Electricity + Control July 2016

DRIVES, MOTORS + SWITCHGEAR

Il

– Integrator limit – Derivative gain – Proportional gain

Kd Kp

PID

– Proportional Integral Derivative

Abbreviations/Acronyms

• One, proportional to the accumulated position error which helps to cancel out any long-term error, or ‘steady state’ error Approximately 2 000 times per second, a servo tick occurs, and the filter, operating on the commanded position and the actual position for each servo tick, produces an output calculated as follows:

Figure 2: Rotor only using the program default settings.

Output = Kp X pos_error – Kd X (pos_error-prev_pos_error) + Ki X integral_error

The term pos_error is simply the current command position minus the actual position. Note the negative sign for Kd. The integrator limit (IL) sets a limit to how much the integral error can grow over time. Without this limit a huge integral_error could accumulate, resulting in a large setpoint overshoot when the set position

was reached. Uncontrolled integral_error is known colloquially as ‘integrator wind- up’ and is a major source of system instability. Note that the Kd magnitude is proportional to the difference be- tween successive pos_error values. Fast changes result in the output be- ing reduced by the subtracted Kd term. The result is a stabilising effect on system stability.

Figure 3: Rotor only but tuned for optimum response.

Analysis of the response graphs

Figure 2 • This test uses the default PID settings. The Step Size is set to 1 000 encoder counts or half a revolution of the motor shaft, and the graph length is set to two seconds • The Rise Time is 0,017 seconds • The overshoot is zero • The Steady State Error is 0,2%. This is the result of the integral term Ki being zero. Note that any system friction would increase the Steady State Error Figure 3 • The PID settings have been adjusted to produce no overshoot and zero steady state error. The Rise Time is now much longer as the result of the larger derivative (Kd) setting Figure 4 • The combination of the default PID settings and the presence of coupled load inertia results in the overshoot seen. The settling time now exceeds the rise time Figure 5 • With the same load inertia, the servo parameters have been adjusted to produce no overshoot and zero steady state error • Note the large value for Kd

Figure 4: 3:1 inertia match – default settings.

Figure 5: 3:1 inertia match – optimum settings.

July ‘16 Electricity+Control

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