Contained in this strategy, in the event that efficiency is over loaded, the difference between the latest control returns and the real yields are given returning to the newest enter in of integrator with an increase out of K a to allow the latest collected value of this new integrator will be remaining on a real worth. New obtain away from an enthusiastic anti-windup control can often be selected because the K good = step one / K p to eliminate brand new dynamics of the minimal current.
Fig. 2.37 shows the newest technology from integrator windup to have an excellent PI current control, that is produced by a huge change in brand new source well worth. Fig. 2.37A reveals the fresh new results away from a recently available controller without an anti-windup handle. Because of its soaked efficiency current, the actual newest shows a huge overshoot and you will a long setting day. Additionally, Fig. 2.37B reveals a current controller that have an enthusiastic anti-windup manage. In the event that production try saturated, the new built-up value of the brand new integrator is going to be kept in the a best really worth, leading to a far better abilities.
2.six.dos.1 Growth solutions procedure of the new proportional–integral latest operator
Select the handle data transfer ? c c of one’s most recent control are within this 1/10–1/20 of modifying volume f s w and you may lower than 1/25 of sampling regularity.
The newest tips 1 and you may 2 is actually compatible with each other, we.e., this new changing regularity are dependent on the necessary bandwidth ? c c to possess current-control.
several.dos.2 Steady region of solitary-cycle DC-hook current-control
According to the Nyquist stability criterion, a system can be stabilized by tuning the proportional gain under the condition, i.e., the magnitude is not above 0 dB at the frequency where the phase of the open-loop gain is (-1-2k)? (k = 0, 1, 2.?) [ 19 ]. Four sets of LC-filter parameter values from Table 12.1 , as listed in Table 12.2 , are thus used to investigate the stability of the single-loop DC-link current control. Fig. 12.4 shows the Bode plots of the open-loop gain of the single-loop DC-link current control Go, which can be expressed as
Figure 12.4 . Bode plots of the open-loop gain Go of the single-loop DC-link current control (kpdc = 0.01) corresponding to Table II. (A) Overall view. (B) Zoom-in view, 1000–1900 Hz. (C) Zoom-in view, 2000–3500 Hz.
where Gdel is the time delay, i.e., G d e l = e ? 1.5 T s and Gc is the DC-link current PI controller, i.e., Gc sitios de citas profesionales = kpdc + kidc/s. The proportional gain kpdc of the PI controller is set to 0.01 and the integrator is ignored since it will not affect the frequency responses around ?c1 and ?c2. It can be seen that the CSC system is stable in Cases II, III, and IV. However, it turns out to be unstable in Case I, because the phase crosses ?540 and ?900 degrees at ?c1 and ?c2, respectively.
To further verify the relationship between the LC-filter parameters and the stability, root loci in the z-domain with varying kpdc under the four sets of the LC-filter parameters are shown in Fig. 12.5 . It can be seen that the stable region of kpdc becomes narrow from Case IV to Case II. When using the LC-filter parameters as Cases I, i.e., L = 0.5 mH and C = 5 ?F, the root locus is always outside the unity circle, which indicates that the system is always unstable. Thus, the single-loop DC-link current control can be stabilized with low resonance frequency LC filter, while showing instability by using high resonance frequency LC filter. The in-depth reason is that the phase lag coming from the time delay effect becomes larger at the resonances from low frequencies to high frequencies, which affect the stability of the single-loop DC-link current control.