Control system

A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large Industrial control systems which are used for controlling processes or machines.

For continuously modulated control, a feedback controller is used to automatically control a process or operation. The control system compares the value or status of the process variable (PV) being controlled with the desired value or setpoint (SP), and applies the difference as a control signal to bring the process variable output of the plant to the same value as the setpoint.

For sequential and combinational logic, software logic, such as in a programmable logic controller, is used.

Objectives
The control systems must achieve the following objectives:

Be stable and robust against perturbations and errors in the models.
Be efficient according to a pre-established criterion avoiding abrupt and unreal behaviors.

Needs of process supervision

Limitations of the visualization of the acquisition and control systems.
Control vs. process monitoring
Control software. Control loop closure.
Collect, store and visualize information.
Data mining.

Classification of control systems according to their behavior and measurement
Control: selection of the inputs of a system so that the states or outputs change according to a desired way. The elements are:

It always exists to verify the achievement of the objectives established in the planning.
Measurement. To control it is essential to measure and quantify the results.
Detect deviations. One of the inherent functions of control is to discover the differences that arise between execution and planning.
Establish corrective measures. The object of control is to foresee and correct errors.
Control factors; Quantity, Time, cost, Quality.

Controller: (Electronics). It is an electronic device that emulates the ability of human beings to exert control. By means of four control actions: compare, calculate, adjust and limit.

Process: progressively continuous operation or natural development, marked by a series of gradual changes that follow one another in a relatively fixed way and that lead to a determined result or purpose. Artificial or voluntary progressive operation consisting of a series of actions or controlled movements, systematically directed towards a specific result or purpose. Examples: chemical, economic and biological processes.

Supervision: act of observing the work and tasks of another (individual or machine) that may not know the subject in depth.

Open loop control system
It is that system in which only the process acts on the input signal and results in an independent output signal to the input signal, but based on the first one. This means that there is no feedback to the controller so that the controller can adjust the control action. That is, the output signal is not converted into an input signal for the controller.

Example 1: A tank with a garden hose. As long as the key remains open, the water will flow. The height of the water in the tank can not cause the key to close and therefore does not serve us for a process that needs content or concentration control.
Example 2: When making a toast, what we do is control the toasting time of itself by entering a variable (in this case the degree of toasting we want). In short, the one we introduce as a parameter is time.

These systems are characterized by:

Be simple and easy to concept.
Nothing ensures its stability before a disturbance.
The output does not compare with the entry.
Be affected by disturbances. These can be tangible or intangible.
The accuracy depends on the previous calibration of the system.

Closed loop control system
These are the systems in which the control action is a function of the output signal. Closed loop systems use feedback from a final result to adjust the control action accordingly.

The control in closed loop is essential when one of the following circumstances occurs:

When a process is not possible to regulate by man.
A large-scale production that requires large facilities and man is not capable of handling.
Monitoring a process is especially difficult in some cases and requires attention that the man can easily lose due to fatigue or dismissal, with the consequent risks that this may cause the worker and the process.

Their characteristics are:

Be complex, but broad in number of parameters.
The output is compared to the input and affects you to control the system.
Your property feedback.
Be more stable to internal disturbances and variations.

An example of a closed loop control system would be the hot water tank we use to bathe.

Another example would be a highly sensitive level regulator of a deposit. The movement of the buoy produces more or less obstruction in a jet of air or gas at low pressure. This translates into pressure changes that affect the valve of the passage valve, causing it to open more the closer you are to the maximum level.

Types of control systems
The control systems are grouped into three basic types:

Man made control systems
Like the electrical or electronic systems that are permanently capturing signals of the state of the system under their control and that when detecting a deviation of the pre-established parameters of the normal operation of the system, act by means of sensors and actuators, to take the system back to its operational conditions normal operating. A clear example of this will be a thermostat, which consecutively captures temperature signals. As soon as the temperature drops or rises and goes out of range, it works by lighting a cooling or heating system.

By their causality they can be: causal and not causal
A system is causal if there is a causal relationship between the outputs and the system inputs, more explicitly, between the output and the future values of the input.

According to the number of inputs and outputs of the system, they are called: by their behavior

From an input and output or SISO (single input, single output).
Of one input and multiple outputs or SIMO (single input, multiple output).
Of multiple inputs and one output or MISO (multiple input, single output).
Of multiple inputs and multiple outputs or MIMO (multiple input, multiple output).

According to the equation that defines the system, it is called:

Linear, if the differential equation that defines it is linear.
Non-linear, if the differential equation that defines it is non-linear.

