5 SERVO SERVO SYSTEMS SYSTEMS
5.4 SYSTEM SYSTEM RESPONSE RESPONSE
5.4 SYSTEM SYSTEM RESPONSERESPONSE
How well a servomechanism responds to a particular
How well a servomechanism responds to a particular change in input signal, inchange in input signal, in terms of transient response and overshoot, is
terms of transient response and overshoot, is a measure of its overall performance.a measure of its overall performance.
Any servomechanism will take a finite time to start to move and also to settle down Any servomechanism will take a finite time to start to move and also to settle down
at a new position.
at a new position. 'Settling Time' is defined 'Settling Time' is defined as the time taken to apas the time taken to approach a finalproach a final steady state within specific limits.
steady state within specific limits. The diagram below The diagram below shows the response of a shows the response of a RPCRPC system to a step input.
system to a step input.
Unless special precautions
Unless special precautions are taken a are taken a servomechanism will oscillate. servomechanism will oscillate. The diagramThe diagram above, when the output response reaches the required value at point 'x',
above, when the output response reaches the required value at point 'x', the loadthe load has acquired considerable mo
has acquired considerable momentum and consequmentum and consequently overshoots. ently overshoots. The error nowThe error now increases in the opposite sense and a reverse-torque is
increases in the opposite sense and a reverse-torque is applied which brings theapplied which brings the load to rest at point 'y
load to rest at point 'y', and then accelerates it back ', and then accelerates it back in the opposite direction where itin the opposite direction where it again overshoots the de
again overshoots the desired position, at point Z. sired position, at point Z. This process can continuThis process can continuee indefinitely if the frictional losses in the system are negligible, and system would indefinitely if the frictional losses in the system are negligible, and system would oscillate continuously.
oscillate continuously. This is This is called 'huncalled 'hunting'. ting'. To avoid To avoid oscillation and oscillation and subsequentsubsequent hunting, some form of damping is required.
hunting, some form of damping is required.
5.5 DAMPING 5.5 DAMPING
Different amounts of damping produces different response curves.
Different amounts of damping produces different response curves.
•• UnderdampedUnderdamped - - When overshoots anWhen overshoots and transient oscillations d transient oscillations are observed atare observed at the output of a system the s
the output of a system the servomechanism is said to be ervomechanism is said to be underdamped.underdamped.
•• Critically damped - WhenCritically damped - When the system responds to an error in such a way thatthe system responds to an error in such a way that the output moves to the required position at the
the output moves to the required position at the fastest possible rate withoutfastest possible rate without producing
producing overshoots overshoots it is it is said to said to be critically be critically damped. damped. This is This is a theoreticala theoretical position and provides the divis
position and provides the division between underdamping and overdamping.ion between underdamping and overdamping.
•• OverdampedOverdamped - - When no When no overshoots are overshoots are produced, bproduced, but a time ut a time lag is lag is introducedintroduced into the system, the servomechanism is
into the system, the servomechanism is said to be overdamped.said to be overdamped.
In practice, servo sys
In practice, servo systems are designed to be slightly underdamped in order totems are designed to be slightly underdamped in order to reduce response delays. Th
reduce response delays. This is shown by the dotted line is is shown by the dotted line in the diagram. in the diagram. ThisThis degree of damping is often called
degree of damping is often called 'ideal damping'ideal damping'.'.
Under ideally damped conditions, the system reaches the r
Under ideally damped conditions, the system reaches the r equired position moreequired position more quickly than when critically
quickly than when critically damped, but it overswings the demanded position anddamped, but it overswings the demanded position and has to move back onto it.
has to move back onto it. This means the system takes slightly longThis means the system takes slightly longer to reach theer to reach the steady state.
steady state.
5.5.1
5.5.1 FRICTIONAL FORCES WHICH PRODUCE DAMPINGFRICTIONAL FORCES WHICH PRODUCE DAMPING There are frictional forces inherent in a
There are frictional forces inherent in a servo system, which provide damping.servo system, which provide damping.
These are cou
These are coulomb friction and lomb friction and viscous friction. viscous friction. Another friction present Another friction present when thewhen the servo is at rest is stiction.
servo is at rest is stiction.
5.5.1.1 Stiction 5.5.1.1 Stiction Stiction is present in
Stiction is present in the system when the system when it is at rest. it is at rest. This initial friction must This initial friction must bebe overcome in
overcome in order for order for the system the system to move. to move. Once moving, Once moving, stiction falls to stiction falls to zero. zero. TheThe
engineering
engineering
FUNDAMENTALSFUNDAMENTALS5.5.1.2
5.5.1.2 Coulomb Coulomb FrictionFriction
Coulomb Friction is a constant force
Coulomb Friction is a constant force independent of speed and is demonstrated byindependent of speed and is demonstrated by the rubbing friction between two plates. The diagram below shows a s
the rubbing friction between two plates. The diagram below shows a s ystem bothystem both undamped and
undamped and damped with Coudamped with Coulomb friction. lomb friction. The number of oThe number of overshoots in thevershoots in the system using Coulomb friction is proportional to the size of the initial error, the larger system using Coulomb friction is proportional to the size of the initial error, the larger the error the greater the number of overshoots.
the error the greater the number of overshoots.
