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Unformatted text preview: MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Aeronautics and Astronautics 16.060: Principles of Automatic Control Fall 2003 PROBLEM SET 2 Due: 9/18/2003 Problem 1: Block Diagram Manipulation Do Problem 3.27 on page 95 of Van de Vegte. Note that there are two block diagrams hereyou need to find the closed-loop transfer function C ( s ) /R ( s ) for each one. Problem 2: Linearization The following diagram represents a typical spring-mass-dashpot system subject to an external force f ( t ). The mass of the object is m , and the damping factor of the dashpot is c . However, the force due to the spring is non-linear and is given by f k ( x ) = kx 2 / 3 . l l l m E E E B B B B B B B B l l l l l l l l l f Q Q x c Q Q Q Q Q Figure 1: Spring-Mass-Dashpot System 1. Find the differential equation of motion for the system. 2. Linearize the equation about the point x = x . Make sure you explain what youre doing at each step of the linearization process. 3. Using your linearized model, derive the transfer function of the system. Take the external force to be the input, and the position of the mass to be the output.output....
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