Control systemThe two states in normal operation are dynamic and steady[1]。
aboutConstant value control systemWhen the control system has no input (including disturbance) changes, the whole system will finally reach a balanced state, that is, each link in the system will not act temporarily, and the output is relatively static. This state is called steady state.
When the system in steady state receives a disturbance, the steady state is destroyed, all links start to act, and the output changes until the next steady state is established, which is called dynamic.
dynamic process
Dynamic process, also known as transient process, refers toThe response process of the system's output from the initial state to the final state under the action of typical input signals[2]。
Dynamic performance
Dynamic performance refers to the properties, characteristics and functions of the system in the dynamic process.
Steady state performance
Steady state process refers to the expression of system output when time t tends to infinity under the action of typical input signals[2]。The performance of the system in steady state is called steady state performance.
In the actual control system, some input signals are random and can not be replaced by typical input signals. In this case, the theory of random process needs to be used for processing.
Connotation and expansion
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one
The main reason of dynamic process is that the actual control system has inertia, friction and other factors to interfere, and the system output cannot reproduce the changes of input.
two
According to the system structure and parameter selection, the dynamic process is shown asattenuation、DivergenceandConstant amplitude oscillationThree forms.In general,The dynamic process of an actual system must be attenuated, or the system must be stable.
three
Usually inStep functionIt is generally considered that step input is the most severe for the system to measure or calculate the dynamic performance of the system under the action of[2]。
performance index
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The index describing the steady state of the stable system under the action of unit step input and the dynamic process changing with time t is called dynamic performance index.[1-2]
As shown in the overview diagram, the dynamic performance indicators mainly include:
one
Rise time tr refers to the time required for the phase to rise from 0.1 times to 0.9 times of the final value. For an oscillating system, it can also be defined as the time required for the response to rise from zero to the final value for the first time;
two
Peak time tp refers to the time required for the response to exceed its final value and reach the first peak;
three
Adjustment time ts refers to the shortest time required for the response to reach and remain within ± 5% (or ± 2%) of the final value;
four
Overshootσ%Refers to the ratio of the difference between the maximum deviation value and the final value of the response and the final value;
five
Attenuation ratio n refers to the ratio of two adjacent wave peaks in the same direction on the waveform diagram;
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In addition, there are oscillation frequency, oscillation period, oscillation times, maximum deviation, etc.
In addition to the above single performance indicators, there are also comprehensive performance indicators of the system, which are mainly reflected in the form of integral[1]。
For performance evaluation, rise time and peak time can evaluate system response speed, overshoot can evaluate system damping degree, adjustment time reflects the comprehensive situation of response speed and damping degree, and attenuation ratio is generally between 4:1 and 10:1.
During actual selection, overall situation of specific process and system shall be considered and reasonable control requirements shall be put forward.General performance indicators may have contradictions, so it is necessary to compromise between accuracy, rapidity and stability and make reasonable trade-offs.[1]
