S NAGA MALLESWARA REDDY

Feedback Systems process signals and as such are signal processors. The processing part of a feedback system may be electrical or electronic, ranging from a very simple to a highly complex circuits. Simple analogue feedback control circuits can be constructed using individual or discrete components, such as transistors, resistors and capacitors, etc, or by using microprocessor-based and integrated circuits (IC's) to form more complex digital feedback systems.

As we have seen, open-loop systems are just that, open ended, and no attempt is made to compensate for changes in circuit conditions or changes in load conditions due to variations in circuit parameters, such as gain and stability, temperature, supply voltage variations and/or external disturbances. But the effects of these "open-loop" variations can be eliminated or at least considerably reduced by the introduction of Feedback.

A feedback system is one in which the output signal is sampled and then fed back to the input to form an error signal that drives the system. In the previous tutorial about Closed-loop Systems, we saw that in general, Feedback is comprised of a subcircuit that allows a fraction of the output signal from a system to modify the effective input signal in such a way as to produce a response that can differ substantially from the response produced in the absence of such feedback.

Feedback Systems are very useful and widely used in amplifier circuits, oscillators, process control systems as well as other types of electronic systems. But for feedback to be an effective tool it must be controlled as an uncontrolled system will either oscillate or fail to function. The basic model of a feedback system is given as:

Feedback System Block Diagram Model

This basic feedback loop of sensing, controlling and actuation is the main concept behind a feedback control system and there are several good reasons why feedback is applied and used in electronic circuits:

• Circuit characteristics such as the systems gain and response can be precisely controlled.
• Circuit characteristics can be made independent of operating conditions such as supply voltages or temperature variations.
• Signal distortion due to the non-linear nature of the components used can be greatly reduced.
• The Frequency Response, Gain and Bandwidth of a circuit or system can be easily controlled to within tight limits.

Whilst there are many different types of control systems, there are just two main types of feedback control namely: Negative Feedback and Positive Feedback.

Positive Feedback Systems

In a "positive feedback control system", the set point and output values are added together by the controller as the feedback is "in-phase" with the input. The effect of positive (or regenerative) feedback is to "increase" the systems gain, ie, the overall gain with positive feedback applied will be greater than the gain without feedback. For example, if someone praises you or gives you positive feedback about something, you feel happy about yourself and are full of energy, you feel more positive.

However, in electronic and control systems to much praise and positive feedback can increase the systems gain far too much which would give rise to oscillatory circuit responses as it increases the magnitude of the effective input signal.

An example of a positive feedback systems could be an electronic amplifier based on an operational amplifier, or op-amp as shown.

Positive Feedback System

Positive feedback control of the op-amp is achieved by applying a small part of the output voltage signal at Vout back to the non-inverting ( + ) input terminal via the feedback resistor, RF.

If the input voltage Vin is positive, the op-amp amplifies this positive signal and the output becomes more positive. Some of this output voltage is returned back to the input by the feedback network.

Thus the input voltage becomes more positive, causing an even larger output voltage and so on. Eventually the output becomes saturated at its positive supply rail.

Likewise, if the input voltage Vin is negative, the reverse happens and the op-amp saturates at its negative supply rail. Then we can see that positive feedback does not allow the circuit to function as an amplifier as the output voltage quickly saturates to one supply rail or the other, because with positive feedback loops "more leads to more" and "less leads to less".

Then if the loop gain is positive for any system the transfer function will be: Av = G / (1 – GH). Note that if GH = 1 the system gain Av = infinity and the circuit will start to self-oscillate, after which no input signal is needed to maintain oscillations, which is useful if you want to make an oscillator.

Although often considered undesirable, this behaviour is used in electronics to obtain a very fast switching response to a condition or signal. One example of the use of positive feedback is hysteresis in which a logic device or system maintains a given state until some input crosses a preset threshold. This type of behaviour is called "bi-stability" and is often associated with logic gates and digital switching devices such as multivibrators.

We have seen that positive or regenerative feedback increases the gain and the possibility of instability in a system which may lead to self-oscillation and as such, positive feedback is widely used in oscillatory circuits such as Oscillators and Timing circuits.

Negative Feedback Systems

In a "negative feedback control system", the set point and output values are subtracted from each other as the feedback is "out-of-phase" with the original input. The effect of negative (or degenerative) feedback is to "reduce" the gain. For example, if someone criticises you or gives you negative feedback about something, you feel unhappy about yourself and therefore lack energy, you feel less positive.

Because negative feedback produces stable circuit responses, improves stability and increases the operating bandwidth of a given system, the majority of all control and feedback systems is degenerative reducing the effects of the gain.

