What is a non-minimum phase control system?

👉 Non-minimum Phase (NMP) systems are causal and stable systems whose inverses are causal but unstable. [ 2] Having a delay in our system or a model zero on the right half of the s-plane (aka Right-Half Plane or RHP) may lead to a non-minimum phase system.

What do you mean by minimum and non-minimum phase systems give an example of each?

Minimum phase system: It is a system in which poles and zeros will not lie on the right side of the s-plane. In particular, zeros will not lie on the right side of the s-plane. Non-minimum phase system: It is a system in which some of the poles and zeros may lie on the right side of the s-plane.

How do you find the minimum phase transfer function?

A transfer function G(s) is minimum phase if both G(s) and 1/G(s) are causal and stable. Roughly speaking it means that the system does not have zeros or poles on the right-half plane. Moreover, it does not have delay.

Why is it called non minimum phase?

Systems that are causal and stable whose inverses are causal and unstable are known as non-minimum-phase systems. A given non-minimum phase system will have a greater phase contribution than the minimum-phase system with the equivalent magnitude response.

What do you mean by maximum and minimum phase system?

A causal stable LTI system E with transfer function H(z) with all zeros inside the unit circle is called minimum phase. Definition. A causal stable system E with transfer function H(z) with all zeros outside the unit circle is called maximum phase.

What is the special about minimum phase filter?

Minimum phase filters sometimes are called minimum energy delay filters because the energy of the impulse response is maximally concentrated toward the beginning of the impulse response. All zeroes in a maximum phase FIR filter are outside or on the unit circle.

What is a right half plane zero?

The right-half-plane (RHP) zero has the same 20 dB/decade rising gain magni- tude as a conventional zero, but with 90° phase lag instead of lead. This characteristic is difficult if not impossible to compensate. The designer is usually forced to roll off the loop gain at a relatively low frequency.

What is group delay in RF?

Group delay is a measurement of the time taken by the modulated signal to get through the system. Group Delay is measured in seconds. For an ideal filter, the phase will be linear and the group delay would be constant.

Why is it called non-minimum phase?

What is the left half plane?

Let L be the y-axis. The open left half-plane HOL is the area of P on the left of L. That is, where x<0: HOL:={(x,y):x∈R<0}

What is a non-minimum phase system?

Is a working definition of a non-minimum phase system something like: a system that contains zeros in the right half of the s plane? If so, can anyone point out to a relatively simple mechanical system example that is non minimum phase, something like a modified version of the classical spring/mass/damper? Thank you.

What is the minimum phase system for this magnitude response?

The transfer function (s+2)/ (s^2 + 3s + 1) is the minimum phase system for this particular magnitude response, and the other two transfer functions are non-minimum phase systems, which hopefully is obvious from the fact that there is additional phase.

Is the inverse of my System a minimum phase system?

Since the inverse of your system is not causal, it is not a minimum phase system. To get a better insight into the concept, consider two transfer functions G 1 ( s) = s − 1 s + 2 and G 2 ( s) = s + 1 s + 2. Both the transfer functions are causal and their inverses are also causal. Both the transfer functions are stable.

Is there a way to quantify the difficulty of linear non-minimum phase control?

There are theoretical results (Theorem of Bode) that you can find in any classical control theory book that quantify the difficulty of controlling a linear non minimum phase system in terms of its zeroes in the complex right half plane. The response of a non minimum phase system to a step input has an “undershoot”.