Michel Dambrine

Anti-windup based dynamic output feedback controller design with performance consideration for constrained Takagi-Sugeno systems

This paper proposes an LMI-based method to guarantee the closed-loop regional stability and performance for Takagi-Sugeno systems that are subject to input saturation, state constraints, and also amplitude-bounded disturbance. Based on the Lyapunov stability tool, the proposed method provides conditions to simultaneously design the dynamic output feedback controller and its anti-windup compensator. By solving a convex optimization problem, these conditions are derived such that a tradeoff between the upper bound on the nominal ?2 gain for exogenous disturbance and the minimal size of the domain of attraction can be found. This method is simple and systematic, allowing dealing with a very large class of constrained nonlinear systems. The effectiveness of the proposed method is illustrated with numerical examples.

Robust H ∞ control design for switching uncertain system: Application for turbocharged gasoline air system control

Combining turbocharger with downsizing has now become a key technique for gasoline engine to improve performances such as fuel economy and drivability in the automotive industry. The technology potential is fully exploited only with an efficient air path management system. In this context, this paper proposes a robust controller based on switching Takagi-Sugeno (TS) model to manage the air path of a downsized engine. The time-varying modeling uncertainties and the bounded measurement noises will be explicitly taken into account during the control design. In addition, the new proposed strategy handles easily the nonlinearities and facilitates considerably the global stability analysis of the whole air system. Finally, this generic approach can be generalized to others more complex turbocharger systems with some small adaptations.

Tracking-error model-based PDC control for mobile robots with acceleration limits

This paper presents a new technique for tracking-error model-based PDC control for nonholonomic vehicles. Briefly, this technique consists of rewriting the kinematic error model of the tracking problem for mobile robot into a fuzzy TS representation and finding a stabilizing controller by solving LMI conditions for tracking-error model. The state variables are filtered using a TS fuzzy observer. The reference trajectory is built with taking into account the acceleration limits of the mobile robot. Experimental results are presented here to show the efficiency of the proposed approach.

Multi-objective control design for turbocharged spark ignited air system: A switching Takagi-Sugeno model approach

This paper proposes a linear matrix inequality (LMI) approach to the multi-objective synthesis of switching Takagi-Sugeno (T-S) controller. The design objectives of the closed-loop system include the robustness performance w.r.t model uncertainties and bounded disturbance, the convergence speed, and the constraints on the control input. All objectives are derived from the Lyapunov approach and they are formulated as LMI conditions. Thus, controller design task amounts to solving a LMI optimization problem. The air system control problem of a turbocharged spark ignited (TCSI) engine is used to illustrate the validity of the proposed method..

Relation between Exponential Stability and Input-to-State Stability of Time-Delay Systems

The main contribution of this paper is to establish a link between the exponential stability of an unforced system and the input-to-state stability (ISS) via the Lyapunov-Krasovskii methodology. A new theorem is provided, which proves that an unforced system whose trivial solution is exponentially stable is input-to-state stable if submitted to a perturbation which can be of an arbitrary size.

Augmented observer approach for high-impedance haptic system with time delay

Among others measures of performance, a haptic device may be characterized by its behavior in the implementation of a virtual wall in terms of the biggest value of the virtual stiffness leaving stable the device. This value depends on many factors including time delays and the virtual world implementation. The paper proposes a new architecture for this latter one based on the use of an augmented state observer which contributes to improve without additional costs the performance of a haptic device with respect to the standard implementation based on the use of the backward finite difference method. In order to compute the stability boundaries of the device in terms of virtual wall parameters, a new LMI criterion for the stability of discrete-time systems with time-varying delay is given. Some numerical simulation results are included to prove the effectiveness of the proposed approach.

Robust H ∞ control for the turbocharged air system using the multiple model approach

This work deals with the modeling and control of the air system of a turbocharged spark ignited (TCSI) engine. The main purpose is to design a set of nonlinear controllers based on the original physical models of the systems. The proposed strategy is based on the multiple model control approach. Linear Matrix Inequality (LMI) conditions are derived from the Lyapunovs direct method in order to compute the controller for the multiple model subject to bounded noises. The disturbances attenuation is addressed via an H∞ constraint. In comparison with existing approaches, the proposed strategy handles more easily the nonlinearities and alleviates significantly the calibration and implementation tasks. Moreover, the feedback gains are readily tuned with few parameters. Finally, this method can be generalized to others more complex turbocharging systems with some adaptations.