An example of a negative feedback system is an electronic amplifier based on an operational amplifier as shown.

Negative Feedback System

Negative feedback control of the amplifier is achieved by applying a small part of the output voltage signal at Vout back to the inverting ( – ) input terminal via the feedback resistor, Rf.

If the input voltage Vin is positive, the op-amp amplifies this positive signal, but because its connected to the inverting input of the amplifier, and the output becomes more negative. Some of this output voltage is returned back to the input by the feedback network of Rf.

Thus the input voltage is reduced by the negative feedback signal, causing an even smaller output voltage and so on. Eventually the output will settle down and become stabilised at a value determined by the gain ratio of Rf ÷ Rin.

Likewise, if the input voltage Vin is negative, the reverse happens and the op-amps output becomes positive (inverted) which adds to the negative input signal. Then we can see that negative feedback allows the circuit to function as an amplifier, so long as the output is within the saturation limits.

So we can see that the output voltage is stabilised and controlled by the feedback, because with negative feedback loops "more leads to less" and "less leads to more".

Then if the loop gain is positive for any system the transfer function will be: Av = G / (1 + GH).

The use of negative feedback in amplifier and process control systems is widespread because as a rule negative feedback systems are more stable than positive feedback systems, and a negative feedback system is said to be stable if it does not oscillate by itself at any frequency except for a given circuit condition.

Another advantage is that negative feedback also makes control systems more immune to random variations in component values and inputs. Of course nothing is for free, so it must be used with caution as negative feedback significantly modifies the operating characteristics of a given system.

Classification of Feedback Systems

Thus far we have seen the way in which the output signal is "fed back" to the input terminal, and for feedback systems this can be of either, Positive Feedback or Negative Feedback. But the manner in which the output signal is measured and introduced into the input circuit can be very different leading to four basic classifications of feedback.

Based on the input quantity being amplified, and on the desired output condition, the input and output variables can be modelled as either a voltage or a current. As a result, there are four basic classifications of single-loop feedback system in which the output signal is fed back to the input and these are:

• Series-Shunt Configuration – Voltage in and Voltage out or Voltage Controlled Voltage Source (VCVS).
• Shunt-Shunt Configuration – Current in and Voltage out or Current Controlled Voltage Source (CCVS).
• Series-Series Configuration – Voltage in and Current out or Voltage Controlled Current Source (VCCS).
• Shunt-Series Configuration – Current in and Current out or Current Controlled Current Source (CCCS).

These names come from the way that the feedback network connects between the input and output stages as shown.

Series-Shunt Feedback Systems

Series-Shunt Feedback, also known as series voltage feedback, operates as a voltage-voltage controlled feedback system. The error voltage fed back from the feedback network is in series with the input. The voltage which is fed back from the output being proportional to the output voltage,Vo as it is parallel, or shunt connected.

Series-Shunt Feedback System

For the series-shunt connection, the configuration is defined as the output voltage to the input voltage. Most inverting and non-inverting operational amplifier circuits operate with series-shunt feedback producing what is known as a "voltage amplifier". As a voltage amplifier the ideal input resistance, Rin is very large, and the ideal output resistance, Rout is very small.

Then the "series-shunt feedback configuration" works as a true voltage amplifier as the input signal is a voltage and the output signal is a voltage, so the transfer gain is given as: Av = Vout ÷ Vin.

Shunt-Series Feedback Systems

Shunt-Series Feedback, also known as shunt current feedback, operates as a current-current controlled feedback system. The feedback signal is proportional to the output current, Io flowing in the load. The feedback signal is fed back in parallel or shunt with the input as shown.

Shunt-Series Feedback System

For the shunt-series connection, the configuration is defined as the output current to the input current. In the shunt-series feedback configuration the signal fed back is in parallel with the input signal and as such its the currents, not the voltages that add.

This parallel shunt feedback connection will not normally affect the voltage gain of the system, since for a voltage output a voltage input is required. Also, the series connection at the output increases output resistance, Rout while the shunt connection at the input decreases the input resistance, Rin.

Then the "shunt-series feedback configuration" works as a true current amplifier as the input signal is a current and the output signal is a current, so the transfer gain is given as: Ai = Iout ÷ Iin.

Series-Series Feedback Systems

Series-Series Feedback Systems, also known as series current feedback, operates as a voltage-current controlled feedback system. In the series current configuration the feedback error signal is in series with the input and is proportional to the load current, Iout. Actually, this type of feedback converts the current signal into a voltage which is actually fed back and it is this voltage which is subtracted from the input.

