1 Introduction
2 Identification of dynamic models
2.1 Eigensystem realization algorithm method
2.2 Multivariable Output Error State-Space method
3 Cascade control
3.1 Current control
3.2 Speed control
3.3 Position control
4 Speed control loop model
4.1 State-space description of PI regulator
4.2 State-space description of notch filter
4.3 State-space description of low-pass filter
4.4 State-space description of the open-loop system
4.5 State-space description of the closed-loop system
4.6 Transformation between physical and machine parameters without reduction
5 Formulation of velocity controller tuning optimization task
5.1 Influence of amplitude characteristics
5.2 Influence of system unit step response
5.3 Influence of system distance from stability limit
5.4 The overall objective function
5.5 Boundary conditions of the optimization task
6 Simulation testing of developed optimization procedure
Parameters of objective function | ||
---|---|---|
Limit amplitude | Alim [dB] | −20 |
Optimal overshoot | ooptim [1] | 0.2 |
Limit distance from the stability limit | elim [1] | 0.5 |
6.1 Load state hm0
Machine parameters of velocity regulator | ||||
---|---|---|---|---|
Block | Parameter | Before optim. | After optim. | |
PI regulator | Amplification | Kh [1] | 30 | 27.7023 |
Integration constant | Tih [1] | 2000 | 656.3242 | |
Notch filters | Suppressed frequency | fZ1 [Hz] | 25 | 24.6693 |
fZ2 [Hz] | 135 | 135.3730 | ||
Damp | DZ1 [dB] | −5 | −71.928 | |
DZ2 [dB] | −5 | −93.4601 | ||
Bandwidth | WZ1 [Hz] | 30 | 34.3881 | |
WZ2 [Hz] | 80 | 24.1172 |
6.2 Comparison of load states
7 Verification of auto-tuning algorithm on real machine
7.1 Table without load — hm0
Kp (A.s) | Tn (A) | Damping-notch (dB) | Frequency (Hz) | Bandwidth (Hz) | Damping-notch (dB) | Frequency (Hz) | Bandwidth (Hz) | |
---|---|---|---|---|---|---|---|---|
Filter 1 | Filter 2 | |||||||
Setting 1 | 117.25 | 17,250 | 4.7 | 200 | 300 | 66 | 989 | 165 |
Setting 2 | 117.25 | 17,250 | 26 | 152 | 95 | 19 | 1500 | 300 |
Original setting | 100 | 1000 | Without filter | Without filter |
7.2 Table with one load — hm1 (~5 t)
Kp (A.s) | Tn (A) | Damping-notch (dB) | Frequency (Hz) | Bandwidth (Hz) | Damping-notch (dB) | Frequency (Hz) | Bandwidth (Hz) | |
---|---|---|---|---|---|---|---|---|
Filter 1 | Filter 2 | |||||||
Setting 1 | 108 | 10,780 | 6 | 175 | 223 | 10 | 989 | 165 |
Setting 2 | 150 | 10,000 | 12 | 160 | 100 | 2 | 350 | 120 |
Original setting | 100 | 1000 | Without filter | Without filter |
7.3 Table with two loads — hm2 (~10 t)
Kp (A.s) | Tn (A) | Damping-notch (dB) | Frequency (Hz) | Bandwidth (Hz) | Damping-notch (dB) | Frequency (Hz) | Bandwidth (Hz) | Damping-notch (dB) | Frequency (Hz) | Bandwidth (Hz) | |
---|---|---|---|---|---|---|---|---|---|---|---|
Filter 1 | Filter 2 | Filter 3 | |||||||||
Setting 1 | 131 | 13,088 | 5 | 380 | 250 | 7 | 156 | 271 | 29 | 1200 | 122 |
Setting 2 | 126 | 12,566 | 6.6 | 159 | 318 | 9 | 1204 | 160 | 3 | 390 | 159 |
Original setting | 100 | 1000 | Without filter | Without filter | Without filter |