A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Continuous-Time Switched H∞ Proportional-Integral observer: Application for sideslip and road bank angles estimation

International audience— In this work, a Continuous-Time Switched H ∞ Proportional-Integral (CTSH ∞ PI) observer is presented. The estimation method is based on a proportional-integral observer introduced by [13], [11], [12]. The estimation method is used to estimate simultaneously the state variables and unknown inputs of switched systems. A design method is established using a common Lyapunov function and H ∞ norm. Its stability and global convergence conditions are proved and expressed in term of LMIs. All conditions are established under given switching signals. The estimation method is applied in vehicle dynamics to estimate simultaneously the vehicle sideslip angle and road bank angle. Moreover, the switching signal is deduced from measured premise variables. Simulation tests with experimental data are included to demonstrate the advantage of this method

Second order sliding mode observers for fault reconstruction in power networks

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.This paper proposes a 2-sliding mode observer to detect and reconstruct a certain class of load altering faults in a power network. The observer design is based on the recently proposed multivariable super-twisting structure. The IEEE benchmark power networks used to test the scheme are modelled as a semi-explicit class of differential algebraic equations (DAEs). For the purpose of developing the detection scheme, only the phase angles of the generators are measured, which represent a subset of the differential states of the DAEs. The objective is to estimate the differential states (the phase angles and frequencies of the generators), the algebraic states (the phase angles of the load bus tensions) and to reconstruct a class of load altering faults affecting the network. The proposed observer is assessed in simulation on two IEEE benchmarks: the 9-bus and 14-bus networks, so as to verify its capability to correctly estimate the differential and algebraic states of the network in spite of its complexity and uncertainty. Moreover, the capability of the proposed scheme to detect the presence of a load altering fault, to exactly identify its position in the network, and to precisely reconstruct the shape of the fault itself is shown and discussed

An active fault tolerant control approach to an offshore wind turbine model

The paper proposes an observer based active fault tolerant control (AFTC) approach to a non-linear large rotor wind turbine benchmark model. A sensor fault hiding and actuator fault compensation strategy is adopted in the design. The adapted observer based AFTC system retains the well-accepted industrial controller as the baseline controller, while an extended state observer (ESO) is designed to provide estimates of system states and fault signals within a linear parameter varying (LPV) descriptor system context using linear matrix inequality (LMI). In the design, pole-placement is used as a time-domain performance specification while H∞ optimization is used to improve the closed-loop system robustness to exogenous disturbances or modelling uncertainty. Simulation results show that the proposed scheme can easily be viewed as an extension of currently used control technology, with the AFTC proving clear “added value” as a fault tolerant system, to enhance the sustainability of the wind turbine in the offshore environment

A smooth model for periodically switched descriptor systems

Switched descriptor systems characterized by a repetitive finite sequence of modes can exhibit state discontinuities at the switching time instants. The amplitudes of these discontinuities depend on the consistency projectors of the modes. A switched ordinary differential equations model whose continuous state evolution approximates the state of the original system is proposed. Sufficient conditions based on linear matrix inequalities on the modes projectors ensure that the approximation error is of linear order of the switching period. The theoretical findings are applied to a switched capacitor circuit and numerical results illustrate the practical usefulness of the proposed model

Observer based active fault tolerant control of descriptor systems

The active fault tolerant control (AFTC) uses the information provided by fault detection and fault diagnosis (FDD) or fault estimation (FE) systems offering an opportunity to improve the safety, reliability and survivability for complex modern systems. However, in the majority of the literature the roles of FDD/FE and reconfigurable control are described as separate design issues often using a standard state space (i.e. non-descriptor) system model approach. These separate FDD/FE and reconfigurable control designs may not achieve desired stability and robustness performance when combined within a closed-loop system.This work describes a new approach to the integration of FE and fault compensation as a form of AFTC within the context of a descriptor system rather than standard state space system. The proposed descriptor system approach has an integrated controller and observer design strategy offering better design flexibility compared with the equivalent approach using a standard state space system. An extended state observer (ESO) is developed to achieve state and fault estimation based on a joint linear matrix inequality (LMI) approach to pole-placement and H∞ optimization to minimize the effects of bounded exogenous disturbance and modelling uncertainty. A novel proportional derivative (PD)-ESO is introduced to achieve enhanced estimation performance, making use of the additional derivative gain. The proposed approaches are evaluated using a common numerical example adapted from the recent literature and the simulation results demonstrate clearly the feasibility and power of the integrated estimation and control AFTC strategy. The proposed AFTC design strategy is extended to an LPV descriptor system framework as a way of dealing with the robustness and stability of the system with bounded parameter variations arising from the non-linear system, where a numerical example demonstrates the feasibility of the use of the PD-ESO for FE and compensation integrated within the AFTC system.A non-linear offshore wind turbine benchmark system is studied as an application of the proposed design strategy. The proposed AFTC scheme uses the existing industry standard wind turbine generator angular speed reference control system as a “baseline” control within the AFTC scheme. The simulation results demonstrate the added value of the new AFTC system in terms of good fault tolerance properties, compared with the existing baseline system

A Sliding Mode based Cascade Observer for Estimation and Compensation Controller

The sliding mode observer can estimate the system state and the unknown disturbance, while the traditional single-layer one might still suffer from high pulse when the output measurement is mixed with noise. To improve the estimation quality, a new cascade sliding mode observer containing multiple discontinuous functions is proposed in this letter. It consists of two layers: the first layer is a traditional sliding mode observer, and the second layer is a cascade observer. The measurement noise issue is considered in the source system model. An alternative method how to design the observer gains of the two layers, together with how to examine the effectiveness of the compensator based closed-loop system, are offered. A numerical example is provided to demonstrate the effectiveness of the proposed method. The observation structure proposed in this letter not only smooths the estimated state but also reduces the control consumption

Integral Sliding Mode Control for Markovian Jump T-S Fuzzy Descriptor Systems Based on the Super-Twisting Algorithm

This paper investigates integral sliding mode control problems for Markovian jump T-S fuzzy descriptor systems via the super-twisting algorithm. A new integral sliding surface which is continuous is constructed and an integral sliding mode control scheme based on a variable gain super-twisting algorithm is presented to guarantee the well-posedness of the state trajectories between two consecutive switchings. The stability of the sliding motion is analyzed by considering the descriptor redundancy and the properties of fuzzy membership functions. It is shown that the proposed variable gain super-twisting algorithm is an extension of the classical single-input case to the multi-input case. Finally, a bio-economic system is numerically simulated to verify the merits of the method proposed