Eric William Zurita-Bustamante

A Comparison Between the GPI and PID Controllers for the Stabilization of a DC–DC “Buck” Converter: A Field Programmable Gate Array Implementation

This paper presents a comparison between two stabilizing average output feedback controllers implemented on a field programmable gate array (FPGA) facility. A generalized proportional integral (GPI) controller and a proportional integral derivative (PID) controller are implemented using an FPGA, and their respective performances are duly compared. The GPI controller is found to present a better dynamic response than the PID controller in terms of the settling time while exhibiting a greater degree of robustness regarding disturbance rejection represented by severe changes in static and dynamic loads. The average controllers and their corresponding pulsewidth modulation actuators are implemented using a Spartan 3E1600 FPGA.

Sliding Mode Control Devoid of State Measurements

An input-output approach is presented for sliding mode control of linear and nonlinear switched systems of the differentially flat type. Two sliding mode control design options are presented: (1) a Delta-Sigma modulation implementation of a robust continuous output feedback controller design, such as the Active Disturbance Rejection Control scheme and (2) An Integral reconstructor-based approach, involving a suitable linear combinations of iterated integrals of the available system input and the measured output of the system. These reconstructors provide the synthesis of a suitably compensated stabilizing sliding surface coordinate function for stabilization or trajectory tracking problems. The relation of the second approach with Delta-Sigma modulation is also established. Two experimental case studies are presented including nonlinear mechanical plants: An under-actuated convey crane and a DC-motor-Single-link manipulator system.

On the sensorless rotor position control of the permanent magnet synchronous motor: An active disturbance rejection approach

This paper presents a rotor position sensorless control for the permanent magnet synchronous motor (PMSM), based on an active disturbance rejection control technique and an integral reconstructor for the rotor position estimation. The control law uses a generalized proportional integral observer (GPIO) for estimating and compensating the unknown uncertainties which the PMSM system is subject. The control law is designed in the a-p coordinate as it is just like the integral reconstructor of the PMSM rotor position. The validity and robustness of the proposed scheme is verified via realistic co-simulations using Matlab/Simulink and PSIM packages.

On a linear input–output approach for the control of nonlinear flat systems

ABSTRACT The need for observers, or other means of state- or phase variables-on-line computations, is revisited from the perspective of structural integral reconstructors. The problem addressed is the regulation, via simplified pure integration dynamics, of the large class of static, or dynamic, feedback linearisable systems (i.e. differentially flat systems), subject to additive exogenous disturbances and where nonlinearities are purposefully neglected. Integral reconstructors of the simplified input-to-flat output dynamics, directly lead to generalised proportional integral controllers, which are also shown to be equivalent to classical compensation networks. Their robust version, addressed here as flat filters, are found to be quite useful in the approximate (i.e. practical) control of perturbed differentially flat systems. The controller design is based on their simplified, perturbed, and pure integration dynamics. Flat filters evade for the need of nonlinear asymptotic observers and other, on-line, explicit output time derivatives computations. Simulation and challenging experimental examples are provided to validate this linear approach to the control of nonlinear flat systems.

The Challenging Case of Underactuated Systems

Underactuated systems, which are nondifferentially flat, are treated in the context of trajectory tracking tasks to illustrate the effectiveness of ADRC in the control of nonlinear systems via their controllable tangent linearizations around a given equilibrium point. The trajectories may take the operating point significantly far away from the linearization point, and the neglected nonlinearities may be substantially excited by the features of the desired reference trajectory. In spite of these classical obstacles to tangent linearization-based control, the ADRC scheme yields a quite robust and precise closed-loop performance.

Extensions of ADRC

This chapter presents some extensions of the ADRC control method to important classes of systems that are of common interest in both engineering-oriented applications and research trends found in the literature. The chapter starts with the structural state reconstruction of MIMO systems, i.e., it demonstrates that in linear multivariable systems, the state can be expressed in terms of linear combinations of iterated integrals of inputs and outputs (see [1] for details).

Generalities of ADRC

This chapter exposes the Active Disturbance Rejection Control methodology in its most general form within the realm of nonlinear dynamic systems. The need for disturbance estimation–disturbance cancellation, or, alteratively, direct disturbance cancellation without observers is portrayed as part of a fundamental procedure to grant robustness on a linear controller performance. The controller is based on a substantially simplified model of the system. In this regard, flatness plays a crucial role since the simplified system model adopts the form of a set of controlled pure integration chains, with additive bounded disturbances.

Chapter 5 – Case Studies

In this chapter, some miscellaneous applications of ADRC control are presented. The topics range from robotic systems: nonlinear manipulators of one and two degrees of freedom, controlled by nonlinear motors, to the control of Thomsons jumping ring. The idea is to present a wide range of applicability of ADRC schemes and the underlying ease of actual implementation in laboratory rigs. Some examples are dealt with using Flat Filtering Controllers, a dual alternative to observer-based ADRC controllers.

Merging Flatness, GPI Observation, and GPI Control with ADRC

In this chapter we develop two techniques for the problem of Active Disturbance Rejection Control of differentially flat systems, the GPI extended state observer and the flat filtering approach.

FPGA Implementation of PID Controller for the Stabilization of a DC-DC “Buck” Converter

Actually the development of control systems in embedded systems presents a great advantage in terms of easy design, immunity to analog variations, possibility and implement complex control laws and design a short time (Mingyao Ma et al., 2010). One of the devices that allows embedded systems arrangements are field-programmable gate array (FPGA). Several advantages of using FPGAs in industrial applications can be seen in (Joost & Salomon, 2005).