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I am wondering about different categorizations of control loops. One categorization differentiates control loops with respect to what inputs they take:

  1. Open control loops.
  2. Closed control loops.

1a. Open control loops without external inputs.

1b. Open control loops with external inputs, also known as feedforward.

An example of 1a would be a temperature controller that simply switches on and off based on a timer. It has no actual knowledge of the conditions of the process it affects, but it's set-point (duration of on- and off-time) would ideally be based on some model of the process it affects.

An example of 1b would be the same temperature controller, only in this scheme, it also takes into account the opening and closing of the entrance door. Perhaps the on-time is increased as some function of how long the entrance door was open.

An example of 2 would be a thermostat taking into account the temperature of the room it affects.

Are there more categories within this categorization? Are there other categorizations? For example, in what categorization would cascade control be a distinct category?

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    $\begingroup$ A rose by any other name. What a control algorithm is called is often not as important as whether it does what it needs to. There are all sorts of funky ones and names - don't forget to throw in discrete time ones like the Deadbeat. $\endgroup$
    – Abel
    May 13, 2023 at 5:14

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The categorization you have mentioned is one common way to categorize control loops based on their inputs. However, there are other ways to categorize control loops as well, such as based on their control objectives, signal types, and control actions.

One example of a categorization based on control objectives is:

Regulatory control loops, which are used to maintain a process variable at a desired set point. Safety control loops, which are used to ensure that a process operates within safe limits. Quality control loops, which are used to maintain a product or process quality within desired specifications.

Another categorization based on signal types includes:

Analog control loops, which use continuous signals (e.g., voltage or current) to control a process variable. Digital control loops, which use discrete signals (e.g., on/off signals) to control a process variable. Hybrid control loops, which use both analog and digital signals to control a process variable.

Cascade control is a type of control loop that can be categorized based on its control action. In cascade control, there are two or more control loops in series, where the output of the primary loop is used as the set point for the secondary loop. The primary loop typically controls a fast-acting variable, while the secondary loop controls a slow-acting variable. This type of control loop is used to improve control performance by reducing the effects of disturbances on the process variable.

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Another way to answer your question would be to frame it in Block Diagrams! The algebra of bock diagrams allows you to visualise all the basic operations you could do on your inputs/outputs like addition/subtraction/multiplication.

If the block diagrams for two systems can't be reduced to analogous block diagrams, then you could call them a different 'category' if you wanted to.

Open-loop/closed-loop and cascade control are named for attributes of their block diagram structure, but there are many more named for their function as @MechaTrex notes. An example to add is the state observer, which could have a block diagram like this:

State observer

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