Gerasimos G. Rigatos

Nonlinear Control and Filtering Using Differential Flatness Approaches

This monograph presents recent advances in differential flatness theory and analyzes its use for nonlinear control and estimation. It shows how differential flatness theory can provide solutions to complicated control problems, such as those appearing in highly nonlinear multivariable systems and distributed-parameter systems. Furthermore, it shows that differential flatness theory makes it possible to perform filtering and state estimation for a wide class of nonlinear dynamical systems and provides several descriptive test cases. The book focuses on the design of nonlinear adaptive controllers and nonlinear filters, using exact linearization based on differential flatness theory. The adaptive controllers obtained can be applied to a wide class of nonlinear systems with unknown dynamics, and assure reliable functioning of the control loop under uncertainty and varying operating conditions. The filters obtained outperform other nonlinear filters in terms of accuracy of estimation and computation speed. The book presents a series of application examples to confirm the efficiency of the proposed nonlinear filtering and adaptive control schemes for various electromechanical systems. These include: industrial robots; mobile robots and autonomous vehicles; electric power generation; electric motors and actuators; power electronics; internal combustion engines; distributed-parameter systems; and communication systems. Differential Flatness Approaches to Nonlinear Control and Filtering will be a useful reference for academic researchers studying advanced problems in nonlinear control and nonlinear dynamics, and for engineers working on control applications in electromechanical systems.

Nonlinear Kalman Filtering Based on Differential Flatness Theory

This chapter analyzes a new filtering method for nonlinear dynamical systems which is based on differential flatness theory and is known as Derivative-free nonlinear Kalman Filter. First, the filtering method is applied to lumped dynamical systems, that is systems which are described by ordinary differential equations. Moreover, the problem of distributed nonlinear filtering is solved, that is the problem of fusion of the outcome of distributed local filtering procedures (local nonlinear Kalman Filters) into one global estimate that approximates the system’s state vector with improved accuracy.

Differential Flatness Theory and Flatness-Based Control

The chapter analyzes the concept of differential flatness theory-based control, both for lumped dynamical systems (that is for systems which are described by ordinary differential equations) and for distributed parameter systems (that is for systems which are described by partial differential equations).

Nonlinear Dynamical Systems and Global Linearizing Control Methods

This chapter overviews the theory of nonlinear dynamical systems. Next, it outlines differential geometry and Lie algebra-based control as the predecessor of differential flatness theory-based control.

Differential Flatness Theory and Industrial Robotics

This chapter analyzes the use of nonlinear control and filtering methods to the solution of industrial robotics problems, such as the adaptive control of MIMO robotic manipulators without prior knowledge of the robot’s dynamical model, adaptive control of underactuated robotic manipulators, that is robots having less actuators than their degrees of freedom, observer-based adaptive control of MIMO robotic manipulators in which uncertainty is not related only to the unknown dynamic model of the robot but also comes from the inability to measure all elements of the robot’s state vector, and Kalman Filter-based control of MIMO robotic manipulators. Finally, differential flatness theory is proposed for developing a control scheme over a communication network that is characterized by transmission delays or losses in the transmitted information.

Differential Flatness Theory and Electric Power Generation

This chapter analyzes the use of differential flatness theory-based methods for nonlinear filtering and nonlinear control for the problem of electric power generation. Power generators of various types are considered such as DFIGs and PMSGs, while the mode of operation of these generators can be either stand-alone (single machine infinite bus model), or the generators can function as part of the power grid and can be interacting through their connection lines. The chapter shows how differential flatness theory can provide efficient solutions to the following problems: (i) adaptive control of distributed power generators, (ii) state estimation-based control of PMSG, (iii) state estimation-based control of DFIG, (iv) state estimation-based control and synchronization of distributed power generators of PMSG type.

Nonlinear Adaptive Control Based on Differential Flatness Theory

This chapter analyzes differential flatness theory-based adaptive fuzzy control for complex nonlinear dynamical systems. It is shown that all single-input single-output dynamical systems admit static feedback linearization and can be transformed to a linear canonical (Brunovsky) form. For the latter description the design of a flatness-based adaptive fuzzy controller becomes possible. Moreover, it is shown that multi-input multi-output dynamical systems which admit dynamic feedback linearization can be transformed to a decoupled and linear canonical form for which the design of the flatness-based adaptive fuzzy controller is a straightforward procedure. Moreover, for nonlinear systems that admit dynamic feedback linearization the transformation to a decoupled and linear canonical form is also possible in several cases. For such systems, one can follow again a systematic procedure for the design of the flatness-based adaptive fuzzy controller.

Differential Flatness Theory for Electric Motors and Actuators

The chapter examines and analyzes the use of differential flatness theory-based nonlinear filtering and control methods, for solving nontrivial problems associated with electric motors and actuators and with motion transmission systems. To this end, differential flatness theory is used for adaptive control of the DC motor, for adaptive control of the induction motor, for state estimation-based control of the DC motor, and finally for state estimation-based control of asynchronous electric motors.

Differential Flatness Theory in the Background of Other Control Methods

The chapter demonstrates that differential flatness theory is in the background of other control methods, such as backstepping control and optimal control. First, the chapter shows that differential flatness theory is in the background of backstepping control. The method assumes that the system is already found or can be transformed to the so-called triangular form. The controller design proceeds by showing that each row of the state-space model of the nonlinear system stands for a differentially flat system, where the flat output is chosen to be the associated state variable. Next, for each subsystem which is linked with a row of the state-space model a virtual control input is computed, that can invert the subsystem’s dynamics and can eliminate the subsystem’s tracking error. From the last row of the state-space description, the control input that is actually applied to the nonlinear system is found. This control input contains recursively all virtual control inputs which were computed for the individual subsystems associated with the previous rows of the state-space equation. Thus, by tracing the rows of the state-space model backwards, at each iteration of the control algorithm, one can finally obtain the control input that should be applied to the nonlinear system so as to assure that all its state vector elements will converge to the desirable setpoints. The proposed flatness-based control method can solve efficiently several nonlinear control problems. Indicative evaluation results are presented in the manuscript in the form of simulation experiments. Next, the chapter shows that differential flatness theory is in the background of optimal control. Finally, the aforementioned implementation of flatness-based control in cascading loops is used to solve the problem of boundary control of distributed parameter systems, that is control of nonlinear PDEs using as control inputs their boundary conditions.

Differential Flatness Theory in Mobile Robotics and Autonomous Vehicles

The chapter analyzes the use of nonlinear filtering and control methods based on differential flatness theory in steering control, localization and autonomous navigation of land vehicles, unmanned surface vessels and unmanned aerial vehicles. It is shown that through the application of differential flatness theory one can obtain solution for the following non-trivial problems: state estimation-based control of autonomous vehicles, state estimation-based control of cooperating vehicles, distributed fault diagnosis for autonomous vehicles, velocity control of 4-wheel autonomous vehicles under model uncertainties and external disturbances, active control of vehicle suspensions, state estimation-based control unmanned aerial vehicles of the quadrotor type, state estimation-based control of unmanned surface vessels of the hovercraft type.