Compensation Using the process field G PF (s) transfer function

Analysis of Bode diagram The Bode plot is popular, because many properties of process field are well read. Recorded the measured values or the identified model the following compensation technique are also used. It must be concluded if the process field has or hasn't got integral effect. It possible from the phase plot. It must be concluded if the process field has or hasn't got integral effect. It possible from the phase plot. It is necessary to determine how many time constants belongs to the process field and how close to each other these time constants. It is necessary to determine how many time constants belongs to the process field and how close to each other these time constants. It possible from the Bode plot.

Without integral effect PI compensation European structure

Without integral effect It is possible to determine from the phase plot of process field transfer function. (sufficiently low frequencies the phase shift is nearly zero.) In this case the most commonly used structure is the PI, if the process field model has got more than three poles relatively close to each other, then offered to use the PIDT structure. The quality properties of the closed loop depends on the phase margin of the G 0 (s) open loop transfer function.

Transfer function of PI compensation There are two variables. First step we chose the K C = 1, and T I = 1 rad/sec. values! In case of PIDT must be: T I > 4T D and T D > 5T conditions.

PI compensation Tenfold value of ω I the amplitude gain nearly 0. and the phase shift -5,7°

The principle of compensation of PI First we chose a considers appropriate phase margin! Rule: In case of more than 3 and relatively close to each other time constants 90°> pm > 70°; In other case pm > 45° pm: phase margin On the phase plot of process field must be looking for the chosen phase margin and the corresponding frequency will be the future ω C gain-crossover frequency. At the chosen phase margin (pm) the phase shift is ps = pm + 5.7° - 180°. The controller gain K C value to be chosen so, that at the future ω C gain-crossover frequency will be unit the K 0 loop-gain. The reciprocal value of the amplitude gain at the future gain/crossover frequency on the amplitude plot of the g 0 (the g 0 is the G 0 (s) open-loop transfer function with K C = 1 value) will be the actual K C.

The PI compensation process Have to plotted the process field Bode plot. Have to plotted the process field Bode plot. On the phase plot must be looking for the future gain- crossover frequency which is corresponding the following phase shift: ps = pm + 5, On the phase plot must be looking for the future gain- crossover frequency which is corresponding the following phase shift: ps = pm + 5, A tenth of this frequency is ω I, and T I is the reciprocal of ω I. A tenth of this frequency is ω I, and T I is the reciprocal of ω I. Must plot the Bode diagram of. Must plot the Bode diagram of. On this g0 Bode plot have to be looking for the frequency which is corresponding the chosen phase margin, next have to read the gain at this frequency. The K C controller gain is equal the reciprocal value of the readings gain. (In dB the readings value changes the sign) On this g0 Bode plot have to be looking for the frequency which is corresponding the chosen phase margin, next have to read the gain at this frequency. The K C controller gain is equal the reciprocal value of the readings gain. (In dB the readings value changes the sign)

The identified LTI model from the measured values The model seems to be self-adjusting nature. (Without integral effect) If the equitation is known, you can determine the time cons- tants, but they have generally become during the identification. When the number of the roots 4, and they are relatively close to each other is the search phase shift value: ps° ≈ pm ≈

Bode plot of G PF (s) It can be seen the rounding is permitted, but must be documented!

Determination of the T I and the g 0 Based on the above figure 10w I = 0.4 rad/sec., and so w I = 0.04 rad/sec. Creating the reciprocal value: T I = 25 sec. The g 0 open/loop transfer function with K C = 1: On the Bode plot of g0 should look for the k C gain which corresponding the phase margin = 70°.

Bode plot of g 0 (s) The gain of the controller converted from dB: K C = 47.9

To check this, the Bode plot of G 0 (s) With the rounding inaccuracy is the required phase margin.

Step response of the closed-loop It needs tuning. The integral time constant is big. There aren’t overshoot, and steady-state error

With integral effect PDT1 compensation European stucture

Analysis of Bode diagram The Bode plot is popular, because many properties of process field are well read. Recorded the measured values or the identified model the following compensation technique are also used. It must be concluded if the process field has or hasn't got integral effect. It possible from the phase plot. It must be concluded if the process field has or hasn't got integral effect. It possible from the phase plot. It is necessary to determine how many time constants belongs to the process field and how close to each other these time constants. It is necessary to determine how many time constants belongs to the process field and how close to each other these time constants. It possible from the Bode plot.

Transfer function of the PDT1 compensation There are three variables. The first step you choose K C = 1, T D = 0.9 rad/sec, and T = 0.1 rad/sec. Case PDT1 compensation must be T D > 5T.

Bode plot of PDT1 The φ max phase shift depends on the A D differential gain. Present example A D = 9, and so φ max = 54.9°.

The principle of compensation of PDT First we chose a considers appropriate phase margin! Rule: In case of more than 3 and relatively close to each other time constants 90°> pm > 70°; In other case pm > 45°. pm: phase margin On the phase plot of process field must look for the chosen phase margin and the corresponding frequency will be the future ω C gain-crossover frequency. At the chosen phase margin (pm) the phase shift is ps = pm – 54.9° - 180°. The controller gain K C value to be chosen so, that at the future ω C gain-crossover frequency will be unit the K 0 loop-gain. The reciprocal value of the amplitude gain at the future gain/crossover frequency on the amplitude plot of the g 0 (the g 0 is the G 0 (s) open-loop transfer function with K C = 1 value) will be the actual K C.

The PDT1 compensation process Have to plotted the process field Bode plot. Have to plotted the process field Bode plot. On the phase plot have to look for the future gain-crossover frequency which is corresponding the following phase shift: ps = pm – (Assuming A D = 9) On the phase plot have to look for the future gain-crossover frequency which is corresponding the following phase shift: ps = pm – (Assuming A D = 9) If A D = 9 then this frequency-third equals ω D, and this frequency of three-times is ω T. The reciprocal values of the counted frequencies are T D and T. If A D = 9 then this frequency-third equals ω D, and this frequency of three-times is ω T. The reciprocal values of the counted frequencies are T D and T. Must plot the Bode diagram of. Must plot the Bode diagram of. On this g0 Bode plot have to be looking for the frequency which is corresponding the chosen phase margin, next have to read the gain at this frequency. The K C controller gain is equal the reciprocal value of the readings gain. On this g0 Bode plot have to be looking for the frequency which is corresponding the chosen phase margin, next have to read the gain at this frequency. The K C controller gain is equal the reciprocal value of the readings gain.

The identified LTI model The model has got integral effect, because has a zero root in the denominator. If the equitation is known, you can determine the time constants, but they have generally become during the identification. When the number of the roots 4, and they are relatively close to each other the phase margin be: The search phase shift value is: ps° ≈ 65 – =

A G E (s) Bode diagramja Assuming that A D = 9.

Determination of T I and g 0 Based on above figure w D = 0.47 rad/sec. és w T = 4.2 rad/sec. and so T D = 2.1 sec., és T = 0.24 sec. The open-loop transfer function with K C = 1 g 0 is : On the Bode plot of g0 should look for the k C gain which corresponding the phase margin = 65°.

Bode plot of g 0 (s) A kompenzáló tag erősítése átváltva K C = 92.3

Step response of feedback system Possible, but not necessary additional tuning.