Application of feedback linearization to tracking and almost disturbance decoupling control of the AMIRA ball and beam system

This paper studies the tracking and almost disturbance decoupling problem of the nonlinear AMIRA ball and beam system based on the feedback linearization approach. The main contribution of this study is to construct a controller, under appropriate conditions, such that the resulting closed-loop system is valid for any initial condition and bounded tracking signal with the following characteristics: input-to-state stability with respect to disturbance inputs and almost disturbance decoupling. Two examples on the almost disturbance decoupling problem, which cannot be solved via Ref. 1, are proposed in this paper exploiting the fact that the tracking and the almost disturbance decoupling performances are easily achieved by our proposed approach

Feedback Linearization of Nonlinear Systems: Robustness and Adaptive Control.

Feedback linearization provides an effective means of designing nonlinear control systems. This method permits one to have an exactly equivalent linear system by using a coordinate transformation and state feedback. Once the nonlinear system is transformed to a linear system, one can proceed with well developed control technologies for linear systems. Feedback linearization is based on a model of the real system. If there is mismatch between the model and the real plant, feedback linearization does not yield an exactly linear system. The question of robustness then arises: will a controller based on the model be stable when applied to the real plant? We have developed a theoretical approach to analyze robustness of feedback linearization of SISO (Single-Input Single-Output) systems. We have also considered the dimensional reduction of a high dimensional model which is not a standard singularly perturbed system. Specifically we have found sufficient conditions for boundedness and convergence of the system trajectories when feedback linearization based on a nominal mathematical model is applied to an uncertain real plant which may have parametric and structural uncertainties as well as unmodeled dynamics. The developed approach does not require the restrictive conditions which are commonly used in the previously developed methods of robustness analysis. Furthermore, for parametric uncertainties a nonlinear adaptive control of feedback linearizable processes is proposed. The main feature of the proposed nonlinear adaptive control system is that it is relatively straightforward and simple. For this adaptive control system we have found sufficient conditions for stability of the output regulation and tracking of feedback linearizable systems using the second method of Lyapunov. Examples of the robustness analysis and the adaptive control for unstable chemical and biochemical reactors are given

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

Design of an Integral Suboptimal Second-Order Sliding Mode Controller for the Robust Motion Control of Robot Manipulators

The formulation of an integral suboptimal second-order sliding mode ((ISSOSM) control algorithm, oriented to solve motion control problems for robot manipulators, is presented in this paper. The proposed algorithm is designed so that the so-called reaching phase, normally present in the evolution of a system controlled via the sliding mode approach, is reduced to a minimum. This fact makes the algorithm more suitable to be applied to a real industrial robot, since it enhances its robustness, by extending it also to time intervals during which the classical sliding mode is not enforced. Moreover, since the algorithm generates second-order sliding modes, while the model of the controlled electromechanical system has a relative degree equal to one, the control action actually fed into the plant is continuous, which provides a positive chattering alleviation effect. The assessment of the proposal has been carried out by experimentally testing it on a COMAU SMART3-S2 anthropomorphic industrial robot manipulator. The satisfactory experimental results, also compared with those obtained with a standard proportional-derivative controller and with the original suboptimal algorithm, confirm that the new algorithm can actually be used in an industrial context

Control of non-minimum-phase nonlinear systems through constrained input-output linearization

Proceedings of the 2006 American Control Conference, pp. 4522-4527.This paper presents a novel control method that provides optimal output-regulation with guaranteed closedloop asymptotic stability within an assessable domain of attraction. The closed-loop stability is ensured by requiring state variables to satisfy a hard, second-order Lyapunov constraint. Whenever input-output linearization alone cannot ensure asymptotic closed-loop stability, the closed-loop system evolves while being at the hard constraint. Once the closed-loop system enters a state-space region in which input-output linearization can ensure asymptotic stability, the hard constraint becomes inactive. Consequently, the nonlinear control method is applicable to stable and unstable processes, whether non-minimum- or minimum-phase. The control method is implemented on a chemical reactor with multiple steady states, to show its application and performance

A final report of research on stochastic and adaptive systems

Final report."March 1982."Bibliography: p. 26-31.Air Force Office of Scientific Research Grant AFOSR-77-3281Bby Michael Athans, Sanjoy K. Mitter, Lena Valavani

Nonlinear system identification and control using dynamic multi-time scales neural networks

