4.3(a) Servomechanism
Open Loop Control System
Suppose that we wish to control the position of a radar scanner. Suppose also that we have a motor capable of driving the scanner and some means of controlling the motor. Such an arrangement is illustrated in figure 164.
Figure 162: OPEN LOOP CONTROL SYSTEM
The control element controls the magnitude and direction of the input to a power amplifier, whose output drives the motor at the desired speed in the required direction. The motor, in turn, moves the load in accordance with the input demand.
The control element could be calibrated with a scale indicating the required position of the load. Then when we set the control dial for the required position, we hope that the load (possibly unseen) is doing what we are telling it to do.
In practice, however, the accuracy of control is limited because there are several factors, other than the input, that affect the output (e.g. variations in the output load, in the amplifier characteristics or in the motor circuit). We have no means of controlling these variations in the open loop system and, because of the resulting inaccuracy; open loop systems are hardly ever used.
Closed Loop Control System
If we observe what the load is doing and make appropriate corrections at the input, the system is no longer open loop; it is now, in effect, a closed loop system, the human operator completing the loop between output and input. He/she compares the desired effect with the actual effect and adjusts the system so as to reduce the error between them. He/she is thus, in this connection, an 'error detector’, and the amount of error which the person observes determines how adjustments are made to the input to produce the desired results.
However, to measure the error and take the necessary correcting action, we have 'built in' the human operator as an essential element. A more effective and efficient control can be obtained by replacing the human operator with an automatic control system. The response of the automatic system is generally quicker and more accurate than that of a human operator, and the automatic arrangement is not subject to fatigue. In addition, of course, the automatic system gives a saving in manpower.
The essential features of the closed loop system are as follows:
The feedback of information concerning the behaviour of the load.
The comparison of this information with the behaviour demanded by the input.
The production of an error signal proportional to the difference between the desired behaviour and the actual behaviour.
The amplification of the error signal to control the power into a servomotor.
The movement of the load by the servomotor in such a direction as to reduce the error signal to zero, at which point the output is the same as that demanded by the input.
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The block schematic diagram of a basic closed loop control system is illustrated below. In this arrangement:
θI is the input demand, which in this case is in the form of a shaft angle.
θ0 is the output shaft angle of the load.
The control element converts the demand θI into some form suitable for operation of the error detector, e.g. produces a voltage proportional to θi.
The feedback element does the same for the output angle θ0, e.g. produces a voltage proportional to θ0.
Figure 163: CLOSED LOOP CONTROL SYSTEM
The error detector has two inputs applied to it, one due to θI and the other due to θ0; it produces an error signal e proportional to the difference between the two inputs, i.e. (θI - θ0).
The error signal operates the amplifier which, in turn, causes the motor to rotate until θ0 equals θI (output equals demand); at this point the error signal is zero and the drive from the motor ceases, the output load having taken up the position demanded by the input.
4.3(b) Servomechanism
Practical Closed Loop Control System
The input demand θI sets the angle of the transmitter (CX) rotor. The resulting alternating field in the control transformer stator induces a voltage in the transformer rotor and this voltage is fed as an error or misalignment signal to the amplifier. The amplifier output is used to drive an ac servomotor that turns the output shaft and also the rotor of the control transformer through output angle θ0.
Figure 164: PRACTICAL CLOSED LOOP SYSTEM
When the output shaft is turned into alignment with the setting of the input shaft (θ0
= θI) the transformer rotor is at right angles to the transmitter rotor and its own stator field. In this position there is no error signal induced in the transformer rotor, there is no input to the amplifier or servomotor, and the motor stops. The output has now taken up the position demanded by the input.
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Servomechanisms
To be classed as a servomechanism, an automatic control system must have:
a) Error actuation.
b) Power amplification.
c) Closed loop control.
d) Continuous operation, or 'follow-up' properties, i.e. if the load is disturbed from the demanded position, it always tends to return to it.
The system is said to be error-actuated because it is the error between the output demanded by the input and the actual output which starts the action. The final net input to the amplifier is the error signal and not the input demand.
We must have torque amplification to be able to drive heavy loads. The servo therefore contains an amplifier that supplies the necessary driving power to the servomotor; the motor provides the required torque.
The servo also has a closed loop system;
Error detector - amplifier - motor and load - error detector...
Finally, continuous operation is assured in a servomechanism because any variation in the output from that demanded by the input automatically produces a difference between output and input, and hence an error signal. The error signal again starts the correcting action.
A servomechanism has many applications, covering a wide range of power requirements.
Types of Servo
There are two main classes of servomechanism - remote position control (rpc) servos and speed control servos.
a) RPC servos – These are used to control the angular or linear position of a load.
b) Speed Control Servos – These are used to control the speed of a load. In this case, the speed of the driving motor is made proportional to the input demand usually a voltage).
