Contained in this system, if the yields try over loaded, the essential difference between brand new control production while the actual production are fed returning to the latest enter in of your own integrator which have a gain away from K a to let the fresh new accumulated value of new integrator would be left in the an actual worth. The newest obtain regarding an enthusiastic anti-windup control is commonly picked given that K a good = step one / K p to avoid the new dynamics of one’s limited voltage.
Fig. dos.37 reveals the fresh new sensation out of integrator windup having a great PI most recent controller, that is made by a big change in new site worth. Fig. 2.37A shows the brand new overall performance out-of a current controller versus a keen anti-windup handle. Due to the soaked productivity voltage, the actual latest showcases a large overshoot and a long form day. At the same time, Fig. dos.37B reveals a recent control with a keen anti-windup handle. In the event that output was saturated, the new gathered value of new integrator are going to be remaining at an effective right worth, causing a significantly better overall performance.
2.6.2.step one Gains selection procedure for the fresh proportional–integral most recent control
Discover control data transfer ? c c of the most recent controller to be in this 1/10–1/20 of incontri fitness veloci altering frequency f s w and lower than 1/twenty five of your own sampling frequency.
The steps step 1 and 2 are compatible collectively, i.elizabeth., the latest modifying regularity should be determined by the required data transfer ? c c to own current control.
12.2.dos Secure area for unmarried-circle 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 = 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.