Lecture 2.5

Complex Testing

Варіант 1

1.1 Explain the notion of control systems stability: determination of control systems stability using their step response characteristics.

Lecture 2.5

1.2 Explain feedback loops of control systems: definition, classification, block diagrams of control systems with feedback loops.

A feedback loop is a common and powerful tool when designing a control system. Feedback loops take the system output into consideration, which enables the system to adjust its performance to meet a desired output response.

When talking about control systems it is important to keep in mind that engineers typically are given existing systems such as actuators, sensors, motors, and other devices with set parameters, and are asked to adjust the performance of those systems. In many cases, it may not be possible to open the system (the "plant") and adjust it from the inside: modifications need to be made external to the system to force the system response to act as desired. This is performed by adding controllers, compensators, and feedback structures to the system.

E(s) = the error signal.

The function E(s) is known as the error signal. The error signal is the difference between the system output (Y(s)), and the system input (X(s)). Notice that the error signal is now the direct input to the system G(s). X(s) is now called the reference input. The purpose of the negative feedback loop is to make the system output equal to the system input, by identifying large differences between X(s) and Y(s) and correcting for them.

The equivalent transfer function of anti-parallel coupling of dynamic links is equal to forward path transfer function divided by one plus (for negative feedback) or minus (for positive feedback) the product of transfer functions in forward and feedback paths.

If a feedback loop has a value (transfer coefficient) of one then we call this a unity feedback.

It turns out that negative feedback is almost always the most useful type of feedback. When we subtract the value of the output from the value of the input (our desired value), we get a value called the error signal. The error signal shows us how far off our output is from our desired input.

Positive feedback has the property that signals tend to reinforce themselves, and grow larger. In a positive feedback system, noise from the system is added back to the input, and that in turn produces more noise. As an example of a positive feedback system, consider an audio amplification system with a speaker and a microphone. Placing the microphone near the speaker creates a positive feedback loop, and the result is a sound that grows louder and louder. Because the majority of noise in an electrical system is high-frequency, the sound output of the system becomes high-pitched.

Feedback loops may beproportional and differential.