Adaptive tracking control of switched linear systems with multiple disturbance observers

This paper deals with model reference adaptive control for an uncertain switched linear system in the presence of disturbances in the state and control input based on time-dependent switching methods. A novel composite disturbance observer-based adaptive controller with adaptive laws is proposed in a tracking problem of uncertain switched linear system. First, two disturbance observers are proposed to estimate disturbances. Then, a hybrid switched adaptive controller based on state feedback and disturbance observers is designed. Thereafter, based on time-dependent switching signals included dwell-time (DT), average dwell-time (ADT), and the mode-dependent approaches of DT and ADT, a globally uniformly ultimately bounded stability of the closed-loop switched linear system is proved. Finally, the theoretic achievement is applied to a highly manoeuvrable aircraft technology vehicle to demonstrate the significance of the proposed method.

Robust Simultaneous Stabilization Using Derivative State Feedback

In simultaneous stabilization of continuous time switched linear system models of inertially coupled dynamic systems with bounded persistent external disturbance and internal parameter variations, the generalized proportional integral derivative (PID) controller suffers from a serious drawback. It loses the ability to guarantee exponential stability of the closed-loop error response, which is the difference between the actual and the desired closed-loop responses. The high value of the hardware gain has no control over the situation. On the contrary, the derivative state feedback (DSF) controller effectively employs the hardware gain in diminishing the effects of external and internal disturbances. These facts are proved and illustrated by suitable examples. The proposed method of simultaneous stabilization is shown to be an easier alternative to solve Diophantine equations encountered. The method for single input single output (SISO) systems is also shown to extend seamlessly to the control of multiple input multiple output (MIMO) square models with equal number of inputs and outputs. The shortcoming of the method is pointed out when the models are not square. The advantages of the proposed methodology over the existing methods are outlined. Finally, an efficient time domain simulation scheme is presented for the numerical study of such models in time and transfer function domain with nonzero initial conditions.

Inversion-Based Approach for Detection and Isolation of Faults in Switched Linear Systems

This paper addresses the problem of the left inversion of switched linear systems from a diagnostics perspective. The problem of left inversion is to reconstruct the input of a system with the knowledge of its output, whose differentiation is usually required. In the case of this work, the objective is to reconstruct the system’s unknown inputs, based on the knowledge of its outputs, switching sequence and known inputs. With the inverse model of the switched linear system, a real-time Fault Detection and Isolation (FDI) algorithm with an integrated Fuzzy Logic System (FLS) that is capable of detecting and isolating abrupt faults occurring in the system is developed. In order to attenuate the effects of unknown disturbances and noise at the output of the inverse model, a smoothing strategy is also used. The results are illustrated with an example. The performance of the method is validated experimentally in a dc-dc boost converter, using a low-cost microcontroller, without any additional components.

Switched Linear Model of a Stratified Hot Water Tank for Control of Micro-CHP Systems

We present a switched linear system approach for modeling the complex nonlinear dynamics associated with temperature inversion occurring in thermally stratified hot water tanks. Such tanks are commonly used for thermal energy storage, particularly in low- to medium-temperature waste heat recovery applications. By separating the influence of temperature inversion from the internal heat transfer between states in the governing differential equations, we paramaterize the nonlinearity using a vector of discrete variables. This vector is then used to define the switching between a set of linear, discrete time models. The proposed switched model is validated against a reduced-order nonlinear model of the thermal energy storage and then integrated with a fuel cell model to capture the dynamics of a micro-combined heat and power system. Simulation results demonstrate the importance that temperature inversion has on the stratification dynamics which in turn has implications for control of such systems.

Modelling and region stability analysis of wind turbines with battery energy storage system based on switched system with multi-equilibriums

This paper deals with the modelling and control for wind turbine combined with a battery energy storage system (WT/BESS). A proportional-integral (PI) controller of pitch angle is applied to adjust the output power of WT, and a method for battery scheduling is presented for maintaining the state of charging (SOC) of BESS. When the battery level is below the lower limit, we increase the expected output power of wind turbine through raising the operation point to charge the battery. Considering the effect of charging/discharging, a switched linear system model with two equilibriums is presented firstly for such WT/BESS system. The region stability is analyzed and an approach for estimating the corresponding stable region is also given. The effectiveness of the proposed results is demonstrated by a numerical example.

Robust Stabilization of Linear Switched Systems with Unstable Subsystems

This paper deals with the robust stability of a class of uncertain switched systems with possibly unstable linear subsystems. In particular, conditions for global uniform exponential stability are presented. In addition, a procedure to design a mode dependent average dwell time switching signal that stabilizes a switched linear system composed of diagonalizable subsystems is established, even if all of them are stable/unstable and time-varying (within design bounds). An illustrative example of the stabilizing switching law design and numerical results are presented.