The signals or variables of the dynamic systems are a function of time. And according to it these systems are:

Of continuous time, if the model of the system is a differential equation, and therefore time is considered infinitely divisible. The variables of continuous time are also called analog.
Of discrete time, if the system is defined by an equation for differences. Time is considered divided into periods of constant value. The values of the variables are digital (binary, hexadecimal systems, etc.), and their value is only known in each period.
Of discrete events, if the system evolves according to variables whose value is known when a certain event occurs.

According to the relationship between the variables of the systems, we will say that:

Two systems are coupled, when the variables of one of them are related to those of the other system.
Two systems are decoupled, if the variables of both systems have no relation.

Depending on the evolution of the variables of a system in time and space, they can be:

Stationary, when its variables are constant in time and space.
Not stationary, when their variables are not constant in time or space.

According to the response of the system (value of the output) with respect to the variation of the system input:

The system is considered stable when any bounded input signal produces a bounded response of the output.
The system is considered unstable when there is at least one bounded entry that produces an unbounded response to the output.

If they compare or not, the entry and exit of a system, to control the latter, the system is called:

Open loop system, when the output to be controlled, does not compare with the value of the input signal or reference signal.
System closed loop, when the output to be controlled is compared with the reference signal. The output signal is carried by the input signal to be compared, is called signal feedback or feedback.

Depending on the possibility of predicting the behavior of a system, that is, its response, they are classified as:

Deterministic system, when its future behavior is predictable within tolerance limits.
Stochastic system, if it is impossible to predict future behavior. The system variables are called random.

Natural control systems
Natural control systems, including biological systems. For example, human body movements as the act of indicating an object that includes as components of the biological control system the eyes, arm, hand, finger and brain of man. At the entrance the movement is processed and the exit is the direction to which reference is made.

Mixing control systems
Mixing control systems, which components are ones made by man and the others are natural. It is the control system of a man who drives his vehicle. This system is made up of the eyes, the hands, the brain and the vehicle. The entrance is manifested in the direction that the driver must follow on the road and the exit is the current direction of the car. Another example may be the decisions made by a politician before an election. This system is composed of eyes, brain, ears, mouth. The entrance is manifested in the promises announced by the politician and the exit is the degree of acceptance of the proposal by the population.

A control system can be pneumatic, electrical, mechanical or of any type, its function is to receive inputs and coordinate one or several answers according to its control loop (for what is programmed).

Predictive control, are the control systems that work with a predictive system, and not active as the traditional (execute the solution to the problem before it begins to affect the process). In this way, it improves the efficiency of the process by rapidly counteracting the effects.

Open-loop and closed-loop control
There are two common classes of control action: open loop and closed loop. In an open-loop control system, the control action from the controller is independent of the process variable. An example of this is a central heating boiler controlled only by a timer. The control action is the switching on or off of the boiler. The process variable is the building temperature.This controller operates the heating system for a constant time regardless of the temperature of the building.

In a closed-loop control system, the control action from the controller is dependent on the desired and actual process variable. In the case of the boiler analogy, this would utilise a thermostat to monitor the building temperature, and feed back a signal to ensure the controller output maintains the building temperature close to that set on the thermostat. A closed loop controller has a feedback loop which ensures the controller exerts a control action to control a process variable at the same value as the setpoint. For this reason, closed-loop controllers are also called feedback controllers.

Feedback control systems
In the case of linear feedback systems, a control loop including sensors, control algorithms, and actuators is arranged in an attempt to regulate a variable at a setpoint (SP). An everyday example is the cruise control on a road vehicle; where external influences such as gradients would cause speed changes, and the driver has the ability to alter the desired set speed. The PID algorithm in the controller restores the actual speed to the desired speed in the optimum way, with minimal delay or overshoot, by controlling the power output of the vehicle's engine.

Control systems that include some sensing of the results they are trying to achieve are making use of feedback and can adapt to varying circumstances to some extent. Open-loop control systems do not make use of feedback, and run only in pre-arranged ways.

Logic control
Logic control systems for industrial and commercial machinery were historically implemented by interconnected electrical relays and cam timers using ladder logic. Today, most such systems are constructed with microcontrollers or more specialized programmable logic controllers (PLCs). The notation of ladder logic is still in use as a programming method for PLCs.

Logic controllers may respond to switches and sensors, and can cause the machinery to start and stop various operations through the use of actuators. Logic controllers are used to sequence mechanical operations in many applications. Examples include elevators, washing machines and other systems with interrelated operations. An automatic sequential control system may trigger a series of mechanical actuators in the correct sequence to perform a task. For example, various electric and pneumatic transducers may fold and glue a cardboard box, fill it with product and then seal it in an automatic packaging machine.

PLC software can be written in many different ways – ladder diagrams, SFC (sequential function charts) or statement lists.

