Feedback Systems - Control Systems - Electrical Engineering (EE) PDF Download

Table of Contents
1. Introduction
2. Feedback system block-diagram model
3. Positive feedback systems
4. Negative feedback systems
5. Classification of single-loop feedback systems
6. Practical remarks on feedback
7. Summary
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Introduction

Feedback systems process signals and therefore act as signal processors. The processing element of a feedback system may be electrical or electronic and can range from very simple analogue circuits built from discrete components (transistors, resistors, capacitors) to complex digital systems implemented with microprocessors and integrated circuits (ICs).

• Open-loop systems do not compensate for changes in operating conditions or component variations (gain, temperature, supply voltage, load, external disturbances). The effects of such variations can often be reduced - sometimes largely eliminated - by introducing feedback.
• A feedback system samples the output signal and feeds a portion of it back to the input to form an error signal that drives the system. The feedback network effectively modifies the input so the overall response may differ substantially from the open-loop response.
• Feedback is widely used in amplifier circuits, oscillators, process control and many other electronic and electro-mechanical systems. For feedback to be beneficial it must be controlled: uncontrolled feedback can lead to instability or failure to function.

Feedback system block-diagram model

A fundamental model of a single-loop feedback system consists of a forward path with transfer function G, a feedback path with transfer function H, and summing point(s) where the reference input and the feedback signal are combined to form the error. The loop product GH is often called the loop gain or return ratio and determines many closed-loop properties.

Reasons for using feedback include:

• Accurate control of circuit characteristics such as gain and transient response.
• Making circuit behaviour less sensitive to operating conditions (supply variations, temperature, component tolerances).
• Reduction of signal distortion produced by nonlinearities in components.
• Control of frequency response, gain and bandwidth to meet design limits.
• Feedback types are broadly classified into two categories: negative feedback (degenerative) and positive feedback (regenerative).

Positive feedback systems

In a positive feedback (regenerative) system the sampled output is re-applied to the input in phase with the input, so the feedback signal adds to the input. The principal effect of positive feedback is to increase the effective gain of the system.

• Positive feedback increases the loop gain. If the forward gain is G and the feedback factor is H, then for a simple positive feedback connection the closed-loop gain is given by Av = G / (1 - GH).
• If GH = 1 (loop magnitude unity and correct phase), the denominator becomes zero and the closed-loop gain tends to infinity; the system can sustain oscillations without an external input - this is the principle behind oscillators.
• Positive feedback can therefore lead to instability (self-oscillation) if not controlled. However, this same behaviour is deliberately used in circuits that require rapid switching or bi-stable states (for example, multivibrators, Schmitt triggers and certain logic devices).
• An operational amplifier (op-amp) configured with a portion of its output fed back to the non-inverting (+) input is a typical example of positive feedback.

• When a small positive input is applied, the op-amp output becomes more positive, and the returned portion further increases the input, causing the output to drive toward saturation. Similarly, a negative input drives the output to the opposite supply rail. Hence, with positive feedback the amplifier rapidly saturated and cannot operate as a linear amplifier over a useful range.
• Positive feedback is therefore useful for hysteresis and sharp switching thresholds (bi-stability), and for deliberately creating oscillations, but it must be applied with care to avoid unwanted instability in analogue amplifiers.

Negative feedback systems

In a negative feedback (degenerative) system the feedback signal is out of phase with the input (or subtracted from it). The feedback tends to reduce the effective gain of the forward path but improves stability, linearity and bandwidth.

• For a typical negative feedback configuration the closed-loop gain is Av = G / (1 + GH).
• Negative feedback reduces sensitivity to variations in component values and operating conditions and suppresses distortion due to nonlinearities.
• An op-amp example is an amplifier that returns a portion of the output to the inverting (-) input. The returned signal subtracts from the input and stabilises the output at a value set by the feedback network.

• With negative feedback the circuit can operate linearly over a wide range so long as the closed-loop output remains within supply limits. Negative feedback follows the rule "more leads to less" and "less leads to more", which is why it tends to stabilise the system.
• Although negative feedback generally improves stability, if the loop introduces sufficient phase shift then the effective feedback may become regenerative at some frequency. If the loop gain magnitude equals unity when the loop phase shift is 180°, the feedback becomes positive at that frequency and the system can oscillate; this is the principle checked in stability criteria such as Nyquist and Bode plots.

Classification of single-loop feedback systems

Feedback systems are also classified according to the nature of the input and output variables (voltage or current) and by how the feedback network connects to the input and output (series or shunt). There are four basic single-loop feedback configurations:

• Series-Shunt (Voltage in - Voltage out) - Voltage is applied at the input in series with the error signal and the output voltage is sampled (shunt) to provide the feedback; this is a voltage amplifier (voltage-controlled voltage source, VCVS).
• Shunt-Shunt (Current in - Voltage out) - Output voltage is sampled and converted to a current that is fed back in shunt with the input; this is a transresistance (current-to-voltage) configuration (current-controlled voltage source, CCVS).
• Series-Series (Voltage in - Current out) - Output current is sensed and fed back in series with the input; this is a transconductance (voltage-to-current) configuration (voltage-controlled current source, VCCS).
• Shunt-Series (Current in - Current out) - Output current is sampled and returned in series at the output while the feedback is applied in shunt at the input; this behaves as a current amplifier (current-controlled current source, CCCS).