Series-Series Feedback System

For the series-series connection, the configuration is defined as the output current to the input voltage. Because the output current, Io of the series connection is fed back as a voltage, this increases both the input and output impedances of the system. Therefore, the circuit works best as a transconductance amplifier with the ideal input resistance, Rin being very large, and the ideal output resistance, Rout is also very large.

Then the "series-series feedback configuration" functions as transconductance type amplifier system as the input signal is a voltage and the output signal is a current. then for a series-series feedback circuit the transfer gain is given as: Gm = Vout ÷ Iin.

Shunt-Shunt Feedback Systems

Shunt-Shunt Feedback Systems, also known as shunt voltage feedback, operates as a current-voltage controlled feedback system. In the shunt-shunt feedback configuration the signal fed back is in parallel with the input signal. The output voltage is sensed and the current is subtracted from the input current in shunt, and as such its the currents, not the voltages that subtract.

Shunt-Shunt Feedback System

For the shunt-shunt connection, the configuration is defined as the output voltage to the input current. As the output voltage is fed back as a current to a current-driven input port, the shunt connections at both the input and output terminals reduce the input and output impedance. therefore the system works best as a transresistance system with the ideal input resistance, Rinbeing very small, and the ideal output resistance, Rout also being very small.

Then the shunt voltage configuration works as transresistance type voltage amplifier as the input signal is a current and the output signal is a voltage, so the transfer gain is given as: Rm = Iout ÷ Vin.

Feedback Systems Summary

We have seen that a Feedback System is one in which the output signal is sampled and then fed back to the input to form an error signal that drives the system, and depending on the type of feedback used, the feedback signal which is mixed with the systems input signal, can be either a voltage or a current.

Feedback will always change the performance of a system and feedback arrangements can be either positive (regenerative) or negative (degenerative) type feedback systems. If the feedback loop around the system produces a loop-gain which is negative, the feedback is said to be negative or degenerative with the main effect of the negative feedback is in reducing the systems gain.

If however the gain around the loop is positive, the system is said to have positive feedback or regenerative feedback. The effect of positive feedback is to increase the gain which can cause a system to become unstable and oscillate especially if GH = -1.

We have also seen that block-diagrams can be used to demonstrate the various types of feedback systems. In the block diagrams above, the input and output variables can be modelled as either a voltage or a current and as such there are four combinations of inputs and outputs that represent the possible types of feedback, namely: Series Voltage Feedback, Shunt Voltage Feedback, Series Current Feedback and Shunt Current Feedback.

The names for these different types of feedback systems are derived from the way that the feedback network connects between the input and output stages either in parallel (shunt) or series.

In the next tutorial about Feedback Systems, we will look at the effects of Negative Feedback on a system and see how it can be used to improve a control systems stability.

In the previous tutorial we saw that systems in which the output quantity has no effect upon the input to the control process are called open-loop control systems, and that open-loop systems are just that, open ended non-feedback systems. But the goal of any electrical or electronic control system is to measure, monitor, and control a process.

One way in which we can accurately Control the Process is by monitoring its output and "feeding" some of it back to compare the actual output with the desired output so as to reduce the error and if disturbed, bring the output of the system back to the original or desired response. The measure of the output is called the "feedback signal" and the type of control system which uses feedback signals to control itself is called a Close-loop System.

A Closed-loop Control System, also known as a feedback control system is a control system which uses the concept of an open loop system as its forward path but has one or more feedback loops (hence its name) or paths between its output and its input. The reference to "feedback", simply means that some portion of the output is returned "back" to the input to form part of the systems excitation.

Closed-loop systems are designed to automatically achieve and maintain the desired output condition by comparing it with the actual condition. It does this by generating an error signal which is the difference between the output and the reference input. In other words, a "closed-loop system" is a fully automatic control system in which its control action being dependent on the output in some way.

So for example, consider our electric clothes dryer from the previous open-loop tutorial. Suppose we used a sensor or transducer (input device) to continually monitor the temperature or dryness of the clothes and feed a signal relating to the dryness back to the controller as shown below.

Closed-loop Control

This sensor would monitor the actual dryness of the clothes and compare it with (or subtract it from) the input reference. The error signal (error = required dryness – actual dryness) is amplified by the controller, and the controller output makes the necessary correction to the heating system to reduce any error. For example if the clothes are too wet the controller may increase the temperature or drying time. Likewise, if the clothes are nearly dry it may reduce the temperature or stop the process so as not to overheat or burn the clothes, etc.

Then the closed-loop configuration is characterised by the feedback signal, derived from the sensor in our clothes drying system. The magnitude and polarity of the resulting error signal, would be directly related to the difference between the required dryness and actual dryness of the clothes.

