Definition - 1st-order system and 2nd-order system

From mathematical or control system point of view, what is the definition of
1) 1st-order system
2) 2nd-order system

Is this, (s+2)/(s+5), considered a 1st-order system?

Thanks.

1st order system contains 1 energy storing element and 1 element which dissipates energy. e.g mass - damper system.

the system given is 1st order system.

second-order system has no zeros in the transfer function.

powersys,
The order of a system is equal to the number of poles. In your example, the number of poles (values of s for which the denominator = 0) = 1. The number of zeros (values of s for which the numerator = 0) = 1. Your example represents a 1 pole, 1 zero system, with a pole at s=-5, and a zero at s=-2.
Regards,
Kral

Is it possible that the pole of a first-order system is a complex number?

Thanks.

powersys,
Not if the transfer function represents a physical system, such as a control system or filter. Poles of a transfer function representing a physical system are either real, or occur in complex pairs. Of course, a pole can be complex, but since it does not represent a physical system, it would be of interest only to pure mathemeticians, not engineers.
Regards,
Kral

Added after 3 minutes:

powersys,
I meant to say "complex conjugate pairs" not "complex pairs".
Regards,
Kral

When we write any equation
suppose x²+4x+4 or
X³+X²+X+1 etc.
How can we comment by looking at the equation whether the System representing equation is 1st or 2nd or 3rd order?

Is it that there is X³ so system is 3 rd order or X² is there so system is 2nd order?
please remove my confusion regarding order of equation
thanks

Kral said:

powersys,
Not if the transfer function represents a physical system, such as a control system or filter. Poles of a transfer function representing a physical system are either real, or occur in complex pairs. Of course, a pole can be complex, but since it does not represent a physical system, it would be of interest only to pure mathemeticians, not engineers.
Regards,
Kral

Added after 3 minutes:

powersys,
I meant to say "complex conjugate pairs" not "complex pairs".
Regards,
Kral

Click to expand...

Assume that there is a 1st-order physical system with complex pole, what will be step response of such system? Can we solve it 'mathematically'?
Thanks

Abhishekabs,
By definition, the order of a system is the value of the highest exponent that appears in the denominator of the transfer function. For your examples, if the polynomials you give appear in the denominator, then the 1st system is 2nd order, and the 2nd system is 3rd order.
Regards,
Kral

Added after 24 minutes:

powersys,
A 1st order system with a complex pole can be solved, but the solution would be meaningless in a physical sense. For example, consider the following transfer function, which has a single complex pole:
F1(s) = 1/(s + (a+jb)) = [1/(a+jb)] / [1 +(1 + (1/a+jb)s].
Calculate the step response of the system represented by this transfer function:
F2(s) = [1/s]F1(s).
The solution is:
f(t) = [1/(a+jb)][1-exp(-t/)a+jb)).
This is a perfectly good mathematical solution, but it has no meaning in a physical sense, because of the 1/(a+jb) factor.
Regards,
Kral

The transfer function you give can be rewritten as,
\[\frac{s+2}{s+5}=1-\frac{3}{s+5}\]
You can see from this that there is direct zeroth-order feedforward term (1) and
there is a first-order term. So if you excite this system with a unit-step
\[u(t)\] function, the response would have a constant step (zeroth order term) plus a first-order response term.

Best regards,
v_c