System & Control

Control theory is an interdisciplinary branch of engineering and mathematics, that deals with the behavior of dynamical systems. The desired output of a system is called the reference. When one or more output variables of a system need to follow a certain reference over time, a controller manipulates the inputs to a system to obtain the desired effect on the output of the system.

System & Control

An example

Consider an automobile's cruise control, which is a device designed to maintain a constant vehicle speed; the desired or reference speed, provided by the driver. The system in this case is the vehicle. The system output is the vehicle speed, and the control variable is the engine's throttle position which influences engine torque output.

Open Loop Controller

A simple way to implement cruise control is to lock the throttle position when the driver engages cruise control. However, on hilly terrain, the vehicle will slow down going uphill and accelerate going downhill. In fact, any parameter different than what was assumed at design time will translate into a proportional error in the output velocity, including exact mass of the vehicle, wind resistance, and tire pressure. This type of controller is called an open-loop controller because there is no direct connection between the output of the system (the engine torque) and the actual conditions encountered; that is to say, the system does not and can not compensate for unexpected forces.

Close Loop Controler

In a closed-loop control system, a sensor monitors the output (the vehicle's speed) and feeds the data to a computer which continuously adjusts the control input (the throttle) as necessary to keep the control error to a minimum (to maintain the desired speed). Feedback on how the system is actually performing allows the controller (vehicle's on board computer) to dynamically compensate for disturbances to the system, such as changes in slope of the ground or wind speed. An ideal feedback control system cancels out all errors, effectively mitigating the effects of any forces that may or may not arise during operation and producing a response in the system that perfectly matches the user's wishes.

A Feed Back System

To avoid the problems 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. velocity or torque of the motor), which is measured with sensors and processed by the controller; the result (the control signal) is used as input to the process, closing the loop.

A Feed Back System

Feedback is a phenomenon whereby some proportion of the output signal of a system is passed (fed back) to the input. This is often used to control the dynamic behavior of the system. Examples of feedback can be found in most complex systems, such as engineering, architecture, economics, thermodynamics, and biology

An example

An example of a complex feedback system is the steering system of an automobile. While driving, a person receives signals from the environment, such as signs and hazards. The driver’s brain processes the information and sends signals to the automobile via the steering wheel and pedals. The automobile responds by changing direction or speed accordingly

In electronic engineering

The processing and control of feedback is engineered into many electronic devices and may also be embedded in other technologies.

If the signal is inverted on its way round the control loop, the system is said to have negative feedback; otherwise, the feedback is said to be positive. Negative feedback is often deliberately introduced to increase the stability and accuracy of a system

Overview of electronic systems and circuits

Electronic systems are used to perform a wide variety of tasks. The main uses of electronic circuits are:

The controlling and processing of data. The conversion to/from and distribution of

electric power. Both these applications involve the creation and/or

detection of electromagnetic fields and electric currents. While electrical energy had been used for some time prior to the late 19th century to transmit data over telegraph and telephone lines, development in electronics grew exponentially after the advent of radio

Overview of Electronic Systems

One way of looking at an electronic system is to divide it into 3 parts:

Inputs – Electronic or mechanical sensors (or transducers). These devices take signals/information from external sources in the physical world (such as antennas or technology networks) and convert those signals/information into current/voltage or digital (high/low) signals within the system.

Signal processors – These circuits serve to manipulate, interpret and transform inputted signals in order to make them useful for a desired application. Recently, complex signal processing has been accomplished with the use of Digital Signal Processors.

Outputs – Actuators or other devices (such as transducers) that transform current/voltage signals back into useful physical form (e.g., by

accomplishing a physical task such as rotating an electric motor).

the closed-loop controller

To avoid the problems 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. velocity or torque of the motor), which is measured with sensors and processed by the controller; the result (the control signal) is used as input to the process, closing the loop.

advantages over open loop controllers

disturbance rejection (such as unmeasured friction in a motor)

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 sensitivity to parameter variations improved reference tracking performance

single-input-single-output (SISO)

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