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Dynamic sliding mode control based on a full-order observer: Underactuated electro-mechanical system regulation

Ordaz Patricio, Romero-Trejo Hugo, Cuvas Carlos, Sandre Omar

International Journal of Applied Mathematics and Computer Science

2024

Vol. 34, no. 1

29--43

This paper concerns the synthesis of a nonlinear robust output controller based on a full-order observer for a class of uncertain disturbed systems. The proposed method guarantees that, in finite time, the system trajectories go inside a minimal neighborhood ultimately bounded. To this end, the attractive ellipsoid method is enhanced by applying the dynamic sliding mode control performance properties. Furthermore, in order to guarantee the stability of the trajectory around the trivial solution in the uniform-ultimately bounded sense, the feasibility of a specific matrix inequality problem is provided. With this feasible set of matrix inequalities, the separation principle of the controller/observer scheme considered also holds. To achieve a system performance improvement, a numerical algorithm based on the small size ultimate bound is presented. Finally, to illustrate the theoretical performance of the designed controller/observer, a numerical example dealing with the stabilization of a disturbed electromechanical system with uncertain and unmodeled dynamics is presented.

Discrete-time output observers for boundary control systems

Emirsajłow Zbigniew

International Journal of Applied Mathematics and Computer Science

2021

Vol. 31, no. 4

613--626

The paper studies the output observer design problem for a linear infinite-dimensional control plant modelled as an abstract boundary input/output control system. It is known that such models lead to an equivalent state space description with unbounded control (input) and observation (output) operators. For this class of infinite-dimensional systems we use the Cayley transform to approximate the sophisticated infinite-dimensional continuous-time model by a discrete-time infinite-dimensional one with all involved operators bounded. This significantly simplifies mathematical aspects of the observer design procedure. As is well known, the essential feature of the Cayley transform is that it preserves various system theoretic properties of the control system model, which may be useful in analysis. As an illustration, we consider an example of designing an output observer for the one-dimensional heat equation with measured controls (inputs) in the Neumann boundary conditions, measured outputs in the Dirichlet boundary conditions and an unmeasured output at a fixed point within the domain. Numerical simulations of this example show that the interpolated continuous-time signal, obtained from the discrete-time observer, can be successfully used for tracking the continuous-time plant output.

Active fault tolerance control of a wind turbine system using an unknown input observer with an actuator fault

Li S., Wang H., Aitouche A., Tian Y., Christov N.

International Journal of Applied Mathematics and Computer Science

2018

Vol. 28, no. 1

69--81

This paper proposes a fault tolerant control scheme based on an unknown input observer for a wind turbine system subject to an actuator fault and disturbance. Firstly, an unknown input observer for state estimation and fault detection using a linear parameter varying model is developed. By solving linear matrix inequalities (LMIs) and linear matrix equalities (LMEs), the gains of the unknown input observer are obtained. The convergence of the unknown input observer is also analysed with Lyapunov theory. Secondly, using fault estimation, an active fault tolerant controller is applied to a wind turbine system. Finally, a simulation of a wind turbine benchmark with an actuator fault is tested for the proposed method. The simulation results indicate that the proposed FTC scheme is efficient.