Parameter Design in High-Speed High-Precision Motion Control

Abstract

The first major task of automation is to replace labor to achieve faster and more precise production. In systems such as CNC machine tools, machining centers, CNC engraving, printing, die-cutting, papermaking, steel rolling, and high-speed rail, it is necessary to control the speed of multiple motors.

The first major task of automation is to replace labor to achieve faster and more precise production. In systems such as CNC machine tools, machining centers, CNC engraving, printing, die-cutting, papermaking, steel rolling, and high-speed rail, it is necessary to control the speed of multiple motors. Or position control, at this time need to use motion control (or follow-up control), in motion control, how to design the structure of the control system? How to determine the PID parameters in the control system? How to determine the feedforward parameters? How to set the parameters of the frequency converter to synchronize the speed between the frequency converters in the speed chain? Only by rationally designing and debugging the parameters of motion control can the system run in a faster and more precise working state.

12.1 Determination of Feedforward Parameters—“Yao’s Trial and Error Method”

The accuracy and speed of many CNC equipment produced by some manufacturers are better than those of other manufacturers. This is not accidental. The design and debugging of the electronic control system are often very critical.

Many people know the PID controller. In fact, in motion control, if only PID is used for adjustment, the control speed and accuracy are not optimal. The reason is that PID control is feedback control, and only the feedback value is measured before passing. Calculate the error between the given value and the feedback value to obtain the control output after PID calculation, so the output always lags behind the generation of the error. For high-precision motion control, you also need to configure feed-forward parameters to improve control accuracy and speed. In this way, the integration depth of PID parameters can be reduced, making the motion control more precise and faster. The block diagram of the CNC system with feedforward unit is shown in Fig. 12.1.

Fig. 12.1

Feedforward + feedback control block diagram

Feedforward parameters include feedforward proportional parameter K₁, feedforward speed parameter K₂ and feedforward acceleration parameter K₃. In general, take K₂ = 0, K₃ = 0, and only use feedforward proportional parameter K₁ to achieve high control accuracy.

Feedforward proportional parameter K₁ can be obtained by calculation. K₁ and encoder resolution R_e1 (10000P/r), rated speed n_e (such as 1000 rpm), feedforward unit (such as D/A output unit of motion controller) output full scale voltage (such as ±10 V) corresponds to the resolution R_e2. As shown in the following formula, where k₀ is a coefficient, which varies with different motion controllers.

$$ K_{1} = k_{0} \frac{{{\text{Re}}_{2} }}{{{\text{Re}}_{1} n_{e} }} $$

(12.1)

The feed-forward proportional parameter K₁ can also be measured by the “trial and error method”, and the method is as follows.

Simply set the three parameters of PID, as long as there is no vibration, set a given speed SV₁, record the speed n₁ of the motor, then set the three parameters of PID to zero, keep the given speed SV₁. The value of K₁ starts from 0 increase until the output speed of the motor is equal to n₁, record the corresponding K₁ value K₁₀, then

$${K}_{1}={K}_{10}$$

(12.2)

If several motors run synchronously, set the three parameters of a PID to zero, change the value of K₁ to make it basically equal to the speed of other motors, then the value of K₁₀ is the result.

“Porcelain trial and error method” can also be used to determine the feed-forward parameters of process control.

12.2 A Simple Adjustment Method of PID Parameters—“Two-Four Rule”

In the motion control system, if the motion controller provides the PID parameter self-tuning algorithm, it can perform self-tuning. If there is no self-tuning function in the motion controller, novices need to adjust the PID parameters by themselves. There are many books that explain this. Finally, let the front and rear attenuation ratio of the overshoot part of the response curve be 4:1. Since most methods require professional equipment for observation, it is sometimes inconvenient to apply in the field, and many novices will be at a loss.

The following introduces a simple method PID parameter determination method—“two-four rule” can be used as a reference for novices, the method is as follows:

• 1. The three parameters of PID are zero, and P gradually increases from 0 until the slight vibration of the motor is heard. At this time, it is P₀, and the ratio P is taken as

  $$P=\frac{{P}_{0}}{2}$$

  (12.3)

• 2. P = 0.5 * P₀, D = 0, I gradually increases from 0 until the slight vibration of the motor is heard, at this time it is I₀, then the integral I is taken as

  $$I=\frac{{I}_{0}}{2}$$

  (12.4)

• 3. P = 0.5 * P₀, I = 0.5 * I₀, D gradually increases from 0 until the slight vibration of the motor is heard, at this time it is D₀, and the differential D is taken as

  $$D=\frac{{D}_{0}}{4}.$$

  (12.5)

12.3 "Yao’s Speed up and Down Rules” of the Frequency Converter in the Speed Chain

In steel rolling, papermaking, textile and other fields, many motion control systems use frequency converters to drive motors, which often fail to maintain synchronization during the speed up and down process, and novices are even at a loss for this. A very important reason here is that the speed-up and down-speed time of each inverter in the speed chain is not adjusted properly. The speed-up and down-speed time of each inverter must be determined by the “Yao’s speed-up and down-speed rule”.