In this thesis, on-line identification algorithm and adaptive control design are proposed for nonlinear singularly perturbed systems which are represented by dynamic neural network model with multi-time scales. A novel on-line identification law for the Neural Network weights and linear part matrices of the model has been developed to minimize the identification errors. Based on the identification results, an adaptive controller is developed to achieve trajectory tracking. The Lyapunov synthesis method is used to conduct stability analysis for both identification algorithm and control design. To further enhance the stability and performance of the control system, an improved . dynamic neural network model is proposed by replacing all the output signals from the plant with the state variables of the neural network. Accordingly, the updating laws are modified with a dead-zone function to prevent parameter drifting. By combining feedback linearization with one of three classical control methods such as direct compensator, sliding mode controller or energy function compensation scheme, three different adaptive controllers have been proposed for trajectory tracking. New Lyapunov function analysis method is applied for the stability analysis of the improved identification algorithm and three control systems. Extensive simulation results are provided to support the effectiveness of the proposed identification algorithms and control systems for both dynamic NN models

Dynamics and control of flexible manipulators

Flexible link manipulators (FLM) are well-known for their light mass and small energy consumption compared to rigid link manipulators (RLM). These advantages of FLM are even of greater importance in applications where energy efficiency is crucial, such as in space applications. However, RLM are still preferred over FLM for industrial applications. This is due to the fact that the reliability and predictability of the performance of FLM are not yet as good as those of RLM. The major cause for these drawbacks is link flexibility, which not only makes the dynamic modeling of FLM very challenging, but also turns its end-effector trajectory tracking (EETT) into a complicated control problem. The major objectives of the research undertaken in this project were to develop a dynamic model for a FLM and model-based controllers for the EETT. Therefore, the dynamic model of FLM was first derived. This dynamic model was then used to develop the EETT controllers. A dynamic model of a FLM was derived by means of a novel method using the dynamic model of a single flexible link manipulator on a moving base (SFLMB). The computational efficiency of this method is among its novelties. To obtain the dynamic model, the Lagrange method was adopted. Derivation of the kinetic energy and the calculation of the corresponding derivatives, which are required in the Lagrange method, are complex for the FLM. The new method introduced in this thesis alleviated these complexities by calculating the kinetic energy and the required derivatives only for a SFLMB, which were much simpler than those of the FLM. To verify the derived dynamic model the simulation results for a two-link manipulator, with both links being flexible, were compared with those of full nonlinear finite element analysis. These comparisons showed sound agreement. A new controller for EETT of FLM, which used the singularly perturbed form of the dynamic model and the integral manifold concept, was developed. By using the integral manifold concept the links’ lateral deflections were approximately represented in terms of the rotations of the links and input torques. Therefore the end-effector displacement, which was composed of the rotations of the links and links’ lateral deflections, was expressed in terms of the rotations of the links and input torques. The input torques were then selected to reduce the EETT error. The originalities of this controller, which was based on the singularly perturbed form of the dynamic model of FLM, are: (1) it is easy and computationally efficient to implement, and (2) it does not require the time derivative of links’ lateral deflections, which are impractical to measure. The ease and computational efficiency of the new controller were due to the use of the several properties of the dynamic model of the FLM. This controller was first employed for the EETT of a single flexible link manipulator (SFLM) with a linear model. The novel controller was then extended for the EETT of a class of flexible link manipulators, which were composed of a chain of rigid links with only a flexible end-link (CRFE). Finally it was used for the EETT of a FLM with all links being flexible. The simulation results showed the effectiveness of the new controller. These simulations were conducted on a SFLM, a CRFE (with the first link being rigid and second link being flexible) and finally a two-link manipulator, with both links being flexible. Moreover, the feasibility of the new controller proposed in this thesis was verified by experimental studies carried out using the equipment available in the newly established Robotic Laboratory at the University of Saskatchewan. The experimental verifications were performed on a SFLM and a two-link manipulator, with first link being rigid and second link being flexible.Another new controller was also introduced in this thesis for the EETT of single flexible link manipulators with the linear dynamic model. This controller combined the feedforward torque, which was required to move the end-effector along the desired path, with a feedback controller. The novelty of this EETT controller was in developing a new method for the derivation of the feedforward torque. The feedforward torque was obtained by redefining the desired end-effector trajectory. For the end-effector trajectory redefinition, the summation of the stable exponential functions was used. Simulation studies showed the effectiveness of this new controller. Its feasibility was also proven by experimental verification carried out in the Robotic Laboratory at the University of Saskatchewan