Simplified Schmid pendulum

Model description: 

Simplified Schmid pendulum:

$$\begin{align*} \ddot{\psi} + a_{21}\omega - a_{11}\sin{\psi} &= -b_1u, \\ \dot{\omega} + a_{22}\omega + a_{12}\sin{\psi} &= b_2u, \end{align*}$$

where $\psi$ is the pendulum angle; $\omega$ is the wheel angular rate; $u$ is the controlling voltage, applied to the motor; $a_{11},a_{21},a_{12},b_1,b_2$ are positive constants, depending on the design parameter of the pendulum. It is assumed that the upper (unstable) equilibrium point corresponds to $\psi=0$.



Time domain: 


Publication details: 

TitleHybrid quantised observer for multi-input-multi-output nonlinear systems
Publication TypeConference Paper
Year of Publication2008
AuthorsFradkov, Alexander L., Andrievsky Boris, and Evans Robin J.
Conference NameIEEE International Conference on Control Applications, 2008. CCA 2008.
Date Published09/2008
Conference LocationSan Antonio, Texas, USA
ISBN Number978-1-4244-2222-7
Accession Number10235153
KeywordsIMO systems, nonlinear control systems, observers, oscillators, pendulums
AbstractLimit possibilities of state estimation under information constraints (limited information capacity of the coupling channel) for multi-input-multi-output (MIMO) nonlinear systems are evaluated. We give theoretical analysis for state estimation of nonlinear systems represented in Lurie form (linear part plus nonlinearity depending only on measurable outputs) with a first-order coder-decoder. It is shown that the upper bound of the limit estimation error is proportional to the upper bound of the transmission error. As a consequence, the upper bound of limit estimation error is proportional to the maximum rate of the coupling signal and inversely proportional to the information transmission rate (channel capacity). The results are applied to state estimation of a nonlinear self-excited mechanical oscillator and a reaction-wheel pendulum.