Two types of input to a servo are:
1. STEP INPUT - created when the input shaft is suddenly rotated from one angular position to another.
2. RAMP INPUT - created when the input shaft is rotated at a
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PERFORMANCE OF SERVOMECHANISMS Response
The response of a servo is the pattern of behaviour of the load when a change is made to the input condition. It has so far been assumed that if the input moves to θi the load will simply follow, its response being a reproduction of the input movement.
The paragraphs that follow will show that matters are not as simple as this.
Figure 167: SIMPLE SERVOMECHANISM
Step Input - No Friction
For this discussion we will assume that the input and output were aligned at θ0, until the input suddenly changes to θi. An error signal proportional to θ0 - θi
appears at the amplifier input and the motor is energised to null the error.
One important point must now be emphasised. The torque delivered by the motor to the load is directly proportional to the error; it acts only on the inertia of the load, which therefore accelerates at a rate proportional to the error. As the error reduces so the acceleration reduces, until it reaches zero with zero error.
But this is not a satisfactory state of affairs, for the load acceleration is in one sense only and that to increase its velocity. Saying that the acceleration is zero at zero error simply means that the load has reached a steady speed when we
require it to be stationary. Further, since there is nothing to stop it, it keeps moving past the required position.
The error signal produced, and, therefore, the torque applied to the load, now reverses in sense to slow down the load. Since, however, the components operate symmetrically about the null, the pattern of deceleration is a mirror image of the original acceleration.
The load stops when it has overshot by the initial error, and from there the performance is repeated. The resulting load oscillation about the demanded position is illustrated graphically in figure 168.
Figure 168: RESPONSE TO A STEP INPUT - NO FRICTION
Ramp Input - No Friction
The description of the response can be followed in the diagram. In the early states of the ramp, while the error signal is small, the load accelerates slowly and lags behind the input.
The error signal grows as the lag increases, building up the acceleration.
Eventually the load speed equals the input speed but since a substantial position error exists it continues to accelerate.
When its speed exceeds that of the input the position error starts to decrease; the acceleration reduces and the load reaches a constant speed at zero position error with no error signal.
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The load speed, however, exceeds the input speed and an overshoot results. That the outcome is a continuous oscillation can be easily imagined from this point.
Figure 169: RESPONSE TO A RAMP INPUT - NO FRICTION
Effect of Restraints
The oscillatory responses are obviously not desirable, and luckily, restraints on the load have a stabilising effect. Various inherent factors are to oppose the load movement; they include static friction, kinetic friction, eddy currents, air resistance, viscous lubricants and many others.
Lumping them all together for the moment the general effect is to reduce the amplitude of each successive swing until gradually the output becomes steady.
The oscillations are known as transients and they are effective during the transient response period, or settling time. Once the .output has settled it has reached the steady state.
While restraints are beneficial in stabilising, or damping, the response, they do have certain detrimental effects. One of these is that power is wasted; another is the introduction of error in the steady state.
Steady State Errors
Examination of the various restraints present would show that their effect is in part due to a small constant magnitude force known as coulomb friction and in part to viscous friction that increases with speed.
Coulomb friction is that part of the frictional force that is independent of speed, e.g.
a shoe on a brake drum.
The resistance due to coulomb friction tends to degrade the sensitivity of a servo, for a torque that overcomes it must: be generated before any movement of the load takes place. To provide this torque the load error must reach some finite size, and any errors less than this will not be corrected. Figure 170 shows the effect of coulomb friction on the response to a step input.
The load comes to rest somewhere within a band of error, known as the dead space, the width of which depends on the amount of coulomb friction. For most modern servos the coulomb friction is very small, and its effect is often neglected.
Figure 170: RESPONSE WITH COULOMB FRICTION TO A STEP INPUT
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Viscous friction does not produce a dead space in the step input case since it has no value when the speed is zero. It does however produce a similar effect when the ramp input is considered.
In the steady state the load is moving with constant speed; it is therefore being resisted by viscous friction. An error signal must be produced to overcome this therefore an error must exist.
The response is illustrated in figure 171 and the error necessary to overcome the friction is known as velocity lag.
The output shaft rotates at the same speed as the input shaft but lags behind it by some constant angle. This positional error is velocity lag.
Coulomb friction may be considered small compared with viscous friction during a ramp input, but, of course, it also contributes to this error. However, the greater part is due to viscous friction, and since this increases with speed the error is generally reckoned to vary directly with speed.
Figure 171: RESPONSE WITH VISCOUS FRICTION TO A RAMP INPUT
Response of a RFC Servo to a Step Input (Negligible Coulomb Friction) Figure 172 shows a basic rpc servo system.
Let us assume that the output shaft is driving a load, and that it has taken up a position which agrees with that demanded by the input shaft (θ0 = θi).
The error signal is therefore zero, and the servo is stationary in a steady state condition.
