Intuition on linear dynamics: open loop control by sequence of steps (1st-order plant)

Antonio Sala, UPV

Difficulty: * ,       Relevance: ,      Duration: 13:13

*Enlace a Spanish version

Summary:

This video proposes using a “step response” test obtained experimentally (or in simulation, but the detail of which equations constitute the model is irrelevant as long as they are linear –and approximately of the first order, without “inertia”–) to do straightforward proportionalities aimed at solving the following problems:

1. Achieve a certain setpoint (reference) by means of a single step increment.

2. Getting to said certain preset setpoint in a given settling time, and then staying there employing TWO steps.

To do this, the appropriate proportionalities are stated, and the performance achieved with the resulting step input profiles is checked in simulation. Since the simulated process is a first-order linear system, everything works perfectly as calculated. If the process were of a higher order (with “inertia”) then there could be overshoot and unexpected transients. An example of this fact (with code practically identical to the one explained here) is discussed in the video [linregla3ord2EN].

This could be considered a special case of what is called open-loop control: calculating an input profile without using sensors. In this simple case, only linearity and superposition are used to obtain that input profile, without needing any transfer function or representation in state variables as other more advanced methodologies do.

None of the computations have needed any theoretical knowledge about linearization or linear differential equations, they have simply used the proportionalities that characterize the response of linear systems (incremental around an operating point).

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.