Non-linear discrete-time observer design by sliding mode

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University, 09/02/2007.Research into observer design for non-linear discrete-time systems has produced many design methods. There is no general design method however and that provides the motivation to search for a new simple and realizable design method. In this thesis, an observer for non-linear discrete-time systems is designed using the sliding mode technique. The equation of the observer error is split into two parts; the first part being a linearized model of the system and the second part an uncertain vector. The sliding mode technique is introduced to eliminate the uncertainty caused by the uncertain vector in the observer error equation. By choosing the sliding surface and the boundary layer, the observer error is attracted to the sliding surface and stays within the sliding manifold. Therefore, the observer error converges to zero. The proposed technique is applied to two cases of observers for nonlinear discrete-time systems. The second case is chosen to be a particular practical system, namely the non-linear discrete-time ball and beam system. The simulations show that the sliding mode technique guarantees the convergence of the observer error for both systems

A Linear Active Disturbance Rejection Control for a Ball and Rigid Triangle System

This paper proposes an application of linear flatness control along with active disturbance rejection control (ADRC) for the local stabilization and trajectory tracking problems in the underactuated ball and rigid triangle system. To this end, an observer-based linear controller of the ADRC type is designed based on the flat tangent linearization of the system around its corresponding unstable equilibrium rest position. It was accomplished through two decoupled linear extended observers and a single linear output feedback controller, with disturbance cancelation features. The controller guarantees locally exponentially asymptotic stability for the stabilization problem and practical local stability in the solution of the tracking error. An advantage of combining the flatness and the ADRC methods is that it possible to perform online estimates and cancels the undesirable effects of the higher-order nonlinearities discarded by the linearization approximation. Simulation indicates that the proposed controller behaves remarkably well, having an acceptable domain of attraction

Robust trajectory tracking for incrementally passive nonlinear systems

In this paper, we study the robust trajectory tracking problem for a class of nonlinear systems with incremental passivity. The velocity of the desired trajectory and parts of the model information are unknown apart from boundedness assumptions. A velocity observer based method and a sliding mode controller are proposed while the asymptotic tracking result is guaranteed by a zero-state detectability condition for both cases. Unlike previous results, the studied systems are not necessarily feedback linearizable nor in a strict feedback form. The ball and beam system is utilized to illustrate the implementation of the proposed tracking control laws. (C) 2019 Elsevier Ltd. All rights reserved

Modeling and Control of the Ball and Beam Process

One of the most difficult problems that an engineer who works with modeling deals with, is the question about how to translate a physical phenomenon into a set of equations. It is usually difficult to capture all dynamics and phenomena, so one usually strives for a set of equations that describes the physical system approximately and adequately with the accuracy for the purpose. In our case, we model the dynamics relevant for control design. The topic of this thesis was to do an in-depth study of the Ball and Beam process. Two different experimental implementation of the Ball and Beam process have been considered, both available at the course lab at the Department of Automatic Control, Lund. The first step consisted of deriving the equations of motion, that is, to do the mathematical modeling of the process. In order to implement this model Modelica has been used. Modelica, which is a powerful language for modeling of physical systems, uses the tool Dymola. Another model was designed also with Modelica but with the help of the extension of the multi body library, which uses a methodology based on object orientation and symbolic manipulation of equations. With this last model it was possible to visualize an animation in real time 3D. The following step of the project was to do control design for the different models. The obtained simulations were shown in Dymola and Simulink. Finally experiments on the real process were developed, based on vision feedback

Observation and control of a ball on a tilting

The ball and plate system is a nonlinear MIMO system that has interesting characteristics which are also present in aerospace and industrial systems, such as: instability, subactuation, nonlinearities such as friction, backlash, and delays in the measurements. In this work, the modeling of the system is based on the Lagrange approach. Then it is represented in the state-space form with plate accelerations as inputs to the system. These have a similar effect as applying torques. In addition, the use of an internal loop of the servo system is considered. From the obtained model, we proceed to carry out the analysis of controllability and observability resulting in that the system is globally weak observable and locally controllable in the operating range. Then, the Jacobi linearization is performed to use the linearized model in the design of linear controllers for stabilization. On the other hand, analyzing the internal dynamics of the ball and plate system turns out to be a non-minimum phase system, which makes it difficult to design the tracking control using the exact model. This is the reason why we proceed to make approximations. Using the approximate model, nonlinear controllers are designed for tracking using different approaches as: feedback linearization for tracking with and without integral action, backstepping and sliding mode. In addition, linear and nonlinear observers are designed to provide full state information to the controller. Simulation tests are performed comparing the different control and observation approaches. Moreover, the effect of the delay in the measurement is analyzed, where it is seen that the greater the frequency of the reference signal the more the error is increased. Then, adding the Smith predictor compensates the delay and reduces the tracking error. Finally, tests performed with the real system. The system was successfully controlled for stabilization and tracking using the designed controllers. However, it is noticed that the effect of the friction, the spring oscillation and other non-modeled characteristics significantly affect the performance of the control.Tesi