[PDF] EXAMPLE PROBLEMS AND SOLUTIONS - eeech (a) Control system; (b) modified block diagram. Taking the inverse Laplace transforms of the preceding three equations, we obtain xl = -ax, + x, + au Rewriting the state and output equations in the standard vector-matrix form, we obtain Obtain a state-space representation of the system shown in [PDF] On Teaching the Simplification of Block Diagrams* the system [1–4]. In control engineering, the block diagram is a primary tool that together with transfer functions can be used to describe cause-and-effect relationships throughout a dynamic system. The manipulation of block diagrams adheres to a mathematical system of rules often known as block diagram algebra.[PDF] Unit 4: Block Diagram Reduction - Computer Science Block Diagram Reduction. Subsystems are represented in block diagrams as blocks, each representing a transfer function. In this unit we will consider how to combine the blocks corresponding to individual subsystems so that we can represent a whole system as a single block, and therefore a single transfer function.