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Embedded Systems November 2000 Vol13_12

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8 SPECTRA ble. Choose an acceptable gain that results in a stable system. Integral control Integral control, or I control, can cor- rect the DC errors of d1e proportional control. The integral gain provides low- frequency stiffness. The most common form of integration is performed as: 111 = l n- 1 + dt *e[t ] Input The e rro r is scaled by time and summed with the previous output. The result is multiplied by a gain factor: U [t ]= K ;* l n Output The higher the integral gain, the fas ter d1e control will correct. Keep in mind that d1e addition of integral gain to pro- portional gain can result in overshoot and ringing, whkh reduce bandwidth, especially wid1 higher integral gains. The inherent 90 degree phase lag, combined wid1 d1e lag in the plant and feedback ystems can cause the system to be unstabl e, if d1e gain and frequency are high enough. PI control Proportional in tegral , or PI, con trol is popula r because it provides the response of a simple P control with the abili ty to eliminate offsets stemming from disturbances. The output of this controller is the sum of two signals, one a scaled proportional and the other a scaled in tegral: U [t ] = K P * e[t ] + K ; * 111 Tuning a PI controller We tune a PI controller in two zones: high and low. We tune the proportion- al gain in the high zone and the inte- gral gain in the low zone. First, nme d1e high end as you did with the simple P controller described previously. This is done with the in te- gral gain set to zero. Watch for insta- bilities resulting from accumulated phase lag in the loop. For the integral tuning, you will again use the square wave command (input); leaving the proportional gain as desired, increase the gain of d1e in tegral control until you have reached the amoun t of overshoot acceptable Embedded Systems Programming NOVEMBER 2000 23 Input 0 90 180 270 360 I I Proportional integral, or PI, control is popular because it provides the response of a simple P control with the ability to eliminate offsets stemming from disturbances. The output of this controller is the sum of two signals, one a scaled proportional and the other a scaled integral. FICiURE la 0 90 180 270 320 Output

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