Process control concepts — spot the incorrect statement: Which of the following statements is wrong in the context of common modelling and control choices for process units?

Introduction / Context:
Control engineers routinely classify systems as lumped-parameter (finite states described by ordinary differential equations) or distributed-parameter (fields described by partial differential equations). They also match controllers to process characteristics. This question checks conceptual clarity by asking you to pick the incorrect statement among mostly correct assertions.

Given Data / Assumptions:

• CSTR refers to a well-mixed reactor approximation.
• Level control practice typically uses proportional (or PI) controllers.
• Distributed-parameter modelling involves spatial variation.
• On–off control switches output and is non-linear.

Concept / Approach:
A CSTR, by definition, assumes perfect mixing, making its dominant dynamics lumped and represented by ordinary differential equations. Conversely, distributed-parameter systems (e.g., heat conduction in a rod) require partial differential equations. Therefore, claiming a CSTR is distributed is wrong in the usual modelling context. The other statements reflect standard practice and definitions.

Step-by-Step Solution:

Verification / Alternative check:
Standard reactor dynamics texts derive CSTR mass and energy balances as ODEs under the well-mixed assumption, consistent with a lumped-parameter model.

Why Other Options Are Wrong (if chosen):

Common Pitfalls:
Confusing “large volume” with “distributed.” A big tank is still lumped if well-mixed; spatial gradients are neglected by design.

Final Answer:
A continuously stirred tank reactor (CSTR) can be considered as a distributed-parameter system.