The terms "series" and "shunt" describe how the feedback signal is connected at the input or output: a series connection inserts the feedback in series with the input (affecting input impedance), while a shunt connection applies the feedback in parallel with the input (affecting input impedance in the other direction). Similarly at the output, series feedback tends to raise output impedance and shunt feedback tends to lower it. The choice of topology depends on the desired input/output impedance and the physical nature of the signals to be controlled.

Series-Shunt feedback systems (Voltage in - Voltage out)

Series-shunt feedback is used when both the input and the output are voltages and a voltage amplifier is required. The error voltage is inserted in series with the input and the feedback is proportional to the output voltage (sampled in shunt).

• Most inverting and non-inverting op-amp amplifier circuits implement series-shunt feedback and act as voltage amplifiers.
• For an ideal voltage amplifier in this configuration, input resistance (Rin) is very large and output resistance (Rout) is very small.
• The closed-loop voltage gain is Av = Vout ÷ Vin and is dimensionless (volts/volts).

Shunt-Series feedback systems (Current in - Current out)

Shunt-series feedback (also described as shunt current feedback) is appropriate when both the input and the output are currents and a current amplifier is needed. The feedback signal is proportional to the output current and is returned in parallel (shunt) with the input current.

• In this configuration the signals that add are currents rather than voltages.
• The shunt at the input reduces the effective input resistance and the series at the output increases the output resistance.
• The current gain is given by Ai = Iout ÷ Iin and is dimensionless (amperes/amperes).

Series-Series feedback systems (Voltage in - Current out)

Series-series feedback converts a voltage input to a current output (transconductance). The sampled output current is converted to a voltage and fed back in series with the input.

• This topology raises both input and output impedances, so it is suitable when a large input impedance and a large output impedance are required.
• The transconductance gain is given by Gm = Iout ÷ Vin.

Shunt-Shunt feedback systems (Current in - Voltage out)

Shunt-shunt feedback is used when a current input is converted to a voltage output (transresistance). The output voltage is sensed and an equivalent current is fed back in shunt with the input.

• This topology reduces both input and output impedances and is useful when low impedances are desired at both ends.
• The transresistance gain is given by Rm = Vout ÷ Iin.

Practical remarks on feedback

• Loop gain and stability: The sign and magnitude of the loop gain GH together with the frequency-dependent phase shift determine stability. If the magnitude of GH reaches unity at a frequency where the loop phase shift makes the feedback effectively positive, the closed-loop system can oscillate. Frequency-domain techniques (Bode and Nyquist plots) are used to assess stability and margins.
• Trade-offs: Negative feedback improves linearity and bandwidth but reduces closed-loop gain. It may also increase noise in some configurations and has practical limits due to finite open-loop gain and phase shift of the forward path.
• Impedance effects: Series feedback at the input raises input impedance; shunt feedback at the input lowers input impedance. Series feedback at the output raises output impedance; shunt feedback at the output lowers output impedance. Choose topology according to desired input/output source and load conditions.
• Applications: Negative feedback is widely used in audio amplifiers, instrumentation amplifiers, regulator circuits and control loops to improve accuracy and reproducibility. Positive feedback is used for oscillators, regenerative receivers, hysteresis circuits (Schmitt triggers) and rapid digital switching.
• Design caution: In practical circuits consider component tolerances, temperature dependence, and the frequency response of G and H. Ensure adequate stability margin to avoid unwanted oscillation and to obtain predictable transient response.

Summary

• A feedback system samples the output and feeds a portion of it back to the input to form an error signal that controls the system.
• Feedback can be negative (degenerative) or positive (regenerative). Negative feedback reduces gain, improves stability and bandwidth, and reduces sensitivity to component variations. Positive feedback increases gain and can produce instability or sustained oscillation when the loop condition is met; it is used deliberately in oscillators and switching circuits.
• Closed-loop transfer for simple single-loop systems is commonly written as Gcl = G / (1 ± GH), where the sign depends on the feedback polarity and the exact arrangement. The loop product GH determines many closed-loop properties; stability must be checked when |GH| approaches unity at frequencies where the phase causes effective regeneration.
• There are four basic single-loop connection types based on series/shunt connections at input and output: Series-Shunt (voltage in, voltage out), Shunt-Shunt (current in, voltage out), Series-Series (voltage in, current out), and Shunt-Series (current in, current out). The names indicate how the feedback network is connected and determine the effect on input/output impedances.
• Feedback must be designed with attention to the forward path frequency response and the feedback network so that the desired performance (gain, bandwidth, stability, linearity and impedance) is achieved.