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Servo tuning tools: time versus frequency domain
Motion controllers are abundant on the market, many claim to offer tools that ‘magically’ setup, tune and produce optimum performance for a servo system. What tools are available for the machine builder or system integrator that will allow closed loop servo systems to achieve obtain setup and a high performance and stable system?
There are some key questions to ask. Can the motion controller provide information to a machine builder that may assist in determining mechanical issues, thus allowing fast and cost-effective rectification of structure issues. Does the controller to allow the user to easily add filters to the servo system to compensate for minor errors or to modify the system to safely achieve its performance criteria? How will the system respond if the load changes; will it still be stable?
All motion systems are different, the mass of the load, mounting configuration, mechanical configuration, bearing preload and feedback system can all affect the way a closed loop servo system can respond. To get the optimal performance from a system, the servo loop needs to be optimised for each application.
The type of motion required by the application is also very important in how the loop is to be tuned. For instance, if short moves (10 microns) are to be made then the tuning would be different than if long moves (100mm) are to be optimised. Another consideration is the motion specification required by the application. Is the key specification minimal step and settle, in-position stability or a specified system bandwidth?
The tuning tools available to assist the engineer may be time domain or frequency based tools. Traditional tuning methods were often specified along the lines of “turn this dial up till the system goes unstable and back it off by 10%; or turn this dial down until the system goes unstable and increase it by 10%.” Fine tuning was sometimes done by placing a screw driver onto the servo motor and placing your ear on the end. You may be shocked to find however that, in a recent search through a help file for tuning on one of the most respected machine automation controllers on the market, the wording was near enough identical.
Auto tuning strategies
The phrase “auto tuning” has been bandied about for a long time and different controllers have different methods. Auto tuning is typically a time domain tool, Before auto tuning can be used, a low bandwidth stable system must exist. This means that the user will have to select the appropriate starting place for the auto tune function, with some of the typical settings shown in the table. Whilst the auto tune is good, the optimal gains will be best reached with further tuning, for example using Aerotech’s loop transmission tool. Anyone that relies on Auto tuning alone will never get the optimal performance from any motion system.
So how do phase margin and crossover frequency relate to the final performance of the system? The crossover frequency is the point at which the magnitude of system response crosses the 0dB line. The higher the crossover frequency the better the system will track the command at low frequencies. So if you want a better performing system you should increase this number to 50Hz or even 80Hz. However as this number goes higher there may start to be a trade off in stability or audible noise.
Phase margin is the difference in phase shift of the command from 180° at the point where the magnitude crosses the 0dB point. Phase margin is a key indication of the stability of the system and should be always be above 30 degrees for most applications. The higher this number the more damping the system will have and the system will be fundamentally less sensitive to changes in load, etc. The lower the number, the better the tracking, however the system will be closer to instability.
A frequency response is another tool to measure the response of a system. Specifically, it measures the steady state response of the system output to a sinusoid input. The frequency response of the system can be measured from any input to any output, or more generally between any two signals in the system. When considering the stability of a control system, the system is excited usually at the input to the power amplifier and the response measured just before that input. This provides the response of the entire control loop and is referred to as a loop transmission. The loop transmission is plotted as a gain and phase curve versus frequency, and is commonly called a Bode plot.
The loop transmission can be measured for many discrete frequencies and delineated on a Bode plot. The key purpose is to determine system stability and optimise the system performance by adding the appropriate filters and selecting the best gains for the control law or, in the servo system, the PID and feed forward servo loop. The crossover frequency is defined as the point where the magnitude crosses through zero dB. In general the higher this value is the faster responding the system will be to command inputs.
The phase margin is calculated as the distance away from 180 degrees at the cross over frequency. The phase margin is the amount the phase can change by before making the system unstable. Phase can be changed through the servo loop gains or the application of a filter. In the plot shown of an unloaded motor (figure 2), the gain margin is shown at the point where the phase crosses through 180 and is the distance in dB from zero gain. If the system gain were increased by this amount the servo system would go unstable.
There are recommended minimum values for both gain and phase margin. The minimum phase margin is usually considered to be 30 degrees. Increasing the phase margin has the same effect as increasing the damping in the system. More gain margin reduces overshoot but may lead to long settling times. The recommended gain margin is at least 6db. Getting any closer will result in oscillations at that specific frequency. The magnitude of the response falls off consistently with increasing frequency. The gain and phase margins are easily attained and no resonance modes are present.
Loop shaping goals
Loop shaping involves changing the servo-loop gains and adding filters to achieve a desired frequency response. The goals are to obtain maximum low frequency gain to improve tracking at low frequencies, and to obtain maximum gain crossover frequency. The aim is to meet the above gains while keeping the gain and phase margins within acceptable limits
The plots below show a well tuned XY table (speed 1mm/s; diameter 50µm; 50Hz bandwidth on each), and what will happen as we increase the speed of the axes. The frequency response of the system will need to be higher, and as we get closer to the crossover frequency the closed loop gain actually rises and therefore the servo loop will make the circles larger. Note that the closed loop additional gain can be corrected by feed forward gains. If the stages have a much lower crossover frequency there will be a lag in actual position and the circle will shift. If the stages are tuned with different crossovers then the fourth plot may happen, due to one axis responding better than the other.
The plots above (figures 4-7) show a system with a cross over of 60Hz, with 55 degrees of phase, gain margin of 18db at 300Hz. Its very easy to see this when running a loop transmission tool. If a load was added to the system, it may introduce a resonance. In the following plot we have added a load that causes a disturbance at about 40Hz.
The loop transmission will show a resonance in the system at about 40Hz and the system will not settle as fast. However, note that the zero dB crossover of the gain curve has plenty of phase margin and so the resonance does not affect the system stability in this case.
If the loop transmission tool allows it, we could reshape the plot by using a notch filter (figure 6). In the case of a controller such as Aerotech’s A3200, you could simply click and drag and shape the notch filter to suit. However as the loop transmission tool provides more complete data about the higher frequency gain margins, we can do something that traditional methods and time based tools would suggest not to do: turn up the gains.
Notice that as the gain is raised, eventually the phase margin diminishes to the point of instability. If the tool is good it should warn you when you break the rules. The loop transmission tool shows what’s going on at higher frequencies and allows you determine better placements of low pass filters rather than the default position of 500 or 100Hz.
Advanced motion controllers from Aerotech also have the ability to ask for the type of motion you require and automatically place filters and set gains based on your motion requirements. After running the loop transmission the auto fit filters, optimise performance and enhanced tracking control (boosts low frequency gains) buttons can be used.
But what about the possibility of a ‘magic Button’? EasiTune by Aerotech is a one-button tuning method that, in the background, analyses the frequency response of a system and applies filters and gains after first determining the type of axis connected to the controller and its frictional content. This is one of the new breed of auto tuning techniques but in the frequency domain.
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