Also, because a closed-loop system has some knowledge of the output condition, (via the sensor) it is better equipped to handle any system disturbances or changes in the conditions which may reduce its ability to complete the desired task.

For example, as before, the dryer door opens and heat is lost. This time the deviation in temperature is detected by the feedback sensor and the controller self-corrects the error to maintain a constant temperature within the limits of the preset value. Or possibly stops the process and activates an alarm to inform the operator.

As we can see, in a closed-loop control system the error signal, which is the difference between the input signal and the feedback signal (which may be the output signal itself or a function of the output signal), is fed to the controller so as to reduce the systems error and bring the output of the system back to a desired value. In our case the dryness of the clothes. Clearly, when the error is zero the clothes are dry.

The term Closed-loop control always implies the use of a feedback control action in order to reduce any errors within the system, and its "feedback" which distinguishes the main differences between an open-loop and a closed-loop system.

Closed-loop systems have many advantages over open-loop systems. The primary advantage of a closed-loop feedback control system is its ability to reduce a system's sensitivity to external disturbances, for example opening of the dryer door, giving the system a more robust control as any changes in the feedback signal will result in compensation by the controller.

Then we can define the main characteristics of Closed-loop Control as being:

• To reduce errors by automatically adjusting the systems input.
• To improve stability of an unstable system.
• To increase or reduce the systems sensitivity.
• To enhance robustness against external disturbances to the process.
• To produce a reliable and repeatable performance.

Whilst a good closed-loop system can have many advantages over an open-loop control system, its main disadvantage is that in order to provide the required amount of control, a closed-loop system must be more complex by having one or more feedback paths. Also, if the gain of the controller is too sensitive to changes in its input commands or signals it can become unstable and start to oscillate as the controller tries to over-correct itself, and eventually something would break. So we need to "tell" the system how we want it to behave within some pre-defined limits.

Closed-loop Summing Points

For a closed-loop feedback system to regulate any control signal, it must first determine the error between the actual output and the desired output. This is achieved using a summing point, also referred to as a comparison element, between the feedback loop and the systems input. These summing points compare a systems set point to the actual value and produce a positive or negative error signal which the controller responds too. where: Error = Set point – Actual

The symbol used to represent a summing point in closed-loop systems block-diagram is that of a circle with two crossed lines as shown. The summing point can either add signals together in which a Plus ( + ) symbol is used showing the device to be a "summer" (used for positive feedback), or it can subtract signals from each other in which case a Minus ( − ) symbol is used showing that the device is a "comparator" (used for negative feedback) as shown.

Summing Point Types

Note that summing points can have more than one signal as inputs either adding or subtracting but only one output which is the algebraic sum of the inputs. Also the arrows indicate the direction of the signals. Summing points can be cascaded together to allow for more input variables to be summed at a given point.

Closed-loop System Transfer Function

The Transfer Function of any electrical or electronic control system is the mathematical relationship between the systems input and its output, and hence describes the behaviour of the system. Note also that the ratio of the output of a particular device to its input represents its gain. Then we can correctly say that the output is always the transfer function of the system times the input. Consider the closed-loop system below.

Typical Closed-loop System Representation

Where: block G represents the open-loop gains of the controller or system and is the forward path, and block H represents the gain of the sensor, transducer or measurement system in the feedback path.

To find the transfer function of the closed-loop system above, we must first calculate the output signal θo in terms of the input signal θi. To do so, we can easily write the equations of the given block-diagram as follows.

The output from the system is equal to:    Output = G x Error

Note that the error signal, θe is also the input to the feed-forward block:  G

The output from the summing point is equal to:    Error = Input - H x Output

If  H = 1 (unity feedback) then:

The output from the summing point will be:    Error (θe) = Input - Output

Eliminating the error term, then:

The output is equal to:    Output = G x (Input - H x Output)

Therefore:    G x Input = Output + G x H x Output

Rearranging the above gives us the closed-loop transfer function of:

The above equation for the transfer function of a closed-loop system shows a Plus ( + ) sign in the denominator representing negative feedback. With a positive feedback system, the denominator will have a Minus ( − ) sign and the equation becomes:  1 - GH.

We can see that when  H = 1 (unity feedback) and G is very large, the transfer function approaches unity as:

Also, as the systems steady state gain G decreases, the expression of:  G/(1 + G) decreases much more slowly. In other words, the system is fairly insensitive to variations in the systems gain represented by G, and which is one of the main advantages of a closed-loop system.

Multi-loop Closed-loop System

Whilst our example above is of a single input, single output closed-loop system, the basic transfer function still applies to more complex multi-loop systems. Most practical feedback circuits have some form of multiple loop control, and for a multi-loop configuration the transfer function between a controlled and a manipulated variable depends on whether the other feedback control loops are open or closed.