Speed-up and down-speed rule: For multiple frequency converters operating according to the speed chain, the output frequency of each frequency converter is inversely proportional to its speed-up and down-speed time. That is, the speed-up and speed-down time is short for high frequency and long for low frequency.

Since the same paper belt or steel belt is dragged, the linear speed of each link in the speed chain is the same. When the system is debugged, it is not necessary to pull the material first, and use the speedometer to measure the linear speed to adjust the linear speed of each link to be consistent, and close to the normal operating speed. Record the frequency of n frequency converters at this time as f₁, f₂, …, f_k, … f_n.

Select a motor with the largest load inertia, and the output frequency of the frequency converter corresponding to the motor is f_k, and set the acceleration time T_ka and deceleration time T_kd of the frequency converter corresponding to the motor according to the process requirements.

The acceleration time T_1a and deceleration time T_1d of the first inverter are determined as follows.

$$ \begin{gathered} T_{1a} = \frac{{f_{k} }}{{f_{1} }}T_{ka} \hfill \\ T_{1d} = \frac{{f_{k} }}{{f_{1} }}T_{kd} \hfill \\ \end{gathered} $$

(12.6)

The acceleration time T_2a and deceleration time T_2d of the second inverter are adjusted as follows.

$$ \begin{gathered} T_{2a} = \frac{{f_{k} }}{{f_{2} }}T_{ka} \hfill \\ T_{2d} = \frac{{f_{k} }}{{f_{2} }}T_{kd} \hfill \\ \end{gathered} $$

(12.7)

The acceleration time T_na and deceleration time T_nd of the nth frequency converter are adjusted by the following method.

$$ \begin{gathered} T_{na} = \frac{{f_{k} }}{{f_{n} }}T_{ka} \hfill \\ T_{nd} = \frac{{f_{k} }}{{f_{n} }}T_{kd} . \hfill \\ \end{gathered} $$

(12.8)

12.4 The Wonderful Effect of “Virtual Axis” in Speed Synchronous Control

In the fields of printing, die-cutting, steel rolling, papermaking, and textile, it is necessary to operate at a certain speed ratio between motors of n stations. The synchronization performance of many synchronous motion control systems is very poor. The phenomenon of asynchronous operation may be caused by your poor synchronous control strategy. Many beginners often use an intuitive control mode to let the rear motor follow the movement of the front motor. The disadvantage of this method is that it is easy to cause the motor at the back are always in a state of micro-oscillation operation. Any motor vibration affects the movement of all motors behind it, a bit like the “look right” command in military training. The latter one looks at the previous one, and after a while everyone stands well, if there is a problem in the front, there will be a problem later, and it will take a long time to adjust.

In order to avoid this problem, you can use the running mode of the virtual axis to solve it.

The specific method is:

• Define an internal imaginary axis in the motion control unit. The set speed of the production line controls this imaginary axis. All motors follow this imaginary axis. Because the imaginary axis has no vibration problems, all motors follow an internal imaginary axis that runs stably. Therefore, there will be no situation where everyone suffers after a problem, and the adjustment speed of the whole line is also fast.

12.5 Approximate Feedforward Parameter K₁

In some control systems, it is impossible or not allowed to measure the feedforward parameter K₁ through field experiments. We can also approximately calculate the feedforward parameter K₁ based on the characteristic parameters of the device.

For example, in a large variable frequency constant pressure water supply pum** station, the pumps are all centrifugal pumps and the rated frequency of the motors is f_e. The controller realizes constant pressure control of the pum** station by controlling the start and stop of the pump and the operating frequency of the frequency converter. Assume that the total water supply head of the pum** station is H_sv. According to the water pump characteristic curve Q-H provided by the pump manufacturer, as shown in Fig. 12.2.

Fig. 12.2

The characteristic curve Q-H of the pump

where H_c is the closed head and H_m is the maximum head. The feedforward parameter K₁ (converted to frequency) is approximately calculated as follows:

$${K}_{1}\approx {f}_{e}\sqrt{\frac{{H}_{SV}}{{H}_{m}}}$$

(12.9)

If H_m = H_c, then

$${K}_{1}\approx {f}_{e}\sqrt{\frac{{H}_{SV}}{{H}_{C}}}$$

(12.10)

This approximate K₁ can greatly reduce the adjustment amplitude of PID, improve the anti-saturation performance of PID, and increase the speed and stability of adjustment.

This method was proposed by Dr. Yao.