Text 9. Servomechanism

 

Servomechanism is an automatic device used to correct the performance of a mechanism by means of an error-sensing feedback. The term servomechanism properly applies only to systems in which the feedback and error-correction signals control mechanical position or one of its derivatives such as velocity or acceleration. Servomechanisms were first used in gunlaying (aiming) and in fire-control and marine-navigation equipment.

Today, applications of servomechanisms include their use in automatic machine tools, satellite-tracking antennas, celestial-tracking systems on telescopes, automatic navigation systems, and antiaircraft-gun control systems.

In many applications, servomechanisms allow high-powered devices to be controlled by signals from devices of much lower power. The operation of the high-powered device results from a signal (called the error, or difference, signal) generated from a comparison of the desired position of the high-powered device with its actual position. The ratio between the power of the control signal and that of the device controlled can be on the order of billions to one.

All servomechanisms have at least these basic components: a controlled device, a command device, an error detector, an error-signal amplifier, and a device to perform any necessary error corrections (the servomotor).

In the controlled device, that which is being regulated is usually position. This device must, therefore, have some means of generating a signal (such as a voltage), called the feedback signal, that represents its current position. This signal is sent to an error-detecting device.

The command device receives information, usually from outside the system, that represents the desired position of the controlled device. This information is converted to a form usable by the system (such as a voltage) and is fed to the same error detector as is the signal from the controlled device.

The error detector compares the feedback signal (representing actual position) with the command signal (representing desired position). Any discrepancy results in an error signal that represents the correction necessary to bring the controlled device to its desired position. The error-correction signal is sent to an amplifier, and the amplified voltage is used to drive the servomotor, which repositions the controlled device.

A typical system using a servomechanism is the communications-satellite–tracking antenna of a satellite Earth station. The objective is to keep the antenna aimed directly at the communications satellite in order to receive and transmit the strongest possible signal. One method used to accomplish this is to compare the signals from the satellite as received by two or more closely positioned receiving elements on the antenna. Any difference in the strengths of the signals received by these elements results in a correction signal being sent to the antenna servomotor. This continuous feedback method allows a terrestrial antenna to be aimed at a satellite 37,007 km (23,000 miles) above the Earth to an accuracy measured in hundredths of a centimetre.

(from Britannica)

 

37. Give a short summary of Text 9:

 

38. Make a list of terms from Text 9 and memorize them.

 

39. Give derivatives of the following words from Text 10 and translate them into Russian:

 

Measurement, exactly, qualitatively, evaluate, reasonable, prespecified, regarding, operator.

 

40. Analyse the structure of the following word-combinations and translate them:

 

Command reference signal, measurement noise, zero steady state error, the worst case exogenous signal.

 

41. Analyse the grammatical structure of the following sentences paying special attention to the italicised words and translate them:

 

1. The plant output y(t) is supposed to follow the command reference signal r(t) as closely as possible.

2. Often the measurement noise n is known to have most of its energy lying in a frequency band [ w1, w2 ].

3. A reasonable requirement to impose is that у track r with "small" error.

4. One approach is to require that the average error over the uncertainty class be small.

5. The other approach is to require that the error response to the worst case exogenous signal from the given class be less than a prespecified value.

 

42. T ranslate Text 10 in writing:

 

Text 10. Performance: Tracking and Disturbance Rejection

 

In the system of Figure 2 the plant output y(t) is supposed to follow or track the command reference signal r(t) as closely as possible despite the disturbances d(t) and the measurement noise n(t). The exogenous signals r,d,n are of course not known exactly as time functions but are known qualitatively. Based on this knowledge the control designer uses certain classes of test signals to evaluate any proposed design. A typical design specification could state that the system is to have zero steady state error whenever the command reference r and disturbance d consist of steps and ramps of arbitrary and unknown magnitude and slope. Often the measurement noise n is known to have most of its energy lying in a frequency band [ w1, w2 ]. In addition to steps and ramps the signals r and d would have significant energy in a low frequency band [ 0, w1 ]. A reasonable requirement to impose is that у track r with "small" error for every signal in this uncertainty class without excessive use of control energy.

There are two approaches to achieving this objective. One approach is to require that the average error over the uncertainty class be small. The other approach is to require that the error response to the worst case exogenous signal from the given class be less than a prespecified value. These correspond to regarding the control system as an operator mapping the exogenous signals to the error and imposing bounds on the norms of these operators or transfer functions.

(from S.P.Bhattacharyya, H. Chapellat, L.H.Keel. Robust Control. The Parametric Approach)