Glossary Positioning Systems

Part IV - Terms of controller technology 

In most positioning systems three parameters are systematically controlled, such as position, speed and torque.

The vast majority of the positioning systems made by Feinmess Dresden GmbH is equipped with tailored control electronics to move a load from a known, defined position to another known, defined one. For precise positioning feedback mechanisms or a closed-loop control circuit is indispensable.
A classic example to highlight the just above said is our PMT160-...-DC-MM with integrated MINIMOT-controller.
 
The closed-loop speed controller governs the continuous movement of a load within a defined time interval or movement with a defined speed from one position to another one. In systems made by Feinmess Dresden GmbH encoders are installed as feedback modules.
 
The torque controller measures the current fed to a motor whose torque coefficient is known in order to generate a defined constant torque.

Tuning of the feedback control circuit 

For tuning the feedback control circuit the amplifying factors K_p, K_i and K_d as well as the feed forward parameters of the digital PID-algorithm, also called PID-filter, are determined:
 
Tuning should always be started with those values output by the controller. These values, as a rule, are averages to establish a secure, vibration-free operation and a rapid, reactive system whose control errors run within a very narrow bandwidth. For optimisation of the system dynamics, the control parameters must be re-set to be matched to the actual application. Such magnitudes like load, acceleration, alignment of the table and power consumption have to be considered when taking respective adjustments.

Setting the control parameters 

For setting the control parameters follow the below specified general rules:

• To achieve proper reaction rate, start always with setting the proportional amplification factor K_p.
• Then ramp up the K_d-value to reduce overshooting and to stabilise the system.
• At last, increase the K_i-value to eliminate the remaining control difference.
• In order to avoid stability problems never set K_p and K_i without K_d.

The purpose of setting is to establish an improved positioning accuracy (for example, static and/or dynamic reduction of the residual control difference) or to eradicate a system fault (vibrating and/or switching off initiated by a too high a control difference).
 
The acceleration plays an important part for the size of the control difference and maximum overshooting, in particular with start or stop. Every speed variation output by the controller results in a small acceleration, which always causes measurable control differences and overshooting. Therefore the smallest acceleration, which is permitted for the actual application, is recommended to be selected. In this way, the maximum overshooting is reduced and setting of the PID-filter simplified.

Settling time 

The settling time is that period between that time at which the measuring table reaches the desired position for the first time and that time at which the table remains in that position within a defined tolerance limits.

Continuous path control 

Continuous path control means that the controller changes the speeds of the single axes that the path is guided through previously defined path reference points. The speed remains the same over the whole path and may vary at start and stop only.

Interpolated movement control 

If the load to be moved has to follow a defined path in order to get from the starting position to the target one, then the axis movements are interpolated. There are two types of interpolation to be distinguished:
Linear interpolation and circular interpolation

Non-interpolated movement 

There are three types of non-interpolated movements: Single axis, simultaneous and synchronous movement. For simultaneous and synchronous movements, several axes are required. The difference is that a simultaneous movement does not run synchronously.

Residual control error 

The residual control error is that difference between the actual and desired positions which remains existent after error correction by the controller.

Differential controller 

The variation of the control error is multiplied with the factor K_d specified by the user, and then re-sent as correction signal. Since this kind of control improves stability, it may also be considered as electronic attenuation. Increasing the K_d-values results in higher system stability. The residual control error, however, is not eradicated as the differentiation of a constant equals zero.

Feed forward control 

In comprehensive PID-algorithms a correction signal will be generated only if a control error exists, that means, there will always be a trailing error. The purpose of the feed forward control is to minimise that trailing error.
Installing a feed forward control the future system behaviour is estimated, and the actual correction signals are matched accordingly.
The corrections are generally created by multiplication of the desired speed with the speed-feed forward-amplification-factor K_vff.
An acceleration-feed forward-correction can be carried out with the same method, too. In this way, the average trailing error can be reduced with accelerations and decelerations. Connecting the feed forward control and PID, the PID-controller only needs to correct the remaining error, which stays existent after the feed forward control to improve the general reaction of the system.

Closed loop control circuit 

The open-loop control circuit describes a system in which the actual position is measured and compared with the rated one, and the difference gets corrected then in order to reach the desired position. Electronic feedback mechanisms installed in closed-loop control circuits improve the positioning accuracy.

Speed profiles 

In order to obtain smooth-running movements at high speeds and to save the motor, speeds have to be varied by the control electronics that optimum results are achieved. For this purpose, rated speed profiles have been introduced which keep the required acceleration and deceleration as low as possible.

Integral-Controller 

The control error is summed up over time, multiplied with a factor K_i specified by the user, and re-sent as correction signal.
 
Since with this method the previous errors are considered as well, the correcting factor does not approach to zero when the control error "e" approaches to zero. A residual control error is avoided in this way.
 
