Minor loop feedback is a classical method used to design stable robust linear

feedback Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause and effect that forms a circuit or loop. The system can then be said to ''feed back'' into itself. The notion of cause-and-effect has to be handle ...

control systems using feedback loops around sub-systems within the overall feedback loop. The method is sometimes called ''minor loop synthesis'' in college textbooks, some government documents. The method is suitable for design by graphical methods and was used before digital computers became available. In World War 2 this method was used to design

gun laying Gun laying is the process of aiming an artillery piece or turret, such as a gun, howitzer, or mortar, on land, at sea, or in air, against surface or aerial targets. It may be laying for either direct fire, where the gun is aimed directly at a ...

control systems. It is still used now, but not always referred to by name. It is often discussed within the context of

Bode plot In electrical engineering and control theory, a Bode plot is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a B ...

methods. Minor loop feedback can be used to stabilize opamps.

Example

Telescope position servo

This example is slightly simplified (no gears between the motor and the load) from the control system for the

Harlan J. Smith Telescope The Harlan J. Smith Telescope is a telescope located at the McDonald Observatory, in Texas, in the United States. This telescope is one of several research telescopes that are part of the University of Texas at Austin observatory perched on M ...

at the McDonald Observatory. In the figure there are three feedback loops: current control loop, velocity control loop and position control loop. The last is the main loop. The other two are minor loops. The forward path, considering only the forward path without the minor loop feedback, has three unavoidable phase shifting stages. The motor inductance and winding resistance form a

low-pass filter A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filt ...

with a bandwidth around 200 Hz. Acceleration to velocity is an

integrator An integrator in measurement and control applications is an element whose output signal is the time integral of its input signal. It accumulates the input quantity over a defined time to produce a representative output. Integration is an importan ...

and velocity to position is an integrator. This would have a total

phase shift In physics and mathematics, the phase (symbol φ or ϕ) of a wave or other periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is expressed in such a s ...

of 180 to 270 degrees. Simply connecting position feedback would almost always result in unstable behaviour.

Current control loop

The innermost loop regulates the current in the torque motor. This type of motor creates torque that is nearly proportional to the

rotor ROTOR was an elaborate air defence radar system built by the British Government in the early 1950s to counter possible attack by Soviet bombers. To get it operational as quickly as possible, it was initially made up primarily of WWII-era syst ...

current, even if it is forced to turn backward. Because of the action of the

commutator In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. Group theory The commutator of two elements, ...

, there are instances when two rotor windings are simultaneously energized. If the motor was driven by a voltage controlled voltage source, the current would roughly double, as would the torque. By sensing the current with a small sensing resister (R_S) and feeding that voltage back to the inverting input of the drive amplifier, the amplifier becomes a voltage controlled current source. With constant current, when two windings are energized, they share the current and the variation of torque is on the order of 10%.

Velocity control loop

The next innermost loop regulates motor speed. The voltage signal from the

Tachometer A tachometer (revolution-counter, tach, rev-counter, RPM gauge) is an instrument measuring the rotation speed of a axle, shaft or disk, as in a motor or other machine. The device usually displays the revolutions per minute (RPM) on a calibrat ...

(a small permanent magnet DC generator) is proportional to the angular velocity of the motor. This signal is fed back to the inverting input of the velocity control amplifier (K_V). The velocity control system makes the system 'stiffer' when presented with torque variations such as wind, movement about the second axis and

torque ripple Torque ripple is an effect seen in many electric motor designs, referring to a periodic increase or decrease in output torque as the motor shaft rotates. It is measured as the difference in maximum and minimum torque over one complete revolution, ge ...

from the motor.

Position control loop

The outermost loop, the main loop, regulates load position. In this example, position feedback of the actual load position is presented by a

Rotary encoder A rotary encoder, also called a shaft encoder, is an electro-mechanical device that converts the angle, angular position or motion of a shaft or axle to Analog signal, analog or Digital signal, digital output signals. There are two main types of ...

that produces a binary output code. The actual position is compared to the desired position by a digital subtractor that drives a DAC (

Digital-to-analog converter In electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function. DACs are commonly used in musi ...

) that drives the position control amplifier (K_P). Position control allows the servo to compensate for sag and for slight position ripple caused by gears (not shown) between the motor and the telescope

Synthesis

The usual design procedure is to design the innermost subsystem (the current control loop in the telescope example) using local feedback to linearize and flatten the gain. Stability is generally assured by

methods. Usually, the

bandwidth Bandwidth commonly refers to: * Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range * Bandwidth (computing), the rate of data transfer, bit rate or thr ...

is made as wide as possible. Then the next loop (the velocity loop in the telescope example) is designed. The bandwidth of this sub-system is set to be a factor of 3 to 5 less than the bandwidth of the enclosed system. This process continues with each loop having less bandwidth than the bandwidth of the enclosed system. As long as the bandwidth of each loop is less than the bandwidth of the enclosed sub-system by a factor of 3 to 5, the phase shift of the enclosed system can be neglected, i.e. the sub-system can be treated as simple flat gain. Since the bandwidth of each sub-system is less than the bandwidth of the system it encloses, it is desirable to make the bandwidth of each sub-system as large as possible so that there is enough bandwidth in the outermost loop. The system is often expressed as a

Signal-flow graph A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the term, is a specialized Flow graph (mathematics), flow graph, a directed graph in which nodes rep ...

and its overall transfer function can be computed from Mason's Gain Formula.

References

{{Reflist

External links

*Li, Yunfeng and Roberto Horowitz.
Mechatronics of Electrostatic Microactuators for Computer Disk Drive Dual-Stage Servo Systems
" ''IEEE/ASME Transactions on Mechatronics'', Vol. 6 No. 2. June 2001. *Dawson, Joel L.
Feedback Systems
" MIT.
Large Telescope Conference 1971
contains full text of Dittmar's presentation. Control theory