proj04

proj04 - Design Project 1 for EE4580 As in the distributed...

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Design Project 1 for EE4580 As in the distributed notes, the linearized model for inverted pendulum consists of two transfer functions. We aim to design G yu ( s )and G θu ( s ) such that the dominant dynamics for the closed-loop system have damping ratio 0.83, and natural frequency 1.83. Moreover the steady-state error for the position of the cart is zero. The design can proceed as follows: 1. We consider first design of G ( s )= num ( s ) den g ( s ) = K gy s + z y s + p g G θu ( s num θu ( s ) den g ( s ) = K s + z θ s + p g such that the transient performance is satisfied. Iterative design method can be employed using both 0 o and 180 o root locus methods. 2. We then modify the compensators into the form G ( s num ( s ) den g ( s ) = K ( s + z y )( s + z ² ) s ( s + p g ) G θu ( s num θu ( s ) den g ( s ) = K s + z θ s + p g with z ² > 0 a very small number. Note that other parameters need be adjusted approri- ately in order to satisfy the transient performance reqirements.
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