This method, however, carries a disadvantage as the factor K_i destabilises the entire closed-loop control circuit. High K_i -values may cause strong system vibrations if not attenuated accordingly.

Circular interpolation 

Circular interpolation designates the ability to move a load along a circular path. For this purpose, the controller must be capable to change the acceleration very rapidly.

Linear interpolation 

In order to move several axes along a straight line, linear interpolation is required. For co-ordinated movement, the controller outputs the required speed for each axis. With correct linear interpolation the acceleration has to be controllable. Some controllers are working on basis of canned acceleration profiles to deliver results, which are similar to linear interpolation.

Open-loop control circuit 

An open-loop control circuit means that the information flow is not closed by position feedback and error correction. Cost-efficient micrometer replacement drive assemblies generally work with open-loop control circuit, if the manual drive is to be replaced by a simple remote control.
Stepping and mini-step motors are frequently applied with open-loop control circuit. The position can be relatively securely detected through pulse counting; the position cannot be precisely predicted when loads, acceleration or speeds are very high. If the system has been inappropriately designed then steps are often skipped or added, respectively.
For cost reasons, positioning systems equipped with open-loop control circuit gain more and more ground. Progress in the mini-step technology and viscose-based dampers built in the motors have improved positioning accuracy and, at the same time, oscillation in the latest designs of stepping motors diminished.
The open-loop control circuit is, by no means, a sign for coarse positioning. At present, cost-efficient units featuring open-loop control circuit are able governing very fine steps. In present time, infeed travels running within the nanometer range can be obtained by piezo-based and electrostrictive units equipped with open-loop control circuit.
In systems with open-loop control circuit the position is detected without encoders. Looking at a piezo-based unit the position is determined through the applied voltage. This calculation, however, is inaccurate as errors occur due to hysteresis, non-linear behaviour and drift being typical for piezo materials. Latest electrostrictive materials behave in a similar way, but are characterised by a considerably less hysteresis.

Optimizing a stable system 

When the system is stable and the performance is to be enhanced, improvement is recommended to be approached to with the existing parameters. The aim of re-adjustment is to get the control error during positioning reduced, and eliminated with the system at rest.
Adjustment depends also on the initial point and desired performance. For further adjustments, Feinmess Dresden GmbH offers a respective guideline.

Oscillation 

When the operating speed approaches to a natural oscillation frequency of the mechanical system, oscillation or vibrations may be excited. Another reason for oscillation is caused by sudden change of the speed and position of the system. Such vibrations reduce the effective torque and end up in deteriorated synchronisation between motor and controller.
 
Settling time and oscillation can be controlled best by damping the motor (for example, through viscose-based dampers). As regards stepping motors, there are various possibilities to change natural frequencies:

• Half-step or micro-step mode
• Alteration of the system inertia
• Rapid passing through the natural vibration range
• Change of the distortion resistance of the drive chain

PID-Controller 

The PID-controller is a combination of proportional, integral and differential controllers. In positioning systems, frequently a control circuit featuring PID-algorithm is installed. The feedback modules influence each other. Knowledge about this interaction is especially important for fine adjustment of a positioning system. For optimum system performance, the coefficients K_p, K_i, and K_d have to be re-adjusted according to the desired movement mechanics and load inertia.

Proportional controller 

The control error (difference between actual and rated positions) is multiplied with the factor K_p specified by the user, and re-sent as correction signal. In this way, the error is reflected in an amplified manner and rapidly corrected. An increased K_p-factor accelerates error correction. If K_p, however, gets too big then a strong overshooting will emerge, and from a certain point on the system itself can be put into vibrations which will result in instability if the system is insufficiently damped only.
K_p cannot completely eradicate the control error "e" since the proportional correction magnitude "K_p * e" approaches to zero as well with decreasing control error "e" which leaves a residual control error.

Control difference 

The control difference is the momentous difference between the fed back actual position and desired one governed by the controller.

Feedback control in a closed-loop control circuit 

Positioning accuracy depends on the way as the controller processes the fed back positions. The most simple controller type is the proportional one. More sophisticated controllers are the differential and integral ones. Best results are delivered by the proportional-integral-differential controller uniting all advantages of the three controller types.

S-curve speed profile 

The trapezium profile is suited to be used in most applications. The only advantage of this profile lies in possible vibrations at the "corner" leading to longer settling times. Regarding critical, vibration-sensitive applications an S-shaped speed profile can be installed to rule acceleration and deceleration. In this way, oscillation caused in a mechanical system by a moving mass is minimised.

Trapezium speed profile 

Following this schematic, the speed ramps up linear until reaching the target speed. When decelerating, the speed ramps down linear to standstill. Plotting the speed over time outputs a trapezium curve. Latest control electronics enable the user controlling acceleration and deceleration. In addition, some controllers offer the possibility to adjust these parameters separately for short or long traverses.

Overshooting width 

The overshooting width means that distance which is passed behind the target position in poorly attenuated control circuits.