tailieunhanh - Advanced Control Engineering - Chapter 3

Time domain analysis Cách thức mà một hệ thống năng động phản ứng với một đầu vào, thể hiện như là một hàm của thời gian, được gọi là thời gian đáp ứng. Việc đánh giá lý thuyết của phản ứng này được cho là được thực hiện trong miền thời gian, và được gọi là phân tích miền thời gian. Có thể để tính toán thời gian đáp ứng của một hệ thống nếu được biết đến sau đây: . bản chất của đầu vào (s), được thể hiện như là một hàm của thời gian. mô hình toán. | 3 Time domain analysis Introduction The manner in which a dynamic system responds to an input expressed as a function of time is called the time response. The theoretical evaluation of this response is said to be undertaken in the time domain and is referred to as time domain analysis. It is possible to compute the time response of a system if the following is known the nature of the input s expressed as a function of time the mathematical model of the system. The time response of any system has two components a Transient response This component of the response will for a stable system decay usually exponentially to zero as time increases. It is a function only of the system dynamics and is independent of the input quantity. b Steady-state response This is the response of the system after the transient component has decayed and is a function of both the system dynamics and the input quantity. Fig. Transient and steady-state periods of time response. 36 Advanced Control Engineering The total response of the system is always the sum of the transient and steady-state components. Figure shows the transient and steady-state periods of time response. Differences between the input function i r in this case a ramp function and system response xo t are called transient errors during the transient period and steady-state errors during the steady-state period. One of the major objectives of control system design is to minimize these errors. Laplace transforms In order to compute the time response of a dynamic system it is necessary to solve the differential equations system mathematical model for given inputs. There are a number of analytical and numerical techniques available to do this but the one favoured by control engineers is the use of the Laplace transform. This technique transforms the problem from the time or t domain to the Laplace or 5 domain. The advantage in doing this is that complex time domain differential equations become relatively simple s