{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

sampled_data_lqr_2009_11_24_01

# sampled_data_lqr_2009_11_24_01 - 18 1 Sampled-Data LQR S...

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 18 - 1 Sampled-Data LQR S. Lall, Stanford 2009.11.24.01 18. Sampled-Data LQR • Implementation of digital controllers • Order of discretization • Sampled-data problem formulation • Equivalent discrete-time problem • Solution of discrete-time problem with cross-terms • Comparison of discrete-time and sampled-data controller • Comparison of continuous-time and sampled-data controller • Performance comparisons at different sampling rates • Variation of cost with sampling rate 18 - 2 Sampled-Data LQR S. Lall, Stanford 2009.11.24.01 The Key Points of This Section • Neither continuous-time design nor discrete-time design are optimal • Both ignore essential features of interconnection of physical systems to digital hard- ware • instead, we use sampled-data design • cost function is continuous-time, accounts for intersample behavior • problem is solved by converting it to a discrete-time problem with same cost 18 - 3 Sampled-Data LQR S. Lall, Stanford 2009.11.24.01 Implementation of Digital Controllers state state samples controller output controller control signal u ( t ) x ( t ) x ç = Ax + Bu S H x d ( k ) u d ( k ) • S is the sampler ; continuous signal x ( t ) is sampled to give discrete signal x d ( k ) = x ( kh ) • H is the hold ; discrete signal is held constant on intervals [ kh, ( k + 1) h ) to give continuous signal u ( t ) 18 - 4 Sampled-Data LQR S. Lall, Stanford 2009.11.24.01 Order of discretization so we have a continuous-time physical system , but need to design a discrete-time controller two approaches 1. design using continuous-time methods, then discretize the controller 2. discretize the plant, then design a controller in discrete-time 18 - 5 Sampled-Data LQR S. Lall, Stanford 2009.11.24.01 implementation of digital controllers which is right? neither method 1 does not account for the effects of sample and hold; it assumes • measurements are available at all times, not just sampling instants • and control signal varies smoothly, not piecewise constant...
View Full Document

{[ snackBarMessage ]}

### Page1 / 18

sampled_data_lqr_2009_11_24_01 - 18 1 Sampled-Data LQR S...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online