Can the non standard type of second order system also use the closed loop characteristic equation to

OK. There is a kind of problem that gives you a response, and asks you to extract the information to find its transfer function, and you can generally find the natural vibration angle frequency and damping ratio through the image. Then, according to the type of the system, the basic form of its open-loop transfer function is set, and at this time, it cannot be directly brought in with the basic form of the second-order system, because not all second-order systems can be converted into the standard form.

However, after we set up the basic form of open-loop, we can find the closed-loop transmission function immediately after that, and after a little transformation, the denominator can be listed in the standard form and the damping ratio and the two functions of the natural oscillation angle frequency, and its transfer function can be found by solving it. The open-loop transmission letter we set up here is not a standard form, but it can also be used to solve the formula, and the final gap is a magnification difference.

The characteristic equation of the so-called system.

Refers to making the loop closed.

An equation in which the denominator of the transfer function is zero.

The significance of this is that the closed-loop pole can be solved, and the closed-loop pole determines the motion mode of the system response.

Quite simply, by definition, the eigenequation is the denominator of the closed loop (0), and I don't think this needs to be explained.

Let me talk about the open-loop case: let the open-loop transfer function gh=a b, then fai=g (1+gh).

The characteristic equation is 1+GH=0, that is, 1+a b=0, that is, (a+b) b=0, that is, a+b=0, which is the intuitive numerator plus denominator.

Anyway, for the characteristic equations, yes"If the closed loop is given, the direct denominator is zero; If you give an open loop, find out the closed loop and let it have a denominator of zero"

This transfer function.

It is not a standard form of second-order system quarrel. It is a closed-loop system with the addition of a zero point.

Consider a second-order system before the zero point is not added, wn 2 = 3,2 * damping ratio.

wn=2, you can get wn=root number 3, damping ratio = 1 root number 3

However, it should be noted that the system has a scale factor of 1 3, and the additional zero point -1 will change the dynamic deficit performance of the system.

Feel free to ask

This transfer function is not a standard form for second-order systems. It is a closed-loop system with the addition of a zero point.

Considering the second-order system before the zero point is not added, wn 2 = 3, 2 * damping ratio * wn = 2, we can get wn = root number 3, damping ratio = 1 root number 3

However, note that the system has a scale factor of 1 3, and the addition of zero point -1 will change the dynamic performance of the system.

First, it is not unaffecting, because the dynamic performance and so on will change, the essence is because the transfer function is not a standard second-order system, and if these two quantities are really required, they can only be calculated in this way.

Second, the scale factor is because after ignoring that zero point, since the standard second-order system form is wn 2 s 2 + 2 * damping ratio * wn + wn 2, so if there is no scale factor, the numerator should be 3, and now it is 1, so there is a scale factor 1 3.

First, according to g (1+g), the open-loop transmission letter g (s+1) (s +s+2) after adding the proportional differentiation is obtained, and then the ratio differentiation of s+1 is removed, and the original open-loop transmission letter of the system is 1 (s +s+2).

Performance indicators: Adjustment time ts: The unit step response c(t) enters the error band by 5% (sometimes 2%), and no longer exceeds the minimum time of the error band.

Overshoot %The ratio of the maximum excess to the steady-state value in the unit step response. Peak time tp: The time it takes for the unit step response c(t) to exceed the steady-state value to reach the first peak.

Structural parameters: directly affect the unit step response performance.

1 s is the Ralcollett transform of the unit step input.

h(s)=g(s)*r(s)；r(s)=1 s, the transfer function g(s) is second-order, and you have not yet learned the basic concepts.

Generally, the culvert is open-loop, and the closed-loop transmission letter can be found by open-loop The characteristic equation is the denominator of the closed-loop Take the negative feedback system as an example Closed-loop = open-loop (1+open-loop). The eigenequation is an equation with a denominator of a closed-loop transfer function of zero. If you are told to open the loop message, you need to find the closed-loop letter first.

If the open-loop transmission letter of a negative feedback closed-loop system is g(s), then the closed-loop transmission function is (s)=g(s) [1+g(s)], and the fractional form of the closed-loop transmission letter must be sorted out and simplified (simplified to the point that it can no longer be simplified), so that the denominator of the simplified closed-loop transmission letter is zero, so as to obtain an equation, which is the characteristic equation, and the solution of the characteristic equation is the root of the characteristic equation, which is also called the pole of the closed-loop transmission signal.

The eigenequation is an equation with a denominator of a closed-loop transfer function of zero. If you are told to open the loop message, you need to find the closed-loop letter first.

If the open-loop transmission signal of a negative feedback closed-loop system is g(s), then the closed-loop transmission signal is (s)=g(s) [1+g(s)].

The fractional form of the closed-loop communication letter must be sorted out and simplified (simplified to the point that it can no longer be simplified), so that the denominator of the simplified closed-loop communication letter is zero, so as to obtain an equation, which is the characteristic equation, and the solution of the characteristic equation is the root of the characteristic equation, which is also called the pole of the closed-loop transmission letter.

I don't understand your question very well, if you know the damping ratio, you can draw a damping line, if the damping line has an intersection point with the root trajectory, and this intersection point can be regarded as the dominant pole, then you can set the intersection point, the form is the form of the root when the standard second-order system is under-damped (the damping is known, only wn is unknown), and then we should pay attention to how many root trajectories the system has, for example, the system is a third-order system, then each parameter k corresponds to 3 eigenroots, and the dominant poles mentioned above are a pair, The third pole can be assumed and should be on the real axis; Substitute the dominant pole you just set into the characteristic equation and compare it with the characteristic equation of the system to get the set parameters!! Find a practice question, try it out, and get a feel for it!!

The typical transfer function is the same, so that the amplification of the input signal is 1, you know, when s=0 is substituted, it reflects the magnification of the system.