The I controller 1 Measuring circuit
D, PD and PID controller 1 Measuring circuit
1. Constructing a position control loop
Construct the closed control loop in accordance with the circuit dia- grams.
Make sure that the test set-up and in particular the linear unit are se- curely attached to a sturdy base!
2. Control direction and offset
Set all controller parameters and the offset to zero.
Danger of injury!
Prior to switching on make sure that no one is within the operating range of the slide!
The slide moves to an end stop after the power supply has been switched on.
Is this really the zero position?
Set a setpoint value w = 5V and the controller gain KP = 1.
Does the slide move to a mid position?
Break the closed control loop by not connecting the measuring sys- tem to the controller.
To which position does the slide move?
Slowly alter the reference variable w.
Does the following condition apply: + w equals + x? If “yes”, then the control direction is correct.
A-168
Exercise 15
Check the effects of the following polarity reversals: Polarity reversal Change of controlled variable x
with increasing reference variable w
Reference variable w
Correcting variable y
Feedback r
Set the closed control loop correctly. Set a reference variable of w = 5 V.
What effect does the re-adjustment of offset have?
3. Transition function and empirical parameterisation
Set a setpoint step-change of w = 5V ± 3V, f= 1Hz. Set the following scales in the oscilloscope:
Time t: 0.1 s/Div Reference variable w: 1 V/Div Controlled variable x: 1 V/Div
Frequency and time scales are to be adjusted if the settling time is too long.
Record the transition function with different controller gains KP and evaluate the quality criteria relative to
A-169
Exercise 15
WORKSHEET
KP xm Ta estat stable/unstable Evaluation
1 5 10 20 30 40 50 55 63
What is the value determined for optimum controller gain?
KPopt =
Where does the limit of stability lie?
KPcrit =
Record the transition function at KPopt.
Value table
A-170
Exercise 15
4. Closed-loop gain
Calculate the maximum closed-loop gain V0max and the closed-loop gain V0opt with optimum parameterisation.
V0max = V0opt =
5. Positional dependence of limit of stability
Set a setpoint step-change of w = 1.5V ± 0.5V at 1Hz. Select the following scales on the oscilloscope:
Time t: 0.1 s/Div
Reference variable w: 0.2 V/Div Controlled variable x: 0.2 V/Div
Transfer the mean value of the setpoint step-change step gradually across the entire transfer range of the slide. It is not possible to dis- play the step responses on the oscilloscope within the above selected scaling. You should therefore establish KPcrit by observing the slide.
w ± 0.5V KPcrit Evaluation 1.5V 2.5V 3.5V 4.5V Value table
A-171
Exercise 15
WORKSHEET
Mark the maximum and minimum critical gain.
In which sections of the transfer range is the stability greatest?
In which section of the transfer range is the stability at its lowest?
6. Other controllers
Set a setpoint step-change of w = 1.5V ± 0.5V. Select the following scales on the oscilloscope:
Time t: 0.1 s/Div
Reference variable w: 0.2 V/Div Controlled variable x: 0.2 V/Div
Set KP = KPopt, and examine whether the quality criteria could be met more effectively by using a different controller combination of the PID controller card.
PI controller
A-172
Exercise 15
PD controller
Set KPopt. Now add an increasing D-element.
KPopt KD xm Ta estat stable/unstable Comment
PID controller
Set KPopt. Now add increasing I and D elements.
KPopt KD KI xm Ta estat stable/unstable Comment Value table
A-173
Exercise 16
Closed-loop hydraulics
Contour milling
To learn about a follower control system
To be able to calculate a lag error
To be able to measure a lag error
Follower control system
The purpose of a position control system is not just to position a slide. Often, it is even more important to maintain a specific feed speed, in which case a continuously increasing setpoint value is specified. The control task is then to adapt the actual value to the time characteristics of the setpoint value, whereby the actual value follows the setpoint value with a certain time delay, i.e. the actual value lags behind the setpoint value. This is why closed loop controls of this type are known as follower control systems or servo control system.
Subject Title
Training aim
Technical knowledge
Fig. A16.1:
Closed control loop for follower control system
vsoll Setpoint velocity KS System gain
t Time v Velocity
w Reference variable x Controlled variable
e System deviation KR Transfer coefficient of feedback K Gain of p controller r Feedback variable
A-174
Exercise 16
Lag error
If a constant speed is specified as setpoint value
the actual speed is in fact adapted to the setpoint speed.
There is, however, still a system deviation. This is equivalent to a position deviation, which is known as lag error or following error.
Fig. A16.2 illustrates the displacement-time diagram of a follower control system with constant setpoint input. The mathematical correlations are given below as an explanation.
Calculating the lap error
A lag error can be calculated from the characteristics of the closed con- trol loop (see fig. A16.1). The following applies for a closed control loop: Fig. A16.2:
Lag error with constant feed velocity
Lag error: ex = w - x = const. > 0 Setpoint velocity: vsoll = ∆w / ∆t = const. Actual velocity: vist = ∆x / ∆t = vsoll
A-175
Exercise 16
The closed-loop gain V0 = KP ⋅ KS ⋅ KR produces the fundamental equa- tion for the lag error:
e v
V x =
0
Influences acting on the lag error
As shown by the fundamental equation, the lag error ex is dependent on
the setpoint velocity vset and
the closed-loop gain V0.
As the velocity increases, the lag error becomes larger. If the setpoint velocity is to great, closed-loop control can no longer follow. The set- point velocity is then no longer reached.
The lag error is reduced as a result of high closed-loop gain V0. Since the closed-loop gain is directly influenced by the controller gain KP, a high closed-loop gain also reduces the lag error. The maximum increase of the controller gain is however only possible up to the limit of stability at KPcrit.
Fig. A16.3:
Effect of closed-loop gain on lag error
A-176
Exercise 16
Models for casting moulds are to be produced on a milling machine. The models are to be machined via an end mill cutter. The contour toler- ances concern both dimensional and form deviations. The machining process is to proceed at a constant feed speed. The lag error created as a result of this is to be determined.
Lag error
1. Constructing and commissioning a position control loop 2. Specifying a constant feed speed as reference variable Problem description
Positional sketch