Stabilization by a relay control using non-quadratic Lyapunov functions

International audienceIn this article we consider the stabilization problem by a relay control using non-quadratic Lyapunov functions. First, a general result is proposed for the case of nonlinear systems. A full state relay feedback controller is designed in order to ensure the local asymptotic stability of the closed-loop system. Then, the result is applied to the particular case of LTI systems. A constructive method based on LMI conditions is given in order to design nonlinear switching surfaces and provide an estimation of a non-ellipsoidal domain of attraction. In addition, the approach is extended to observer-based relay feedback. Both linear and nonlinear switching surfaces dependent on the estimated state are designed while using a Luenberger observer. Finally, illustrative examples are proposed in order to show the efficiency of the proposed methods and simulations are performed for a Buck converter structure

Stabilization of Linear Systems Over Gaussian Networks

The problem of remotely stabilizing a noisy linear time invariant plant over a Gaussian relay network is addressed. The network is comprised of a sensor node, a group of relay nodes and a remote controller. The sensor and the relay nodes operate subject to an average transmit power constraint and they can cooperate to communicate the observations of the plant's state to the remote controller. The communication links between all nodes are modeled as Gaussian channels. Necessary as well as sufficient conditions for mean-square stabilization over various network topologies are derived. The sufficient conditions are in general obtained using delay-free linear policies and the necessary conditions are obtained using information theoretic tools. Different settings where linear policies are optimal, asymptotically optimal (in certain parameters of the system) and suboptimal have been identified. For the case with noisy multi-dimensional sources controlled over scalar channels, it is shown that linear time varying policies lead to minimum capacity requirements, meeting the fundamental lower bound. For the case with noiseless sources and parallel channels, non-linear policies which meet the lower bound have been identified

Adaptive Controller Placement for Wireless Sensor-Actuator Networks with Erasure Channels

Wireless sensor-actuator networks offer flexibility for control design. One novel element which may arise in networks with multiple nodes is that the role of some nodes does not need to be fixed. In particular, there is no need to pre-allocate which nodes assume controller functions and which ones merely relay data. We present a flexible architecture for networked control using multiple nodes connected in series over analog erasure channels without acknowledgments. The control architecture proposed adapts to changes in network conditions, by allowing the role played by individual nodes to depend upon transmission outcomes. We adopt stochastic models for transmission outcomes and characterize the distribution of controller location and the covariance of system states. Simulation results illustrate that the proposed architecture has the potential to give better performance than limiting control calculations to be carried out at a fixed node.Comment: 10 pages, 8 figures, to be published in Automatic

Predictive scheme for observer-based control of LTI systems with unknown disturbances

International audienceIn this work, it is shown that the results introduced in [1], that hold for full state measurement, can be extended to partial state measurement. In particular, it is proven that the combination of an observer with the new predictive scheme of [1] leads to a better disturbance attenuation than using the same observer with the standard predictive scheme. Finally, some simulations illustrate the results for constant and time-varying disturbances

Design and control of laser micromachining workstation

The production process of miniature devices and microsystems requires the utilization of non-conventional micromachining techniques. In the past few decades laser micromachining has became micro-manufacturing technique of choice for many industrial and research applications. This paper discusses the design of motion control system for a laser micromachining workstation with particulars about automatic focusing and control of work platform used in the workstation. The automatic focusing is solved in a sliding mode optimization framework and preview controller is used to control the motion platform. Experimental results of both motion control and actual laser micromachining are presented

Hybrid modeling and control of mechatronic systems using a piecewise affine dynamics approach

This thesis investigates the topic of modeling and control of PWA systems based on two experimental cases of an electrical and hydraulic nature with varying complexity that were also built, instrumented and evaluated. A full-order model has been created for both systems, including all dominant system dynamics and non-linearities. The unknown parameters and characteristics have been identi ed via an extensive parameter identi cation. In the following, the non-linear characteristics are linearized at several points, resulting in PWA models for each respective setup. Regarding the closed loop control of the generated models and corresponding experimental setups, a linear control structure comprised of integral error, feed-forward and state-feedback control has been used. Additionally, the hydraulic setup has been controlled in an autonomous hybrid position/force control mode, resulting in a switched system with each mode's dynamics being de ned by the previously derived PWA-based model in combination with the control structure and respective mode-dependent controller gains. The autonomous switch between control modes has been de ned by a switching event capable of consistently switching between modes in a deterministic manner despite the noise-a icted measurements. Several methods were used to obtain suitable controller gains, including optimization routines and pole placement. Validation of the system's fast and accurate response was obtained through simulations and experimental evaluation. The controlled system's local stability was proven for regions in state-space associated with operational points by using pole-zero analysis. The stability of the hybrid control approach was proven by using multiple Lyapunov functions for the investigated test scenarios.publishedVersio