science

Minor loop feedback

Minor loop feedback is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Minor loop feedback rather than just read about it. In short: Minor loop feedback is a classical method used to design stable robust linear feedback 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.

Key takeaways

Minor loop feedback belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Minor loop feedback to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Minor loop feedback from memory before moving on to harder problems.

Reference excerpt

Minor loop feedback is a classical method used to design stable robust linear feedback 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 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. 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 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 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 to the rotor current, even if it is forced to turn backward. Because of the action of the commutator, 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 Tachometer (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 encoder 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) that drives the position control amplifier (KP). 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 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 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 and its overall transfer function can be computed from Mason's Gain Formula.

References

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.

Worked examples

Example 1 — a first encounter with Minor loop feedback

Start with the simplest possible case. Write down what Minor loop feedback claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Minor loop feedback before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Minor loop feedback ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Minor loop feedback

In research: Minor loop feedback appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Minor loop feedback in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Minor loop feedback is common in secondary-school and first-year university syllabi. It links to neighbouring topics Control theory, so understanding it makes those chapters shorter.
In everyday life: Look for Minor loop feedback outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Minor loop feedback in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Minor loop feedback means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Minor loop feedback out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Minor loop feedback in simple terms?

Why does Minor loop feedback matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Minor loop feedback?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Minor loop feedback.