OKX Wallet extension

List of the contents of this article:

• 1, Introduction to non-minimum phase system
• 2、Why is the phase angle of the proportional link of the non-minimum phase system negative 180 degrees instead of 180 degrees
• 3. Why the turbine regulation system is not the minimum phase system

Introduction to the non-minimum phase system

1. The non-minimum phase system refers to a control system with an open-loop pole or an open-loop zero in the right half of the S plane.Minimum phase system - a system in which all open-loop zeros and poles are located in the left half of the S plane.

2. Solve the characteristic equation of the system. According to the query quark information, the non-minimum phase system means that the transfer function of the system contains zero poles, and the real part of the zero point or pole is not zero. For a non-minimum phase system, its phase angle can be obtained by solving the characteristic equation of the system.

3. Because the phase angle change range of the minimum phase system is the smallest, and the phase angle change range of the non-minimum phase system is usually larger than the former, the proportional link cannot be set to a negative number. If it is a negative number, it will turn the original negative feedback into positive feedback, causing system instability.

4. Any non-minimum phase causal system can be cascaded by a minimum phase system and a full-pass system.From the amplitude-frequency response of the minimum phase system, it has the following properties: in a set of causal and stable filters with the same amplitude-frequency response, the minimum phase filter has the smallest phase offset for zero phase.

5. Under certain amplitude and frequency characteristics, the minimum phase shift system is the smallest, also known as the minimum phase shift system.

Why is the phase angle of the proportional link of the non-minimum phase system negative 180 degrees instead of 180 degrees

Because the phase angle of the smallest phase system is the most The range of phase angle change of small, non-minimum phase systems is usually more than the former.Large, the proportional link cannot be set as a negative number. If it is a negative number, the original negative feedback will become positive feedback, resulting in system instability.

In mathematics, 180 degrees and -180 degrees are equivalent, because the difference between them is only the opposite direction, not the difference in size. Therefore, in some cases, we may use both positive 180 degrees and negative 180 degrees to describe the same phase difference.

If the phase angle margin is greater than zero, the system is stable, and vice versa is unstable.

Why turbine adjustment system is non-minimum phase system

water The effect of hitting. The turbine regulation (control) system is a non-minimum phase system. Due to the influence of water strike, coupled with the complex operating conditions of the turbine, the whole system presents nonlinear and uncertain characteristics of time change, so the conventional PID control method has poor control performance in many cases.

If there is a zero or pole with a positive and real part in the transfer function, or there may be a delay link, this link is the non-minimum phase link. For a closed-loop system, if the real part of its open-loop transfer function pole or zero is less than or equal to zero, it is called the smallest phase system.

Nonminimum-phase system is a system that does not meet the minimum phase conditions. For analog signal systems, any system with one or more zeros on the right half-plane of the S plane is a non-minimum phase system.

Any non-minimum phase causal system can be cascaded from a minimum phase system and a full-pass system. From the amplitude-frequency response of the minimum phase system, it has the following properties: in a set of causal and stable filters with the same amplitude-frequency response, the minimum phase filter has the smallest phase offset for zero phase.