On–off control
A thermostat can be described as a bang-bang controller. When the temperature, PV, goes below a SP, the heater is switched on. Another example could be a pressure switch on an air compressor. When the pressure, PV, drops below the setpoint, SP, the pump is powered. Refrigerators and vacuum pumps contain similar mechanisms.

Simple on–off control systems like these are cheap and effective.

Linear control
Linear control systems use linear negative feedback to produce a control signal to maintain the controlled process variable (PV) at the desired setpoint (SP).

Proportional control
Proportional control is a type of linear feedback control system in which a correction is applied to the controlled variable which is proportional to the difference between the desired value (setpoint – SP) and the measured value (process value – PV). Two classic mechanical examples are the toilet bowl float proportioning valve and the fly-ball governor.

The proportional control system is more complex than an on–off control system like a bi-metallic domestic thermostat, but simpler than a proportional-integral-derivative (PID) control system used in something like an automobile cruise control. On–off control will work quite well eventually, over a long time compared to the overall system response time, but is not effective for rapid and timely corrections and responses. Proportional control overcomes this by modulating the output to the controlling device, such as a control valve at a level which avoids instability, but applies correction as fast as practicable by applying the optimum quantity of proportional correction.

A drawback of proportional control is that it cannot eliminate the residual SP–PV error, as it requires an error to generate a proportional output. To overcome this the PI controller was devised, which uses a proportional term (P) to remove the gross error, and an integral term (I) to eliminate the residual offset error by integrating the error over time to produce an "I" component within the controller output.

In some systems there are practical limits to the range of the manipulated variable (MV). For example, a heater can be off or fully on, or a valve can be closed or fully open. Adjustments to the gain simultaneously alter the range of error values over which the MV is between these limits. The width of this range, in units of the error variable and therefore of the PV, is called the proportional band (PB) which is the inverse of the proportional gain. While the gain is useful in mathematical treatments, the proportional band is often referred to in practical situations.

Furnace example
When controlling the temperature of an industrial furnace, it is usually better to control the opening of the fuel valve in proportion to the current needs of the furnace. This helps avoid thermal shocks and applies heat more effectively.

At low gains, only a small corrective action is applied when errors are detected. The system may be safe and stable, but may be sluggish in response to changing conditions. Errors will remain uncorrected for relatively long periods of time and the system is overdamped. If the proportional gain is increased, such systems become more responsive and errors are dealt with more quickly. There is an optimal value for the gain setting when the overall system is said to be critically damped. Increases in loop gain beyond this point lead to oscillations in the PV and such a system is underdamped.

Underdamped
In the furnace example, suppose the temperature is increasing towards a setpoint at which, say, 50% of the available power will be required for steady-state. At low temperatures, 100% of available power is applied. When the process value (PV) is within, say 10° of the SP the heat input begins to be reduced by the proportional controller. This implies a 20° proportional band (PB) from full to no power input, evenly spread around the setpoint value. At the setpoint the controller will be applying 50% power as required, but stray stored heat within the heater sub-system and in the walls of the furnace will keep the measured temperature rising beyond what is required. At 10° above SP, we reach the top of the proportional band (PB) and no power is applied, but the temperature may continue to rise even further before beginning to fall back. Eventually as the PV falls back into the PB, heat is applied again, but now the heater and the furnace walls are too cool and the temperature falls too low before its fall is arrested, so that the oscillations continue.

The temperature oscillations that an underdamped furnace control system produces are unacceptable for many reasons, including the waste of fuel and time (each oscillation cycle may take many minutes), as well as the likelihood of seriously overheating both the furnace and its contents.

Overdamped
Suppose that the gain of the control system is reduced drastically and it is restarted. As the temperature approaches, say 30° below SP (A 60° proportional band (PB) this time), the heat input begins to be reduced, the rate of heating of the furnace has time to slow and, as the heat is still further reduced, it eventually is brought up to setpoint, just as 50% power input is reached and the furnace is operating as required. There was some wasted time while the furnace crept to its final temperature using only 52% then 51% of available power, but at least no harm was done. By carefully increasing the gain (i.e. reducing the width of the PB) this overdamped and sluggish behavior can be improved until the system is critically damped for this SP temperature. Doing this is known as 'tuning' the control system. A well-tuned proportional furnace temperature control system will usually be more effective than on-off control, but will still respond more slowly than the furnace could under skillful manual control.

PID control
Apart from sluggish performance to avoid oscillations, another problem with proportional-only control is that power application is always in direct proportion to the error. In the example above we assumed that the set temperature could be maintained with 50% power. What happens if the furnace is required in a different application where a higher set temperature will require 80% power to maintain it? If the gain was finally set to a 50° PB, then 80% power will not be applied unless the furnace is 15° below setpoint, so for this other application the operators will have to remember always to set the setpoint temperature 15° higher than actually needed. This 15° figure is not completely constant either: it will depend on the surrounding ambient temperature, as well as other factors that affect heat loss from or absorption within the furnace.

