Frequency-domain linear quadratic optimal system design with two-degree-of-freedom configuration

✍ Scribed by Chih-Min Lin; Jiann-Min Wu

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 308 KB
• Volume: 18
• Category: Article
• ISSN: 0143-2087
• DOI: 10.1002/(sici)1099-1514(199701/02)18:1<73::aid-oca590>3.0.co;2-9

✦ Synopsis

The frequency domain approach to linear quadratic optimal control design has been widely investigated in the past. Wiener -Hopf linear quadratic optimal design has been discussed thoroughly by Chang. 1 However, the imbedded plant is restricted to be stable and minimum phase. The problem is resolved partly by Tsai and Wang 2 where the plant can be non-minimum phase but still has to be stable. Youla et al. 3 present an analytical feedback design technique to ensure asymptotic stability of the closed-loop configuration where the optimal controller is synthesized using the Wiener -Hopf approach. A two-degree-of-freedom controller configuration is adopted by Youla and Bongiorno. 4 Two frequency-dependent weighting matrices are shaped by Chen and Wang 5 to synthesize the multipurpose LQG optimal controller. Sternad and Soderstrom 6 treat an optimal feedforward regulator problem by using a polynomial LQG approach for a single-input single-output system.

In this paper, advanced by the parametric two-degree-of-freedom controller configuration and the Wiener -Hopf optimal control approach, 4 the frequency domain two-degree-of-freedom linear quadratic optimal control of a single-input single-output system is derived. In this derivation, more general frequency dependent weighting functions are considered and a different arrangement of spectral factorization is given so that this design method can easily achieve reference signal tracking 7 and frequency shaping. 8 The optimal controller design can