Ming-Li Chiang

Adaptive stabilization of a class of uncertain switched nonlinear systems with backstepping control

Abstract In this paper, we focus on the problem of adaptive stabilization for a class of uncertain switched nonlinear systems, whose non-switching part consists of feedback linearizable dynamics. The main result is that we propose adaptive controllers such that the considered switched systems with unknown parameters can be stabilized under arbitrary switching signals. First, we design the adaptive state feedback controller based on tuning the estimations of the bounds on switching parameters in the transformed system, instead of estimating the switching parameters directly. Next, by incorporating some augmented design parameters, the adaptive output feedback controller is designed. The proposed approach allows us to construct a common Lyapunov function and thus the closed-loop system can be stabilized without the restriction on dwell-time, which is needed in most of the existing results considering output feedback control. A numerical example and computer simulations are provided to validate the proposed controllers.

Hybrid system based adaptive control for the nonlinear HVAC system

An adaptive controller is designed for the nonlinear MIMO heating, ventilating, and air conditioning (HVAC) system. The designed controller has the ability to adapt to the slowly time varying load change of thermal space and maintains good tracking performance for temperature and humidity ratio. Moreover, we integrate a supervisory switching logic into this system to adjust the CO2 concentration of thermal space and the whole closed loop system is modelled as a hybrid system. The obtained control system shows robustness and effectiveness and simulation results are provided to illustrate the control performance

Variable structure based switching adaptive control for a class of unknown switched linear systems

In this paper, we discuss the model reference adaptive control problem of switched linear systems with unknown parameters. Since we do not have information about the system parameters nor the possible abrupt changes of parameters, conventional integral adaptive law do not function well for switched systems. We propose a variable structure based adaptive controller to the switched system and show error convergence and signal boundedness for a class of switching signals by multiple Lyapunov function theory. A sufficient condition for stability and error convergence of the switched system with unknown parameters is given. To improve the chattering phenomenon, we propose a switching adaptive controller that switches between the leakage type and the VS adaptive controller by hysteresis switching algorithm. Simulation results are provided to support the analysis.

Adaptive Control of Switched Systems with Application to HVAC System

In this paper, we discuss the problem of adaptive control of autonomous switched systems. Classical adaptive control for continuous systems has properties such as bounded signals and or convergence of the output error. Here, we derive similar results for switched systems with adaptive control using stability theory of switched systems. Zero output tracking error and bounded signals are shown for a specified class of switched systems with adaptive control. An application to switched HVAC system using adaptive control is discussed and theoretic analysis is provided.

Variable structure model reference adaptive control of unknown switched linear systems with relative degree greater than one

In this paper, we consider the model reference adaptive control (MRAC) problem of switched linear systems in which the parameters and switching time instants are all unknown. We apply the output feedback variable structure (VS) based adaptive controller to switched linear systems with general relative degrees and show error convergence and signal boundedness properties by multiple Lyapunov functions. Specifically, a sufficient condition on the switching signal is obtained to ensure stability and error convergence of the system. Incidentally, the robustness and performance of VS adaptive controllers of the systems with jump parameters, which are only seen by simulations in existing literatures, are shown by thorough theoretical analysis. Simulation results are provided to validate the analysis.

Design and Control of Phase-Detection Mode Atomic Force Microscopy for Reconstruction of Cell Contours in Three Dimensions

Atomic force microscopy (AFM) is capable of producing accurate 3-D images at nanometer resolution. As a result, AFM is widely used in applications related to cell biology, such as the diagnosis and observation of tumor cells. This paper proposes phase-detection mode atomic force microscopy (PM-AFM) for the 3-D reconstruction of cell contours. The proposed three-axis scanning system employs two piezoelectric stages with one and two degrees of freedom, respectively. Accurately rendering the contours of delicate cells required a multi-input multi-output (MIMO) adaptive double integral sliding mode controller (ADISMC) in the xy-plane to overcome uncertainties within the system as well as cross-coupling, hysteresis effect, and external disturbance. An adaptive complementary sliding-mode controller (ACSMC) was installed along the z axis to improve scanning accuracy and overcome the inconvenience of conventional controllers. Phase feedback signals were also used to increase the sensitivity of scanning, while providing faster response times and superior image quality. A comprehensive series of experiments was performed to validate the performance of the proposed system.

Variable structure adaptive backstepping control for a class of unknown switched linear systems

In this paper, we consider adaptive control of switched linear systems with unknown parameters and unknown switching signals. Variable structure (VS) adaptive backstepping control with tuning function for relative degree one case is discussed. The parametrization of tuning function scheme leads the switched system into a non-switched one with a step change in the input channel and thus the stability properties are derived independent of the switching signal. Moreover, a VS adaptive backstepping control to switched linear systems with relative degree one and two are also proposed. Output error convergence and signal boundedness properties are derived by multiple Lyapunov functions. With the proposed VS adaptive backstepping controller, if the switching signal satisfies the average dwell time conditions, then the output error will converge to a designed residue set and all signals will be bounded. Some simulation results are provided to validate the analysis.

Adaptive and Robust Control for Nonlinear HVAC System

In this paper, we design adaptive and robust controller for the nonlinear MIMO heating, ventilating, and air conditioning (HVAC) system, respectively. The designed adaptive controller maintains good tracking performance for temperature and humidity ratio regardless of the slowly time-varying load changes, which are regarded as parametric uncertainties in thermal space. The robust controller considering non-parametric uncertainties is designed so as to remedy the drawback of feedback linearization technique. The obtained control system shows robustness to the non-constant thermal loads and mismatched uncertainties, respectively. Some simulation results are provided to illustrate the satisfactory control performance of the adaptive controller.

Synthesis of static output feedback SPR systems via LQR weighting matrix design

In this paper we propose an approach using linear quadratic regulator (LQR) weighting matrices to synthesize strictly positive real (SPR) systems by static output feedback. The systems being considered are linear time-invariant (LTI). We first recall full state feedback LQR design. The two weighting matrices for state and control input respectively in the performance index are then used as two free parameters to design the SPR controller. By connecting strictly positive realness with full state feedback LQR through the algebraic Riccati equation associated with the latter and imposing well-posed condition in terms of positive definiteness on the weighting matrices, we show that the proposed formula for weighting matrices in this paper can render the resulting closed loop system SPR. The stabilizing static output feedback gain which is designed to make the closed loop system SPR becomes readily available once the two LQR weighting matrices are determined. Moreover, from the derived explicit form of control gain, we can achieve SPR synthesis even when system matrices are partially known. We provide in the end a numerical example to validate the approach.

Integration of Supervisory and Nonlinear Control for a Heating, Ventilating, and Air Conditioning System

In this paper, we propose a supervisory controller for the discrete model of a heating, ventilating and air conditioning (HVAC) system and then design the nonlinear controller for the heating and cooling subsystems within. The HVAC system includes the discrete event dynamics and nonlinear continuous dynamics, both are very complex and challenging. Here we discuss the whole system and systematically design the controller and the interface between continuous and discrete controller.