To resolve these two problems, many feedback control schemes include mathematical extensions to improve performance. The most common extensions lead to proportional-integral-derivative control, or PID control.

Derivative action
The derivative part is concerned with the rate-of-change of the error with time: If the measured variable approaches the setpoint rapidly, then the actuator is backed off early to allow it to coast to the required level; conversely if the measured value begins to move rapidly away from the setpoint, extra effort is applied—in proportion to that rapidity—to try to maintain it.

Derivative action makes a control system behave much more intelligently. On control systems like the tuning of the temperature of a furnace, or perhaps the motion-control of a heavy item like a gun or camera on a moving vehicle, the derivative action of a well-tuned PID controller can allow it to reach and maintain a setpoint better than most skilled human operators could.

If derivative action is over-applied, it can lead to oscillations too. An example would be a PV that increased rapidly towards SP, then halted early and seemed to "shy away" from the setpoint before rising towards it again.

Integral action
The integral term magnifies the effect of long-term steady-state errors, applying ever-increasing effort until they reduce to zero. In the example of the furnace above working at various temperatures, if the heat being applied does not bring the furnace up to setpoint, for whatever reason, integral action increasingly moves the proportional band relative to the setpoint until the PV error is reduced to zero and the setpoint is achieved.

Ramp up % per minute
Some controllers include the option to limit the "ramp up % per minute". This option can be very helpful in stabilizing small boilers (3 MBTUH), especially during the summer, during light loads. A utility boiler "unit may be required to change load at a rate of as much as 5% per minute (IEA Coal Online - 2, 2007)".

Other techniques
It is possible to filter the PV or error signal. Doing so can reduce the response of the system to undesirable frequencies, to help reduce instability or oscillations. Some feedback systems will oscillate at just one frequency. By filtering out that frequency, more "stiff" feedback can be applied, making the system more responsive without shaking itself apart.

Feedback systems can be combined. In cascade control, one control loop applies control algorithms to a measured variable against a setpoint, but then provides a varying setpoint to another control loop rather than affecting process variables directly. If a system has several different measured variables to be controlled, separate control systems will be present for each of them.

Control engineering in many applications produces control systems that are more complex than PID control. Examples of such fields include fly-by-wire aircraft control systems, chemical plants, and oil refineries. Model predictive control systems are designed using specialized computer-aided-design software and empirical mathematical models of the system to be controlled.

Hybrid systems of PID and logic control are widely used. The output from a linear controller may be interlocked by logic for instance.

Fuzzy logic
Fuzzy logic is an attempt to apply the easy design of logic controllers to the control of complex continuously varying systems. Basically, a measurement in a fuzzy logic system can be partly true, that is if yes is 1 and no is 0, a fuzzy measurement can be between 0 and 1.

The rules of the system are written in natural language and translated into fuzzy logic. For example, the design for a furnace would start with: "If the temperature is too high, reduce the fuel to the furnace. If the temperature is too low, increase the fuel to the furnace."

Measurements from the real world (such as the temperature of a furnace) are converted to values between 0 and 1 by seeing where they fall on a triangle. Usually, the tip of the triangle is the maximum possible value which translates to 1.

Fuzzy logic, then, modifies Boolean logic to be arithmetical. Usually the "not" operation is "output = 1 - input," the "and" operation is "output = input.1 multiplied by input.2," and "or" is "output = 1 - ((1 - input.1) multiplied by (1 - input.2))". This reduces to Boolean arithmetic if values are restricted to 0 and 1, instead of allowed to range in the unit interval [0,1].

The last step is to "defuzzify" an output. Basically, the fuzzy calculations make a value between zero and one. That number is used to select a value on a line whose slope and height converts the fuzzy value to a real-world output number. The number then controls real machinery.

If the triangles are defined correctly and rules are right the result can be a good control system.

When a robust fuzzy design is reduced into a single, quick calculation, it begins to resemble a conventional feedback loop solution and it might appear that the fuzzy design was unnecessary. However, the fuzzy logic paradigm may provide scalability for large control systems where conventional methods become unwieldy or costly to derive.

Fuzzy electronics is an electronic technology that uses fuzzy logic instead of the two-value logic more commonly used in digital electronics.

Physical implementation
The range of implementation is from compact controllers often with dedicated software for a particular machine or device, to distributed control systems for industrial process control.

Logic systems and feedback controllers are usually implemented with programmable logic controllers.

Source from Wikipedia