What are the commonly used time domain performance metrics of the system?

It refers to the time-domain expression of the control system according to the output quantity under a certain input.

Analyze system stability, transient, and steady-state performance. Since time domain analysis is a method of analyzing a system directly in the time domain, time domain analysis has the advantage of being intuitive and accurate. The time-domain representation of the output of the system can be obtained from differential equations or from transfer functions.

Get. When the initial value is zero, the transfer function is generally used to study, and the transfer function is used to indirectly evaluate the performance index of the system. Specifically, the performance of the system is analyzed according to the pole and zero point of the transfer function of the closed-loop system.

This is also known as complex frequency domain analysis. Linear differential equations.

The solution of the time-domain analysis discusses the characteristics and performance indicators of the system with the solution of a linear stationary differential equation. Let the differential equation be as follows: where x(t) is the input signal and y(t) is the output signal.

We know that the solution of a differential equation can be expressed as: , where , is the corresponding homogeneous equation.

The general solution is only related to the differential equation (the properties of the system itself or the characteristic equations of the system.

roots). For a stable system, when time tends to infinity, the general solution tends to zero. Therefore, the stability of the system can be analyzed according to the root of the general solution or characteristic equation.

is a special solution and is related to differential equations and inputs. In general, when time tends to infinity, the special solution tends to be a steady-state function. To sum up, for a stable system, for a bounded input, when time tends to infinity, the full solution of the differential equation will tend to be a steady-state function, bringing the system to a new equilibrium state.

In engineering, it is called entering a steady state process. The process before the system reaches a steady state process is called a transient process. Transient analysis is the analysis of various motion characteristics of the output response during a transient process.

Theoretically, it is only when time tends to infinity that a steady-state process is entered, but this is obviously not possible in engineering. In engineering, only the input action is added to the transient process over a period of time, during which the main transient performance metrics are reflected.

The time-domain performance indicators of the control system include adjustment time and overshoot, which are the two most important indicators that reflect the dynamic performance of the system. The corresponding index reflecting the stable, accurate and fast performance of the system is: overshoot reflects the oscillation intensity of the dynamic process, which is the stationarity index, also known as the relative stability performance.

The time response of any stable linear control system under the action of input signals is composed of two parts: dynamic response (or transient response, transient response) and steady-state response. The dynamic response describes the dynamic performance of the system, while the steady-state response reflects the steady-state accuracy of the system. Both are important features of linear control systems.

Therefore, it is necessary to meet the requirements at the same time when designing the system.

Time-domain model. Use differential equations.

The system model described is called a time domain model. Under the external effect and initial conditions of Bunadin, the output response of the system can be obtained by solving the differential equation. This method is intuitive and helps to quickly obtain results with the help of a computer.

However, if the system structure changes or some parameters change, it is necessary to re-list the equation to solve, which is not convenient for the system analysis and design.

When the complex domain model uses the Rasl transform method to solve the differential equation of a linear system, the mathematical model of the control system in the complex domain can be obtained.

Transfer functions. The transfer function can not only characterize the dynamic performance of the system, but also can be used to study the impact of changes in system structure or parameters on the performance of the system.

There are 6 dynamic indicators in the time domain, which are:

Overshoot: The ratio of the maximum deviation beyond the steady-state value in the response curve to the steady-state value is called the maximum oversolve, referred to as the overshoot, which is generally expressed as a percentage.

Transition time: δ is the allowable error range, generally 5% or 2%. If the response curve enters the range and does not exceed the range, the entry time is the transition time. The elapsed transit time indicates the end of the transient state.

Number of oscillations: In the transition time (0 t ts), half of the number of times the response curve passes through the steady state value of the version is called the number of oscillations.

Chang Chain Answer]: B

The steady-state index is an index to measure the steady-state accuracy of the system, and the performance index of the steady-state characteristics is the steady-state error. The dynamic characteristic performance index is an index to evaluate the advantages and disadvantages of the dynamic characteristics of the system system, which is usually defined by some characteristic quantities of the unit step response of the system. Dynamic indicators are usually rise time, peak time, adjustment time, overshoot, attenuation rate, oscillation frequency and period, and number of oscillations.

Answer: B

There are three types of ACD, and the time-domain indicators include steady-state indicators and dynamic indicators. The steady-state index is generally represented by the steady-state position error coefficient kp, the steady-state velocity error coefficient kv and the steady-state acceleration error coefficient ka. Dynamic indicators are usually rise time, peak time, adjustment (adjustment) time, overshoot (maximum overshoot), etc. b, frequency domain indicators include open-loop frequency domain indicators and closed-loop frequency domain indicators.

Open-loop frequency domain indicators refer to phase margins, amplitude margins, deficits, and shear (cut-off balance) frequencies. Closed-loop frequency domain metrics refer to the resonant peak, resonant frequency, and band width (bandwidth).