Minor loop feedback

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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. [1] The method is sometimes called minor loop synthesis in college textbooks, [1] [2] some government documents. [3]

Contents

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. [4] 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. [5]

Example

Telescope position servo

Angular position servo and signal flow graph. thC = desired angle command, thL = actual load angle, KP = position loop gain, VoC = velocity command, VoM = motor velocity sense voltage, KV = velocity loop gain, VIC = current command, VIM = current sense voltage, KC = current loop gain, VA = power amplifier output voltage, LM = motor inductance, IM = motor current, RM = motor resistance, RS = current sense resistance, KM = motor torque constant (Nm/amp), T = torque, M = moment of inertia of all rotating components a = angular acceleration, o = angular velocity, b = mechanical damping, GM = motor back EMF constant, GT = tachometer conversion gain constant,. There is one forward path (shown in a different color) and six feedback loops. The drive shaft assumed to be stiff enough to not treat as a spring. Constants are shown in black and variables in purple. Intentional feedback is shown with dotted lines. Position servo and signal flow graph.png
Angular position servo and signal flow graph. θC = desired angle command, θL = actual load angle, KP = position loop gain, VωC = velocity command, VωM = motor velocity sense voltage, KV = velocity loop gain, VIC = current command, VIM = current sense voltage, KC = current loop gain, VA = power amplifier output voltage, LM = motor inductance, IM = motor current, RM = motor resistance, RS = current sense resistance, KM = motor torque constant (Nm/amp), T = torque, M = moment of inertia of all rotating components α = angular acceleration, ω = angular velocity, β = mechanical damping, GM = motor back EMF constant, GT = tachometer conversion gain constant,. There is one forward path (shown in a different color) and six feedback loops. The drive shaft assumed to be stiff enough to not treat as a spring. Constants are shown in black and variables in purple. Intentional feedback is shown with dotted lines.

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. [6] 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 subtracter 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.

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An electric motor is an electrical machine that converts electrical energy into mechanical energy. Most electric motors operate through the interaction between the motor's magnetic field and electric current in a wire winding to generate force in the form of torque applied on the motor's shaft. Electric motors can be powered by direct current (DC) sources, such as from batteries, or rectifiers, or by alternating current (AC) sources, such as a power grid, inverters or electrical generators. An electric generator is mechanically identical to an electric motor, but operates with a reversed flow of power, converting mechanical energy into electrical energy.

Pulse-width modulation

Pulse-width modulation (PWM), or pulse-duration modulation (PDM), is a method of reducing the average power delivered by an electrical signal, by effectively chopping it up into discrete parts. The average value of voltage fed to the load is controlled by turning the switch between supply and load on and off at a fast rate. The longer the switch is on compared to the off periods, the higher the total power supplied to the load. Along with maximum power point tracking (MPPT), it is one of the primary methods of reducing the output of solar panels to that which can be utilized by a battery. PWM is particularly suited for running inertial loads such as motors, which are not as easily affected by this discrete switching, because their inertia causes them to react slowly. The PWM switching frequency has to be high enough not to affect the load, which is to say that the resultant waveform perceived by the load must be as smooth as possible.

Stepper motor

A stepper motor, also known as step motor or stepping motor, is a brushless DC electric motor that divides a full rotation into a number of equal steps. The motor's position can be commanded to move and hold at one of these steps without any position sensor for feedback, as long as the motor is correctly sized to the application in respect to torque and speed.

In control engineering a servomechanism, sometimes shortened to servo, is an automatic device that uses error-sensing negative feedback to correct the action of a mechanism. On displacement-controlled applications, it usually includes a built-in encoder or other position feedback mechanism to ensure the output is achieving the desired effect.

Synchronous motor Type of AC motor

A synchronous electric motor is an AC motor in which, at steady state, the rotation of the shaft is synchronized with the frequency of the supply current; the rotation period is exactly equal to an integral number of AC cycles. Synchronous motors contain multiphase AC electromagnets on the stator of the motor that create a magnetic field which rotates in time with the oscillations of the line current. The rotor with permanent magnets or electromagnets turns in step with the stator field at the same rate and as a result, provides the second synchronized rotating magnet field of any AC motor. A synchronous motor is termed doubly fed if it is supplied with independently excited multiphase AC electromagnets on both the rotor and stator.

A motor controller is a device or group of devices that can coordinate in a predetermined manner the performance of an electric motor. A motor controller might include a manual or automatic means for starting and stopping the motor, selecting forward or reverse rotation, selecting and regulating the speed, regulating or limiting the torque, and protecting against overloads and electrical faults. Motor controllers may use electromechanical switching, or may use power electronics devices to regulate the speed and direction of a motor.

Brushless DC electric motor Synchronous electric motor powered by an inverter

A brushless DC electric motor, also known as an electronically commutated motor or synchronous DC motor, is a synchronous motor using a direct current (DC) electric power supply. It uses an electronic closed loop controller to switch DC currents to the motor windings producing magnetic fields which effectively rotate in space and which the permanent magnet rotor follows. The controller adjusts the phase and amplitude of the DC current pulses to control the speed and torque of the motor. This control system is an alternative to the mechanical commutator (brushes) used in many conventional electric motors.

