Minor loop feedback
Encyclopedia
Minor loop feedback is a classical method used to design stable robust linear Feedback
control systems using feedback loops around sub-systems within the over all feedback loop. The method is sometimes called minor loop synthesis in college text books, some government documents and course descriptions of electrical engineering classes.
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
control systems. It is still used now, but not always referred to by name. It is often discussed within the context of Bode plot
methods.
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 lowpass filter with a bandwidth around 200 Hz. Acceleration to velocity is an integrator and velocity to position is an integrator. This would have a total phase shift of 180 to 270 degrees. Simply connecting position feedback would almost always result in unstable behaviour.
(actually 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 (KV). The velocity control system makes the system 'stiffer' when presented with torque variations such as wind, movement about the second axis and torque ripple from the motor.
that produces a binary output code. The actual position is compared to the desired position by a digital subtracter that drives a DAC (Digital-to-analog converter
) that drives the position control amplifier (KP).
and its overall transfer function can be computed from Mason's Gain Formula
.
Feedback
Feedback describes the situation when output from an event or phenomenon in the past will influence an occurrence or occurrences of the same Feedback describes the situation when output from (or information about the result of) an event or phenomenon in the past will influence an occurrence or...
control systems using feedback loops around sub-systems within the over all feedback loop. The method is sometimes called minor loop synthesis in college text books, some government documents and course descriptions of electrical engineering classes.
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
Gun laying is the process of aiming an artillery piece, such as a gun, howitzer or mortar on land or at sea against surface or air targets. It may be laying for direct fire, where the gun is aimed similarly to a rifle, or indirect fire, where firing data is calculated and applied to the sights...
control systems. It is still used now, but not always referred to by name. It is often discussed within the context of Bode plot
Bode plot
A Bode plot is a graph of the transfer function of a linear, time-invariant system versus frequency, plotted with a log-frequency axis, to show the system's frequency response...
methods.
Notability
"minor loop feedback" returns 12,200 hits from google. Among them are- ieee documents,
- nasa documents
- university documents.
Telescope position servo
This example is slightly simplifed (no gears between the motor and the load) from the control system for the Harlan J. Smith TelescopeHarlan J. Smith Telescope
The Harlan J. Smith Telescope is a 2.7m 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 atop Mount Locke in the Davis Mountains of west Texas...
at the McDonald Observatory
McDonald Observatory
The McDonald Observatory is an astronomical observatory located near the unincorporated community of Fort Davis in Jeff Davis County, Texas, United States. The facility is located on Mount Fowlkes and Mount Locke in the Davis Mountains of West Texas...
. 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 lowpass filter with a bandwidth around 200 Hz. Acceleration to velocity is an integrator and velocity to position is an integrator. This would have a total phase shift 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 rotor current, even if it is forced to turn backward. Because of the action of the commutater, 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 (RS) 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 TachometerTachometer
A tachometer is an instrument measuring the rotation speed of a shaft or disk, as in a motor or other machine. The device usually displays the revolutions per minute on a calibrated analogue dial, but digital displays are increasingly common...
(actually 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 (KV). The velocity control system makes the system 'stiffer' when presented with torque variations such as wind, movement about the second axis and torque ripple 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 encoderRotary encoder
A rotary encoder, also called a shaft encoder, is an electro-mechanical device that converts the angular position or motion of a shaft or axle to an analog or digital code. The output of incremental encoders provides information about the motion of the shaft which is typically further processed...
that produces a binary output code. The actual position is compared to the desired position by a digital subtracter that drives a DAC (Digital-to-analog converter
Digital-to-analog converter
In electronics, a digital-to-analog converter is a device that converts a digital code to an analog signal . An analog-to-digital converter performs the reverse operation...
) that drives the position control amplifier (KP).
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 Bode plot methods. Usually, the bandwidth 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 pure 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 graphSignal-flow graph
A signal-flow graph is a special type of block diagram—and directed graph—consisting of nodes and branches. Its nodes are the variables of a set of linear algebraic relations. An SFG can only represent multiplications and additions. Multiplications are represented by the weights of the branches;...
and its overall transfer function can be computed from Mason's Gain Formula
Mason's rule
Mason's gain formula is a method for finding the transfer function of a linear signal-flow graph . The formula was derived by Samuel Jefferson Mason and is named after its discoverer...
.
External links
- http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19810006486_1981006486.pdf
- The link above is a searchable pdf. Search for "minor loop synthesis" which is on page 26.
- http://www.iitm.ac.in/downloads/academic/Curriculum/MTechEE2009.pdf
- The link above is a searchable pdf. Search for "minor loop synthesis" which is in the sylibus of EE5650
- http://userspages.uob.edu.bh/ebrgallaf/00506394.pdf a brief history of automatic control
- the link above appears to be scanned. see page 20, right hand column, last paragragh.
- http://ieeexplore.ieee.org/application/enterprise/entconfirmation.jsp?arnumber=00250538
- http://ieeexplore.ieee.org/xpls/abs_all.jsp?tp=&arnumber=1384678
- http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=01280050
- http://www.me.berkeley.edu/~horowitz/Publications_files/All_papers_numbered/45j_Li_Mechatronics_Electrostatic_IEEE_TOM01.pdf
- http://www-mtl.mit.edu/~jldawson/documents/6.302rec18.pdf good