Consider the multi-loop system below.

Any cascaded blocks such as G1 and G2 can be reduced, as well as the transfer function of the inner loop as shown.

After further reduction of the blocks we end up with a final block diagram which resembles that of the previous single-loop closed-loop system.

And the transfer function of this multi-loop system becomes:

Then we can see that even complex multi-block or multi-loop block diagrams can be reduced to give one single block diagram with one common system transfer function.

Closed-loop Motor Control

So how can we use Closed-loop Systems in Electronics. Well consider our DC motor controller from the previous open-loop tutorial. If we connected a speed measuring transducer, such as a tachometer to the shaft of the DC motor, we could detect its speed and send a signal proportional to the motor speed back to the amplifier. A tachometer, also known as a tacho-generator is simply a permanent-magnet DC generator which gives a DC output voltage proportional to the speed of the motor.

Then the position of the potentiometers slider represents the input, θi which is amplified by the amplifier (controller) to drive the DC motor at a set speed N representing the output, θo of the system, and the tachometer T would be the closed-loop back to the controller. The difference between the input voltage setting and the feedback voltage level gives the error signal as shown.

Closed-loop Motor Control

Any external disturbances to the closed-loop motor control system such as the motors load increasing would create a difference in the actual motor speed and the potentiometer input set point.

This difference would produce an error signal which the controller would automatically respond too adjusting the motors speed. Then the controller works to minimize the error signal, with zero error indicating actual speed which equals set point.

Electronically, we could implement such a simple closed-loop tachometer-feedback motor control circuit using an operational amplifier (op-amp) for the controller as shown.

Closed-loop Motor Controller Circuit

This simple closed-loop motor controller can be represented as a block diagram as shown.

Block Diagram for the Feedback Controller

A closed-loop motor controller is a common means of maintaining a desired motor speed under varying load conditions by changing the average voltage applied to the input from the controller. The tachometer could be replaced by an optical encoder or Hall-effect type positional or rotary sensor.

Closed-loop Systems Summary

We have seen that an electronic control system with one or more feedback paths is called a Closed-loop System. Closed-loop control systems are also called "feedback control systems" are very common in process control and electronic control systems. Feedback systems have part of their output signal "fed back" to the input for comparison with the desired set point condition. The type of feedback signal can result either in positive feedback or negative feedback.

In a closed-loop system, a controller is used to compare the output of a system with the required condition and convert the error into a control action designed to reduce the error and bring the output of the system back to the desired response. Then closed-loop control systems use feedback to determine the actual input to the system and can have more than one feedback loop.

Closed-loop control systems have many advantages over open-loop systems. One advantage is the fact that the use of feedback makes the system response relatively insensitive to external disturbances and internal variations in system parameters such as temperature. It is thus possible to use relatively inaccurate and inexpensive components to obtain the accurate control of a given process or plant.

However, system stability can be a major problem especially in badly designed closed-loop systems as they may try to over-correct any errors which could cause the system to loss control and oscillate.

In the next tutorial about Electronics Systems, we will look at the different ways in which we can incorporate a summing point into the input of a system and the different ways in which we can feed signals back to it.

In Electronic Systems, we saw that a system can be a collection of subsystems which direct or control an input signal. The function of any electronic system is to automatically regulate the output and keep it within the systems desired input value or "set point". If the systems input changes for whatever reason, the output of the system must respond accordingly and change itself to reflect the new input value.

Likewise, if something happens to disturb the systems output without any change to the input value, the output must respond by returning back to its previous set value. In the past, electrical control systems were basically manual or what is called an Open-loop System with very few automatic control or feedback features built in to regulate the process variable so as to maintain the desired output level or value.

For example, an electric clothes dryer. Depending upon the amount of clothes or how wet they are, a user or operator would set a timer (controller) to say 30 minutes and at the end of the 30 minutes the drier will automatically stop and turn-off even if the clothes are still wet or damp.

In this case, the control action is the manual operator assessing the wetness of the clothes and setting the process (the drier) accordingly.

So in this example, the clothes dryer would be an open-loop system as it does not monitor or measure the condition of the output signal, which is the dryness of the clothes. Then the accuracy of the drying process, or success of drying the clothes will depend on the experience of the user (operator).

However, the user may adjust or fine tune the drying process of the system at any time by increasing or decreasing the timing controllers drying time, if they think that the original drying process will not be met. For example, increasing the timing controller to 40 minutes to extend the drying process. Consider the following open-loop block diagram.

