Patent ID: 7152083

Claim:
A method of determining a control input signal, comprising: determining a jerk parameter equation, the jerk parameter equation being ∑ i = 0 N ⁢ ( - 1 ) i + 1 ⁢ T i = 1 J determining a first constraint equation, the first constraint equation being ∑ i = 0 N ⁢ ( - 1 ) i ⁢ exp ⁡ ( - σ k ⁢ T i ) ⁢ cos ⁡ ( ω k ⁢ T i ) = 0 ⁢ ⁢ for ⁢ ⁢ k = 1 , 2 , 3 , … determining a second constraint equation, the second constraint equation being ∑ i = 0 N ⁢ ⁢ ( - 1 ) i ⁢ exp ⁡ ( - σ k ⁢ T i ) ⁢ sin ⁡ ( ω k ⁢ T i ) = 0 ⁢ ⁢ for ⁢ ⁢ k = 1 , 2 , 3 , … determining a set of T i values that provides a solution for each of (a) the jerk parameter equation, (b) the first constraint equation and (c) the second constraint equation; selecting the set of T i values to provide a selected set; using the selected set to determine a corresponding transfer function according to the following equation; G ⁡ ( s ) = ∑ i = 0 N ⁢ ⁢ ( - 1 ) i ⁢ exp ⁡ ( - sT i ) coupling the transfer function with a filter function to provide an augmented transfer function; and acting upon an input signal according to the augmented transfer function to provide a control input signal, wherein N is an odd integer, J is the jerk parameter, σ k is the real part of the k th underdamped pole, and ω is the k th natural frequency of a system being controlled.