Time response of a dynamic system

The information about how the system responds to certain inputs is provided by the time response of a dynamic system. To determine the stability of the system and the performance of the controller, we can analyze the time response.

Numerically integration of the system model in time is involved by obtaining the time response of a system. The time response of the control system can be found by finding its equation of motion and for that we need to model the overall system dynamics.

The system could be composed of the mechanical, electrical, or other sub-systems. In addition, each sub-system is expected to have sensors and actuators to sense the environment and to interact with it.
In order to find the transfer function of all the sub-components and use the block diagram, we can use the Laplace transforms. We can use the signal flow diagrams in order to find the interactions among the system components.

According to the objectives, the manipulation of the system final response by adding the feedback or poles and zeros to the system block diagram, can be done. By using the inverse Laplace transforms, the overall transfer function of the system can be found and we can obtain the time response of the system to a test input normally a step input.

The Lab VIEW Control Design and the Simulation Module provides Vis to help us to find these time-domain solutions. To analyze the response of a system to step and impulse inputs, we can use this Time Response Vis. Initial conditions can be applied to both of these responses.

To simulate the response of the system to an arbitrary input, we can use the Time Response Vis.

Rise time (tr) — It is the time required for the dynamic system response to rise from the lower threshold to an upper threshold. The default values are 10% for the lower threshold and90% for the upper threshold.

Maximum overshoot (Mp)—the dynamic system response value that most exceeds the unity, expressed as a percent.

Peak time (tp) — it is the time required to reach the peak value of the first overshoot by the dynamic system response.

Settling time (ts) — it is the time required for the dynamic system response to reach and stay within a threshold of the final value. The default threshold is 1%.

Steady state gain— it is the final value around which the dynamic system response settles to a step input.

Peak value (yp) — it is the value at which the maximum absolute value of the time response occurs.

No comments:

Post a Comment