Open-loop Drying System

Then an Open-loop system, also referred to as non-feedback system, is a type of continuous control system in which the output has no influence or effect on the control action of the input signal. In other words, in an open-loop control system the output is neither measured nor "fed back" for comparison with the input. Therefore, an open-loop system is expected to faithfully follow its input command or set point regardless of the final result.

Also, an open-loop system has no knowledge of the output condition so cannot self-correct any errors it could make when the preset value drifts, even if this results in large deviations from the preset value.

Another disadvantage of open-loop systems is that they are poorly equipped to handle disturbances or changes in the conditions which may reduce its ability to complete the desired task. For example, the dryer door opens and heat is lost. The timing controller continues regardless for the full 30 minutes but the clothes are not heated or dried at the end of the drying process. This is because there is no information fed back to maintain a constant temperature.

Then we can see that open-loop system errors can disturb the drying process and therefore requires extra supervisory attention of a user (operator). The problem with this anticipatory control approach is that the user would need to look at the process temperature frequently and take any corrective control action whenever the drying process deviated from its desired value of drying the clothes. This type of manual open-loop control which reacts before an error actually occurs is calledFeed forward Control

The objective of feed forward control, also known as predictive control, is to measure or predict any potential open-loop disturbances and compensate for them manually before the controlled variable deviates too far from the original set point. So for our simple example above, if the dryers door was open it would be detected and closed allowing the drying process to continue.

If applied correctly, the deviation from wet clothes to dry clothes at the end of the 30 minutes would be minimal if the user responded to the error situation (door open) very quickly. However, this feed forward approach may not be completely accurate if the system changes, for example the drop in drying temperature was not noticed during the 30 minute process.

Then we can define the main characteristics of an "Open-loop system" as being:

• There is no comparison between actual and desired values.
• An open-loop system has no self-regulation or control action over the output value.
• Each input setting determines a fixed operating position for the controller.
• Changes or disturbances in external conditions does not result in a direct output change.
      (unless the controller setting is altered manually)

Any open-loop system can be represented as multiple cascaded blocks in series or a single block diagram with an input and output. The block diagram of an open-loop system shows that the signal path from input to output represents a linear path with no feedback loop and for any type of control system the input is given the designation θi and the output θo.

Generally, we do not have to manipulate the open-loop block diagram to calculate its actual transfer function. We can just write down the proper relationships or equations from each block diagram, and then calculate the final transfer function from these equations as shown.

Open-loop System

The Transfer Function of each block is:

The overall transfer function is:

Then the Open-loop Gain is given simply as:

When G represents the Transfer Function of the system or subsystem, it can be rewritten as:G(s) = θo(s)/θi(s)

Open-loop control systems are often used with processes that require the sequencing of events with the aid of "ON-OFF" signals. For example a washing machines which requires the water to be switched "ON" and then when full is switched "OFF" followed by the heater element being switched "ON" to heat the water and then at a suitable temperature is switched "OFF", and so on.

This type of "ON-OFF" open-loop control is suitable for systems where the changes in load occur slowly and the process is very slow acting, necessitating infrequent changes to the control action by an operator.

Open-loop Control Systems Summary

We have seen that a controller can manipulate its inputs to obtain the desired effect on the output of a system. One type of control system in which the output has no influence or effect on the control action of the input signal is called an Open-loop system.

An "open-loop system" is defined by the fact that the output signal or condition is neither measured nor "fed back" for comparison with the input signal or system set point. Therefore open-loop systems are commonly referred to as "Non-feedback systems".

Also, as an open-loop system does not use feedback to determine if its required output was achieved, it "assumes" that the desired goal of the input was successful because it cannot correct any errors it could make, and so cannot compensate for any external disturbances to the system.

Open-loop Motor Control

So for example, assume the DC motor controller as shown. The speed of rotation of the motor will depend upon the voltage supplied to the amplifier (the controller) by the potentiometer. The value of the input voltage could be proportional to the position of the potentiometer.

If the potentiometer is moved to the top of the resistance the maximum positive voltage will be supplied to the amplifier representing full speed. Likewise, if the potentiometer wiper is moved to the bottom of the resistance, zero voltage will be supplied representing a very slow speed or stop.

Then the position of the potentiometers slider represents the input, θi which is amplified by the amplifier (controller) to drive the DC motor (process) at a set speed N representing the output, θo of the system. The motor will continue to rotate at a fixed speed determined by the position of the potentiometer.

As the signal path from the input to the output is a direct path not forming part of any loop, the overall gain of the system will the cascaded values of the individual gains from the potentiometer, amplifier, motor and load. It is clearly desirable that the output speed of the motor should be identical to the position of the potentiometer, giving the overall gain of the system as unity.

