Control Systems

A proportional–integral–derivative controller (PID controller) is a control loop feedback mechanism control technique widely used in control systems. A PID controller continuously calculates an  error value   {\displaystyle e(t)}  as the difference between a desired setpoint and a measured process variable and applies a correction based on proportional, integral, and derivative terms.  PID  is an initialism for  Proportional-Integral-Derivative , referring to the three terms operating on the error signal to produce a control signal. The theoretical understanding and application dates from the 1920s, and they are implemented in nearly all analogue control systems; originally in mechanical controllers, and then using discrete electronics and latterly in industrial process computers. The PID controller is probably the most-used feedback control design. Referring to the equation ...

To overcome the limitations of the open-loop controller, control theory introduces feedback. A closed-loop controller uses feedback to control states or outputs of a dynamical system. Its name comes from the information path in the system: process inputs (e.g., voltage applied to an electric motor) have an effect on the process outputs (e.g., speed or torque of the motor), which is measured with sensors and processed by the controller; the result (the control signal) is "fed back" as input to the process, closing the loop. Closed-loop controllers have the following advantages over open-loop controllers: disturbance rejection (such as hills in the cruise control example above) guaranteed performance even with model uncertainties, when the model structure does not match perfectly the real process and the model parameters are not exact unstable processes can be stabilized reduced s...

Fundamentally, there are two types of control loops: open loop control and closed loop (feedback) control. In open loop control, the control action from the controller is independent of the "process output" (or "controlled process variable"). A good example of this is a central heating boiler controlled only by a timer, so that heat is applied for a constant time, regardless of the temperature of the building. (The control action is the switching on/off of the boiler. The process output is the building temperature). In closed loop control, the control action from the controller is dependent on the process output. In the case of the boiler analogy this would include a thermostat to monitor the building temperature, and thereby feed back a signal to ensure the controller maintains the building at the temperature set on the thermostat. A closed loop controller therefore has a feedback loop which ensures the controller exerts a control action to give a process out...

Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems with inputs, and how their behavior is modified by feedback. The usual objective of control theory is to control a system, often called the  plant , so its output follows a desired control signal, called the  reference , which may be a fixed or changing value. To do this a  controller  is designed, which monitors the output and compares it with the reference. The difference between actual and desired output, called the  error  signal, is applied as feedback to the input of the system, to bring the actual output closer to the reference. Some topics studied in control theory are stability (whether the output will converge to the reference value or oscillate about it), controllability and observability. Extensive use is usually made of a diagrammatic style known a...

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 mu...

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 l...

Linear control systems use linear negative feedback to produce a control signal mathematically based on other variables, with a view to maintain the controlled process within an acceptable operating range. The output from a linear control system into the controlled process may be in the form of a directly variable signal, such as a valve that may be 0 or 100% open or anywhere in between. Sometimes this is not feasible and so, after calculating the current required corrective signal, a linear control system may repeatedly switch an actuator, such as a pump, motor or heater, fully on and then fully off again, regulating the duty cycle using pulse-width modulation. Proportional control Proportional negative-feedback systems are based on the difference between the required set point (SP) and process value (PV). This difference is called the  error . Power is applied in direct proportion to the current measured error, in the correct sense...

Open-loop and closed-loop control There are two common classes of control systems, open loop control systems, and closed loop control systems. In an open loop control system, the control action from the controller is independent of the "process output". A good example of this is a central heating boiler controlled only by a timer, so that heat is applied for a constant time, regardless of the temperature of the building. (The control action is the switching on/off of the boiler. The process output is the building temperature). In a closed loop control system, the control action from the controller is dependent on the desired and actual process output values. In the case of the boiler analogy this would utilise a thermostat to monitor the building temperature, and thereby feed back a signal to ensure the controller output maintains the building temperature to that set on the thermostat. A closed loop controller therefore has a feedback loop which ensures the cont...

A control system manages, commands, directs or regulates the behaviour of other devices or systems. It can range from a home heating controller using a thermostat controlling a domestic boiler to large Industrial control systems which are used for controlling processes or machines. In the most common form, the feedback control system it is desired to control a process, called the plant, so its output follows a control signal, which may be a fixed or changing value. The control system compares the output of the plant to the control signal, and applies the difference as an error signal to bring the output of the plant closer to the control signal. Overview 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 ...