It will be noted that the r
It will be noted that the response curve of the system using Coulomb frictesponse curve of the system using Coulomb frict ion bringsion brings the system to a steady state but
the system to a steady state but that a positional error is presenthat a positional error is present. t. For this reasonFor this reason coulomb friction is not used i
coulomb friction is not used in practical systems, and although always present n practical systems, and although always present in thein the form of inherent friction, good system
form of inherent friction, good system design keeps it to a minimum.design keeps it to a minimum.
5.5.1.3
5.5.1.3 Viscous Viscous FrictionFriction
Viscous Friction is proportional to velocity and provides satisfactory damping for Viscous Friction is proportional to velocity and provides satisfactory damping for servo systems. When the velocity of the system is zero, viscous friction is zero, and servo systems. When the velocity of the system is zero, viscous friction is zero, and therefore it will not cause a
therefore it will not cause a position error. position error. If the system moves more rapidly, theIf the system moves more rapidly, the viscous friction will
viscous friction will increase, as necessary to increase, as necessary to provide the additional dampingprovide the additional damping required.
required.
The response
The response of a system of a system to a to a ramp input ramp input is shown bis shown below. elow. The oscillations The oscillations of theof the system are damped out, bu
system are damped out, but a constant error is produced. t a constant error is produced. This error is calledThis error is called 'Velocity Lag'
'Velocity Lag'. . The amount of VThe amount of Velocity Lag is proportional to thelocity Lag is proportional to the amount of viscouse amount of viscous damping.
damping.
5.5.1.4
5.5.1.4 Efficiency Efficiency of of Output Output DampingDamping
Both Coulomb and Viscous damping have the great disadvantage of being applied Both Coulomb and Viscous damping have the great disadvantage of being applied to the output of systems.
to the output of systems. This requires large amounThis requires large amounts of energy to control hights of energy to control high power outputs.
power outputs. This inevitably generateThis inevitably generates heat, which es heat, which entails the provision ntails the provision ofof complex cooling systems.
complex cooling systems. It is more efficient to apply dIt is more efficient to apply damping to the inpuamping to the input of thet of the system, where power levels are much lower.
system, where power levels are much lower.
5.5.2
5.5.2 VELOCITY FEEDBACK DAMPVELOCITY FEEDBACK DAMPINGING
A simple and commonly used method of providing damp
A simple and commonly used method of providing damping at the input is to useing at the input is to use Negative Velocity Feedback (NVFB).
Negative Velocity Feedback (NVFB).
A system using NVFB damping is shown in the diagram below
A system using NVFB damping is shown in the diagram below. . The feedback isThe feedback is applied to th
applied to the input and e input and therefore must be therefore must be electrical. electrical. Velocity feedback providesVelocity feedback provides damping similar to viscous friction, but because it is applied to the input, little power damping similar to viscous friction, but because it is applied to the input, little power is required.
is required.
engineering
engineering
FUNDAMENTALSFUNDAMENTALS In servomechanisms, velocity feedback isIn servomechanisms, velocity feedback is achieved by using a tacho-generator (TG)achieved by using a tacho-generator (TG) driven by the output shaft o
driven by the output shaft of the system as shown above. f the system as shown above. A Tacho-generator is aA Tacho-generator is a small electrical generator,
small electrical generator, which is either which is either A.C or D.C. oA.C or D.C. operated. perated. The greatThe great advantage of this type of feedback i
advantage of this type of feedback is that amount of voltage fed back to s that amount of voltage fed back to the system,the system, and therefore the amount of damping, can be controlled by using a si
and therefore the amount of damping, can be controlled by using a si mplemple potentiometer.
potentiometer.
5.5.2.1
5.5.2.1 Velocity Velocity Feedback Feedback CurvesCurves
The diagram below shows the result of applying Velocity
The diagram below shows the result of applying Velocity feedback in the circuitfeedback in the circuit shown in above.
shown in above. As RPC servos are concerned As RPC servos are concerned with the position of the with the position of the load, theload, the velocity lag will only be
velocity lag will only be present when the load is moving and will therefore onlypresent when the load is moving and will therefore only cause a slight increase in the
cause a slight increase in the response time.response time.
5.6
5.6 VELOCITY VELOCITY CONTROL CONTROL SERVOMECHANISMSSERVOMECHANISMS