However, the individual gains of the potentiometer, amplifier and motor may vary over time with changes in supply voltage or temperature, or the motors load may increase representing external disturbances to the open-loop motor control system.

But the user will eventually become aware of the change in the systems performance (change in motor speed) and may correct it by increasing or decreasing the potentiometers input signal accordingly to maintain the original or desired speed.

The advantages of this type of "open-loop motor control" is that it is potentially cheap and simple to implement making it ideal for use in well-defined systems were the relationship between input and output is direct and not influenced by any outside disturbances. Unfortunately this type of open-loop system is inadequate as variations or disturbances in the system affect the speed of the motor. Then another form of control is required.

In the next tutorial about Electronics Systems, we will look at the effect of feeding back some of the output signal to the input so that the systems control is based on the difference between actual and desired values. This type of electronics control system is called Closed-loop Control.

An Electronic System is a physical interconnection of components, or parts, that gathers various amounts of information together with the aid of input devices such as sensors, responds in some way to this information and then uses electrical energy in the form of an output action to control a physical process or perform some type of mathematical operation on the signal.

But electronic control systems can also be regarded as a process that transforms one signal into another so as to give the desired system response. Then we can say that a simple electronic system consists of an input, a process, and an output with the input variable to the system and the output variable from the system both being signals.

There are many ways to represent a system, for example: mathematically, descriptively, pictorially or schematically. Electronic systems are generally represented schematically as a series of interconnected blocks and signals with each block having its own set of inputs and outputs.

As a result, even the most complex of Electronic Control Systems can be represented by a combination of simple blocks, with each block containing or representing an individual component or complete sub-system. The representing of an electronic system or process control system as a number of interconnected blocks or boxes is known commonly as "block-diagram representation".

Block Diagram Representation of a Simple Electronic System

Electronic Systems have both inputs and outputs with the output or outputs being produced byprocessing the inputs. Also, the input signal(s) may cause the process to change or may itself cause the operation of the system to change. Therefore the input(s) to a system is the "cause" of the change, while the resulting action that occurs on the systems output due to this cause being present is called the "effect", with the effect being a consequence of the cause.

In other words, an electronic system can be classed as "causal" in nature as there is a direct relationship between its input and its output. Electronic systems analysis and process control theory are generally based upon this Cause and Effect analysis.

So for example in an audio system, a microphone (input device) causes sound waves to be converted into electrical signals for the amplifier to amplify (a process), and a loudspeaker (output device) produces sound waves as an effect of being driven by the amplifiers electrical signals.

But an electronic system need not be a simple or single operation. It can also be an interconnection of several sub-systems all working together within the same overall system.

Our audio system could for example, involve the connection of a CD player, or a DVD player, an MP3 player, or a radio receiver all being multiple inputs to the same amplifier which in turn drives one or more sets of stereo or home theatre type surround loudspeakers.

But an electronic system can not just be a collection of inputs and outputs, it must "do something", even if it is just to monitor a switch or to turn "ON" a light. We know that sensors are input devices that detect or turn real world measurements into electronic signals which can then be processed. These electrical signals can be in the form of either voltages or currents within a circuit. The opposite or output device is called an actuator, that converts the processed signal into some operation or action, usually in the form of mechanical movement.

Types of Electronic System

Electronic systems operate on either continuous-time (CT) signals or discrete-time (DT) signals. A continuous-time system is one in which the input signals are defined along a continuum of time, such as an analogue signal which "continues" over time producing a continuous-time signal.

But a continuous-time signal can also vary in magnitude or be periodic in nature with a time periodT. As a result, continuous-time electronic systems tend to be purely analogue systems producing a linear operation with both their input and output signals referenced over a set period of time.

For example, the temperature of a room can be classed as a continuous time signal which can be measured between two values or set points, for example from cold to hot or from Monday to Friday. We can represent a continuous-time signal by using the independent variable for time t, and where x(t) represents the input signal and y(t) represents the output signal over a period of time t.

Generally, most of the signals present in the physical world which we can use tend to be continuous-time signals. For example, voltage, current, temperature, pressure, velocity, etc.

On the other hand, a discrete-time system is one in which the input signals are not continuous but a sequence or a series of signal values defined in "discrete" points of time. This results in a discrete-time output generally represented as a sequence of values or numbers.

Generally a discrete signal is specified only at discrete intervals, values or equally spaced points in time. So for example, the temperature of a room measured at 1pm, at 2pm, at 3pm and again at 4pm without regards for the actual room temperature in between these points at say, 1:30pm or at 2:45pm.

