Question

find: a. open-loop transfer function, y(s) r(s) = b(s) a(s) b. closed-loop transfer functions g and h where,y(s) r(s) = g(s)

Answer 1

The question lacks clear context but seems to involve open-loop and closed-loop transfer functions in control systems. The open-loop transfer function is the ratio y(s)/r(s) and the closed-loop transfer function g(s) is found by considering feedback loops in the system. More context is needed to provide a specific answer.

Step-by-step explanation:

The question provided seems to pertain to the field of control systems, specifically regarding the analysis of open-loop and closed-loop transfer functions. Unfortunately, the question's excerpts are fragmented and lack context, making it challenging to provide a precise answer. However, in general terms:

1. The open-loop transfer function y(s)/r(s) is generally denoted as the ratio of the output transfer function y(s) to the input or reference signal r(s), which can be expressed as a mathematical function in terms of s, where s is the complex frequency variable used in the Laplace transform.
2. The closed-loop transfer function, g(s), is obtained by considering the feedback loop and is typically represented by the formula G(s)/(1+G(s)H(s)), where G(s) is the open-loop transfer function and H(s) is the feedback factor.

The 'a' and 'b' parts of the question appear to refer to limits or other algebraic considerations, but due to the lack of a clear context, providing a specific response is not feasible. In a comprehensive curriculum on control systems, which may be part of an engineering course, these principles are key topics.