Study On Nonlinear System Control Theory And Ap-plication

In the last few years we have witnessed the appearance of a series of challenging con-trol engineering problems. There are two common features of these new control problems. First, the interesting range of operation of the system is not necessarily close to an equi-librium, hence nonlinear effects have to be explicitly taken into account for a successful controller design. Second, even though physical modeling allows to accurately identify cer-tain well-defined nonlinear effects, the controller has to deal with high level of uncertainty, mainly due to lack of knowledge of the system parameters and the external disturbance.This situation justifies the need for the development of tools for controller design for uncertain nonlinear systems, which is the main topic of the dissertation. The main contents are outlined as follows.In Chapter 3, it is shown that the linear matrix inequalities that result from the appli-cation of interconnection and damping assignment passivity-based control (IDA-PBC) to general linear time-invariant systems are feasible if and only if the system is stabilizable. A very simple proof of this fact is given that, in contrast to previous results, does not require the assumption that the system has no uncontrollable pole at s=0. A second contribution of the chapter is the proof that, for the case of mechanical systems, the method is applica-ble if and only if a new linear matrix inequality involving the input matrix and the springs stiffness coefficients matrix is satisfied.It is well known that energy-balancing passivity-based control is stymied by the pres-ence of pervasive dissipation. To overcome this problem in electrical circuits, some authors have used power-shaping techniques, where stabilization is achieved by shaping a function akin to power instead of energy. Some extensions of the techniques to general nonlinear systems, yielding static state-feedback control laws, have also been reported. In Chapter 4, we extend these techniques to dynamic feedback control and apply them to nonlinear chemical processes. The stability analysis is carried out using the shaped power function as Lyapunov function.In Chapter 5, a design method on adaptive sliding mode control of systems with mis-matched parametric perturbations is proposed. The method combines immersion and in-variance (I&I) adaptive control with linear sliding mode control (LSMC), which resembles the well-known combining adaptive backstepping with sliding mode control, but is differ-ent from the parameter estimation law, which allows for prescribed dynamics to be assigned to the estimation error and is easier to tune than the backstepping adaptive obtained from Lyapunov redesign. By applying I&I adaptive law and sliding mode to design the con-trollers, not only the mismatched parametric perturbations are automatically overcoming during the sliding mode, but also the property of asymptotical stability of controlled sys-tems is achieved at the same time. Moreover, the knowledge of the upper bound of partial parametric perturbations is not required and the systems do not have to be in strict-feedback form.In Chapter 6, Hamiltonian-based adaptive integral sliding mode control is proposed to deal with the regulation problem of uncertain nonlinear systems, which may possess both parametric uncertainties and unknown nonlinear functions that may represent modeling errors and external disturbances. By utilizing the proposed method, the original nonlinear system is first converted into the port-controlled Hamiltonian (PCH) form by Interconnec-tion and Damping Assignment Passivity-based Control (IDA-PBC), and then a adaptive integral sliding mode control is designed to control the system. The proposed method com-bines immersion and invariance (I&I) adaptive scheme with integral sliding mode control (ISMC), which preserves the advantages of the two methods, namely asymptotic stability of adaptive control in the presence of parametric uncertainties, and robustness with inte-gral sliding mode control for both parametric uncertainties and unknown bounded nonlin-ear functions. The method is different from the approach combining backstepping adaptive scheme and sliding mode control in the parameter estimation law, which allows for pre-scribed dynamics to be assigned to the estimation error and is easier to tune. Finally, the passivity-based control and robust adaptive control of nonlinear systems are outlined, and the perspective of the future studies is also referred in the dissertation.