However, a continuous-time signal, x(t) can be represented as a discrete set of signals only at discrete intervals or "moments in time". Discrete signals are not measured versus time, but instead are plotted at discrete time intervals, where n is the sampling interval. As a result discrete-time signals are usually denoted as x(n)representing the input and y(n) representing the output.

Then we can represent the input and output signals of a system as x and y respectively with the signal, or signals themselves being represented by the variable, t, which usually represents time for a continuous system and the variable n, which represents an integer value for a discrete system as shown.

Continuous-time and Discrete-time System

Interconnection of Systems

One of the practical aspects of electronic systems and block-diagram representation is that they can be combined together in either a series or parallel combinations to form much bigger systems. Many larger real systems are built using the interconnection of several sub-systems and by using block diagrams to represent each subsystem, we can build a graphical representation of the whole system being analysed.

When subsystems are combined to form a series circuit, the overall output at y(t) will be equivalent to the multiplication of the input signal x(t) as shown as the subsystems are
cascaded together.

Series Connected System

For a series connected continuous-time system, the output signal y(t) of the first subsystem, "A"becomes the input signal of the second subsystem, "B" whose output becomes the input of the third subsystem, "C" and so on through the series chain giving A x B x C, etc.

Then the original input signal is cascaded through a series connected system, so for two series connected subsystems, the equivalent single output will be equal to the multiplication of the systems, ie, y(t) = G1(s) x G2(s). Where G represents the transfer function of the subsystem.

Note that the term "Transfer Function" of a system refers to and is defined as being the mathematical relationship between the systems input and its output, or output/input and hence describes the behaviour of the system.

Also, for a series connected system, the order in which a series operation is performed does not matter with regards to the input and output signals as: G1(s) x G2(s) is the same as G2(s) x G1(s). An example of a simple series connected circuit could be a single microphone feeding an amplifier followed by a speaker.

Parallel Connected Electronic System

For a parallel connected continuous-time system, each subsystem receives the same input signal, and their individual outputs are summed together to produce an overall output, y(t). Then for two parallel connected subsystems, the equivalent single output will be the sum of the two individual inputs, ie, y(t) = G1(s) + G2(s).

An example of a simple parallel connected circuit could be several microphones feeding into a mixing desk which in turn feeds an amplifier and speaker system.

Electronic Feedback Systems

Another important interconnection of systems which is used extensively in control systems, is the "feedback configuration". In feedback systems, a fraction of the output signal is "fed back" and either added to or subtracted from the original input signal. The result is that the output of the system is continually altering or updating its input with the purpose of modifying the response of a system to improve stability. A feedback system is also commonly referred to as a "Closed-loop System" as shown.

Closed-Loop Feedback System

Feedback systems are used a lot in most practical electronic system designs to help stabilise the system and to increase its control. If the feedback loop reduces the value of the original signal, the feedback loop is known as "negative feedback". If the feedback loop adds to the value of the original signal, the feedback loop is known as "positive feedback".

An example of a simple feedback system could be a thermostatically controlled heating system in the home. If the home is too hot, the feedback loop will switch "OFF" the heating system to make it cooler. If the home is too cold, the feedback loop will switch "ON" the heating system to make it warmer. In this instance, the system comprises of the heating system, the air temperature and the thermostatically controlled feedback loop.

Transfer Function of Systems

Any subsystem can be represented as a simple block with an input and output as shown. Generally, the input is designated as: θi and the output as: θo. The ratio of output over input represents the gain, ( G ) of the subsystem and is therefore defined as: G = θo/θi

In this case, G represents the Transfer Function of the system or subsystem. When discussing electronic systems in terms of their transfer function, the complex operator, s is used, then the equation for the gain is rewritten as: G(s) = θo(s)/θi(s)

Electronic System Summary

We have seen that a simple Electronic System consists of an input, a process, an output and possibly feedback. Electronic systems can be represented using interconnected block diagrams where the lines between each block or subsystem represents both the flow and direction of a signal through the system.

Block diagrams need not represent a simple single system but can represent very complex systems made from many interconnected subsystems. These subsystems can be connected together in series, parallel or combinations of both depending upon the flow of the signals.

We have also seen that electronic signals and systems can be of continuous-time or discrete-time in nature and may be analogue, digital or both. Feedback loops can be used be used to increase or reduce the performance of a particular system by providing better stability and control. Control is the process of making a system variable adhere to a particular value, called the reference value.

In the next tutorial about Electronic Systems, we will look at a types of electronic control system called an Open-loop System which generates an output signal, y(t) based on its present input values and as such does not monitor its output or make adjustments based on the condition of its output.