured by parameters such as damping factor () and the maximum peak Mp. Ruth

Criteria:
The stability criterion of Routh-Hurwitz for a closed-loop system does not require the calculation of the values \u200b\u200bof the roots of the characteristic equation, this criterion only indicates if the roots are on the right side of the imaginary axis .

Second Order Systems

Mathematically, a second-order system is governed by a differential equation of second order (ie, reducible to terms with second derivatives. From the physical point of view, these systems must be able to store energy and then return late, so they tend to cause oscillations. Typical examples of second-order systems are a set of spring and damper, or an RLC circuit with the "swing" of reactive power between the condenser coil. Reduced order systems


In some cases, higher order systems can be simplified to result in lower-order systems easier to analyze.

A) Dominance: poles and zeros away.
B) Cancellation: Pairs of poles and zeros coming. Definition