Figure 172: BASIC RPC SERVO
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Figure 173: RESPONSE CURVE
Now suppose that the input shaft is suddenly turned through a certain angle in order to bring the load into a new position, i.e. an input known as a 'step input' is applied. The sequence of events is illustrated in figure 173.
(a) The input demand θi is suddenly change to a new value at point a. The output shaft cannot immediately follow this change in demand because of the inertia of the load. Therefore there is now a difference between θ0 and θi and an error signal is produced.
(b) The error signal, after amplification, causes the motor to accelerate in an attempt to bring the output shaft to the new demanded position. Because of the inertia of the load this takes time; there is therefore a time lag during which the output angle θ0 is changing in response to the change in demand (b in figure (b) above).
(c) As the motor turns the load, the output angle θ0 approaches the demand θi. The error signal, which is proportional to (θi - θ0) therefore decreases but the driving force remains until θ0 equals θi at point c; this is the required load position.
(d) By the time θ0 has reached the demanded position, the load has acquired considerable momentum and consequently overshoots (point d).
(e) The error signal now increases in the opposite direction ((θ0 greater than θi) and the motor applies a reverse torque which eventually stops the load and brings it back to the required position at point e.
(f) Once again, however, the momentum of the load carries it past the required position and another overshoot occurs at f.
The load may thus oscillate about its final required position many times before it comes to rest; a servomechanism that does this is said to be 'hunting'.
IMPROVEMENT OF TRANSIENT RESPONSE
For many applications the simple servo using its inherent friction for damping is perfectly adequate. This is usually the case for small position servos, but when large loads are involved the transient response is unsatisfactory.
Time and energy is wasted during this period, and bearing wear is increased. It is evidently desirable to reduce the number of oscillations, and also the response time. Two methods commonly employed are described.
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Viscous Damping
This method is simply a controlled increase of the inherent viscous damping to achieve the required response. One device in use is the eddy current damper as shown in figure 174.
Figure 174: EDDY CURRENT DAMPER
This simple device consists of a thin disc of metal with high electrical conductivity (usually aluminium), which is attached to the output shaft. It spins between the poles of electromagnets mounted round its periphery.
Eddy currents are induced of magnitude proportional to the field strength and to the disc velocity. These eddy currents set up magnetic fields that act against the inducing fields and forces opposing the disc rotation are created.
These forces are closely proportional to the disc velocity, and therefore provide parallels to the inherent viscous forces. Adjusting the current flow to the electromagnets can control them.
Varying degrees of damping can be applied. The next diagram shows some of the stages, coulomb friction being ignored for simplicity. Using only inherent friction under damping is achieved.
Too much extra viscous friction will produce a very sluggish response and the system is over damped. The degree of damping which just prevents any overshoot is known as critical damping.
Slightly less damping than this, to allow one small overshoot, is optimum damping which gives the smallest settling time.
Most designs are aimed at this condition.
Figure 175: DEGREES OF DAMPING - STEP INPUT
The effect on the transients for a ramp input can be similarly adjusted to reduce optimum damping. A snag arises, however, for any increase in viscous friction also increases the velocity lag.
Thus to remove the transient oscillations completely a considerable velocity lag must be expected. Figure 178 illustrates the response for two degrees of damping for a ramp input.
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Velocity Feedback Damping
This form of damping is similar to viscous friction damping in one respect; the compensation produced is proportional to the velocity, or rate of movement, of the output shaft. Velocity feedback damping has the advantage, however, that it consumes very little power.
Figure 176: DEGREES OF DAMPING - RAMP INPUT
In an rpc servo we are required to move the load from one position to another as quickly as possible without causing instability (i.e. hunting) or wasting power.
We have already seen that a step input applied to a servo causes the servomotor to apply a torque, which accelerates the load. As the load gathers speed and approaches the desired position we require some arrangement that will 'anticipate' that the load is going to overshoot and so reverse the motor torque before the desired position is reached.
If the arrangement is adjusted correctly the result is that the load comes to rest just as it reaches the required position; overshooting and hunting are therefore prevented.
For a servomechanism, this arrangement is achieved by attaching a tacho-generator to the output shaft. A tacho-tacho-generator is a small ac or dc tacho-generator that produces a voltage proportional to the angular velocity of the output shaft.
A suitable fraction of this voltage is fed back to the input of the amplifier in opposition to the error signal (negative feedback) to provide the necessary compensation; this is known as velocity feedback damping, because the voltage fed back is proportional to the velocity of the output shaft.
The aim with velocity feedback is to reduce the net input to the amplifier to zero and then to reverse it before the output shaft reaches its required position.
If the amount of feedback is correctly adjusted - and this can be done fairly easily by means of a potentiometer - the forward momentum of the load, acting against the reversed torque, causes the load to come to rest just as it reaches the required
If the amount of feedback is correctly adjusted - and this can be done fairly easily by means of a potentiometer - the forward momentum of the load, acting against the reversed torque, causes the load to come to rest just as it reaches the required