Synchro

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Motion control

Motion control is a sub-field of automation, encompassing the systems or sub-systems involved in moving parts of machines in a controlled manner. Motion control systems are extensively used in a variety of fields for automation purposes, including precision engineering, micromanufacturing, biotechnology, and nanotechnology. The main components involved typically include a motion controller, an energy amplifier, and one or more prime movers or actuators. Motion control may be open loop or closed loop. In open loop systems, the controller sends a command through the amplifier to the prime mover or actuator, and does not know if the desired motion was actually achieved. Typical systems include stepper motor or fan control. For tighter control with more precision, a measuring device may be added to the system. When the measurement is converted to a signal that is sent back to the controller, and the controller compensates for any error, it becomes a Closed loop System.

Servomotor Type of motor

A servomotor is a rotary actuator or linear actuator that allows for precise control of angular or linear position, velocity and acceleration. It consists of a suitable motor coupled to a sensor for position feedback. It also requires a relatively sophisticated controller, often a dedicated module designed specifically for use with servomotors.

Servo drive Electronic amplifier used to power electric servomechanisms

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Reluctance motor Type of electric motor

A reluctance motor is a type of electric motor that induces non-permanent magnetic poles on the ferromagnetic rotor. The rotor does not have any windings. It generates torque through magnetic reluctance.

AC motor Electric motor driven by an AC electrical input

An AC motor is an electric motor driven by an alternating current (AC). The AC motor commonly consists of two basic parts, an outside stator having coils supplied with alternating current to produce a rotating magnetic field, and an inside rotor attached to the output shaft producing a second rotating magnetic field. The rotor magnetic field may be produced by permanent magnets, reluctance saliency, or DC or AC electrical windings.

Amplidyne

An amplidyne is an electromechanical amplifier invented prior to World War II by Ernst Alexanderson. It consists of an electric motor driving a DC generator. The signal to be amplified is applied to the generator's field winding, and its output voltage is an amplified copy of the field current. The amplidyne was used in industry in high power servo and control systems, to amplify low power control signals to control powerful electric motors, for example. It is now mostly obsolete.

A brushed DC electric motor is an internally commutated electric motor designed to be run from a direct current power source. Brushed motors were the first commercially important application of electric power to driving mechanical energy, and DC distribution systems were used for more than 100 years to operate motors in commercial and industrial buildings. Brushed DC motors can be varied in speed by changing the operating voltage or the strength of the magnetic field. Depending on the connections of the field to the power supply, the speed and torque characteristics of a brushed motor can be altered to provide steady speed or speed inversely proportional to the mechanical load. Brushed motors continue to be used for electrical propulsion, cranes, paper machines and steel rolling mills. Since the brushes wear down and require replacement, brushless DC motors using power electronic devices have displaced brushed motors from many applications.

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Vector control, also called field-oriented control (FOC), is a variable-frequency drive (VFD) control method in which the stator currents of a three-phase AC or brushless DC electric motor are identified as two orthogonal components that can be visualized with a vector. One component defines the magnetic flux of the motor, the other the torque. The control system of the drive calculates the corresponding current component references from the flux and torque references given by the drive's speed control. Typically proportional-integral (PI) controllers are used to keep the measured current components at their reference values. The pulse-width modulation of the variable-frequency drive defines the transistor switching according to the stator voltage references that are the output of the PI current controllers.

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High performance positioning system

A high performance positioning system (HPPS) is a type of positioning system consisting of a piece of electromechanics equipment that is capable of moving an object in a three-dimensional space within a work envelope. Positioning could be done point to point or along a desired path of motion. Position is typically defined in six degrees of freedom, including linear, in an x,y,z cartesian coordinate system, and angular orientation of yaw, pitch, roll. HPPS are used in many manufacturing processes to move an object smoothly and accurately in six degrees of freedom, along a desired path, at a desired orientation, with high acceleration, high deceleration, high velocity and low settling time. It is designed to quickly stop its motion and accurately place the moving object at its desired final position and orientation with minimal jittering.

References

  1. 1 2 Kuo, Benjamin C. (1991), Automatic Control Systems , Prentice-Hall, ISBN   978-0-13-051046-4
  2. ↑ Brown, Gordon S.; Campbell, Donald P. (1948), Principles of Servomechanisms, John Wiley & Sons
  3. ↑ Leininger, Gary, Application of the MNA Design Method to a Non-Linear Turbofan Engine (PDF), retrieved 18 Mar 2011
  4. ↑ Bennett, Stuart, A brief History of Automatic Control (PDF), p. 20, archived from the original (PDF) on 2011-10-07, retrieved 18 Mar 2011
  5. ↑ Lundberg, Internal and external op-amp compensation: a control-centric tutorial , retrieved 18 Mar 2011
  6. ↑ Dittmar, David (1–5 Mar 1971). Conference on Large Telescope Design, Proceedings of an ESO (European Southern Observatory)/CERN (Conseil Europeen pour la Recherche Nucleaire) Conference. Geneva, Switzerland (published June 1971). p. 383.
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