Ruslan E. Seifullaev

Sampled-Data Control of Nonlinear Oscillations Based on LMIs and Fridman's Method.

Abstract Emilia Fridmans method based on time-dependent Lyapunov-Krasovsii functionals is extended to nonlinear control systems with sector bounded nonlinearity. Furthermore, this paper considers sampled-data feedback control under uncertain sampling with the known upper bound on the sampling intervals, where the control function is multiplied by bounded scalar nonlinear function in system equation. This special case corresponds to many oscillator control systems, for example, cart-pendulum system. The problem is reduced to feasibility analysis of linear matrix inequalities based on classical results of V.A. Yakubovich about S-procedure.

Speed Gradient Energy and Sampled-Data Control of Cart-Pendulum System

Abstract The possibilities of implementation for energy-based control of nonlinear oscillations are studied. This approach is based on the speed gradient method and energy-based goal functions. The approach is analysed by example of cart-pendulum system control. As a result of the research the algorithm of a swing of the pendulum on the cart is obtained. Vertical stabilization algorithm is based on sampled-data control of linear systems under uncertain sampling with the known upper bound on the sampling intervals. Working capacity of algorithms is confirmed by simulating in MATLAB Simulink. Experimental set-ups controlled by program block LEGO Mindstorms NXT are described.

Linear matrix inequality-based analysis of the discrete-continuous nonlinear multivariable systems

The E.M. Fridman method for analysis of the hybrid linear systems by passing to a system with sawtoothed delay and using the nonstationary Lyapunov-Krasovskii functionals and descriptor variables was extended to the nonlinear multivariable Lur’e systems. Consideration was given to the discrete control in the form of a feedback with bounded above variable step of discretization. At that, in the system equations the control function was multiplied by a bounded scalar nonlinear function. This case corresponds to numerous oscillators such as the “pendulum on cart” system. On the basis of the classical results obtained by V.A. Yakubovich on losslessness of the S-procedure, the problem of estimating the upper boundary of the discretization step comes to analyzing the system of linear matrix inequalities for solvability.

Synchronization of nonlinear systems over intranet: Cart-pendulum case study.

The master-slave synchronization problem for two cart-pendulum systems when both measurement and control signals are transmitted via intranet communication channel is examined. The speed-gradient method for exciting master system and linear state feedback for slave system is used. Theoretical analysis is performed by the nonlinear extension of Fridmans method. Experimental results are presented for a cart-pendulum system constructed from Lego. Theoretical bound for sampling interval guaranteeing synchronization is about h=0.1 sec. Such bounds are positive for control over intranet and very negative for control over internet. However experiments show that real values of the communication delays are even bigger.

Energy control of a pendulum with quantized feedback

The problem of controlling a nonlinear system to an invariant manifold using quantized state feedback is considered by the example of controlling the pendulums energy. A feedback control law based on the speed gradient algorithm is chosen. The main result consisting in precisely characterizing allowed quantization error bounds and resulting energy deviation bounds is presented.

Accuracy of Fridman's estimates for sampling interval: nonlinear system case study

Abstract An attempt to evaluate accuracy of Fridmans sampling interval estimates for nonlinear discrete-continuous systems where the controlled plant belongs to a class of cascade passifiable Lurie systems. Numerical results obtained for master-slave configuration of two mobile robots demonstrate good accuracy of Fridmans estimates: error of the sampling interval estimate is less than 25% of the value obtained from extensive simulation. In contrast, the error obtained by conventional method from quadratic Lyapunov function is more than 75% of the value obtained from simulation.

LEGO Mindstorms NXT Robots and Oscillators in Control Education

Abstract A description and some implementation results for a “Cyber-physical laboratory” project performed jointly by the students of St.Petersburg State University and those of St.Petersburg Phys&Math Lyceum #239 are presented. The goal of the project is to create a complex of robotics and mechatronics networked devices based on LEGO Mindstorms NXT for application in universities and in high schools.