Generalized Proportional Integral Research Articles

Robust input–output sliding mode control of the buck converter

An input–output based feedback controller is proposed for the sliding mode control of a large class of switched systems. The method avoids state measurements, or the use of observers, and it extends the sliding mode control design methodology to input–output descriptions of the plant. The approach regards the average Generalized Proportional Integral (GPI) output feedback controller as a guide for defining the switched implementation of the average sliding mode features via a Sigma–Delta modulation strategy. The considerations are circumscribed to the class of differentially flat systems. Experimental results are presented for a trajectory tracking problem on a DC-to-DC switched power supply of the “buck” type with unknown loads subject to abrupt variations.

GPI observer-based non-linear integral sliding mode control and synchronisation of uncertain chaotic system

An output feedback control scheme for a class of triangular chaotic systems in the presence of system uncertainties, unknown disturbances, parameter perturbations and measurement noises is proposed in this paper. A high gain general proportional integral (GPI) observer is used for the accurate linear estimation of the error states, non-linear endogenous and exogenous disturbances from the noisy output signals of the system, and then a non-linear integral sliding mode controller with active disturbance cancellation is proposed for the tracking control and synchronisation of the chaotic systems. The uncertain Gesino chaotic system is used to validate the proposed control method and the convincing numerical results illustrate the proposed method is effective to deal with various system uncertainties only based on the utilisation of the input-output data.

Position control of very lightweight single-link flexible arms with large payload variations by using disturbance observers

In this article, a robust control scheme for trajectory tracking of very lightweight single-link flexible arms is discussed. Since the payload is one of the most variable parameters in a manipulator, the control is designed to achieve an accurate tracking of the desired tip trajectory for any value of the robot tip mass, or even for a tip mass changing during the maneuver. The proposed controller also guarantees stability for small uncertainties in parameters such as stiffness or motor friction. In addition, the effect of spillover on the performance of the controlled system is analyzed, and it is proven that stability and a good performance are preserved independently from the non-modeled high-order dynamics. The control scheme is based on a two nested loops structure. Each of these loops implements a Generalized Proportional Integral (GPI) controller. Moreover, the outer loop includes a disturbance compensation term based on a disturbance observer, which achieves the required insensitivity to payload changes. The theoretical analysis is supported by an extensive set of numerical simulations which shows controlled system response when variations in the robot payload, or dynamics neglected in the controller design, are considered. Finally, some experiments have been carried out in order to test the performance of the tip trajectory tracking of the proposed control system.

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.

Nonlinear Control for Magnetic Levitation Systems Based on Fast Online Algebraic Identification of the Input Gain

The control of the popular magnetic levitation system is addressed from the viewpoint of adaptive control based on fast, on line, algebraic parameter estimation, exact linearization and generalized proportional integral (GPI) output feedback control. The GPI controller guarantees an asymptotically exponentially stable behavior of the controlled ball position and the possibilities of carrying out rest-to-rest trajectory tracking tasks. The online algebraic parameter estimation approach estimates, quite accurately, and in a very short period of time, the unknown parameter or the magnetic levitation system. The proposed adaptive controller is actually implemented on a laboratory prototype with excellent experimental results for, both, stabilization and trajectory tracking tasks.

Trajectory tracking for the magnetic ball levitation system via exact feedforward linearisation and GPI control

The output feedback control of the popular magnetic ball levitation system is addressed from a suitable combination of several complementary viewpoints. We use: first, recent developments on exact feedforward linearisation controllers for nonlinear flat systems to substantially reduce the linear feedback controller efforts through pre-compensation. Second, an on-line ball velocity estimation strategy is proposed by using a model-based integral reconstructor, which is a linear combination of iterated integrals of the input and the output of the system, thus avoiding the use of traditional observers or noisy derivative estimations. Finally, we use a generalised proportional integral (GPI) controller which compensates the errors in the integral reconstructor and further bestows the enhanced robustness on the closed-loop system via output tracking error iterated integration feedback. This methodology only requires the measurements of the position of the levitated ball and of the control input voltage. The proposed feedback regulation scheme is shown to locally guarantee an asymptotically exponentially stable behaviour of the controlled ball position and, definitely, allows for the possibilities of safely carrying out the rest-to-rest trajectory tracking tasks on the ball position. The proposed output feedback controller is actually implemented on a laboratory prototype with excellent experimental results for, both, stabilisation and trajectory tracking tasks.

Generalised proportional integral torque control for single-link flexible manipulators

In this study, a generalised proportional integral (GPI) output feedback control scheme is proposed to control the torque of a single-link flexible arm for free and constrained motion. The control is based on the properties of differential flat systems. The control is also found to be robust with respect to the motor static friction. The only variable to measure is the torque in the hub by means of only one sensor, which in this case, is constituted by a pair of strain gauges. An hybrid control law is presented to control the manipulator in collision with an object (constrained motion) and when it can freely move (free motion) commanded by an on-line impact detection algorithm. Experiments are presented to verify the goodness of the proposed control law.

SYNCHRONIZATION OF CHAOTIC OSCILLATORS BY MEANS OF GENERALIZED PROPORTIONAL INTEGRAL OBSERVERS

The problem of synchronization of chaotic oscillators, using state observers, is handled through the use of a simplified perturbed linear integration model of the chaotic system output dynamics. The linear simplified model of the chaotic system does not entitle approximate linearizations, nor state coordinate transformations, but, simply, a pure linear integration model with additive unknown but bounded perturbation inputs lumping all the output dynamics nonlinearities. An extended linear state observer (here addressed as Generalized Proportional Integral (GPI) observer) is proposed for the accurate estimation of the phase variables and the perturbation input of the nonlinear output dynamics. The effectiveness of the approach is tested in the synchronization of two study cases: The Genesio–Tesi chaotic system and the Rossler oscillator. As an application of the estimation process, a coding–decoding process involving encrypted messages, in transmitted phase variables, is implemented using a Rossler chaotic system.

Adaptive Controller for Single-Link Flexible Manipulators Based on Algebraic Identification and Generalized Proportional Integral Control

In this paper, we propose a fast online closed-loop identification method combined with an output-feedback controller of the generalized proportional integral (GPI) type for the control of an uncertain flexible robotic arm with unknown mass at the tip, including a Coulomb friction term in the motor dynamics. A fast nonasymptotic algebraic identification method developed in continuous time is used to identify the unknown system parameter and update the designed certainty equivalence GPI controller. In order to verify this method, several informative simulations and experiments are shown.

Sigma-Delta sliding mode control of buck power converters using the Delta operator approach.

In this article, an output feedback discrete time sigma delta-modulation based sliding mode controller is proposed for the stabilization and trajectory tracking of output voltages in a Buck power converter model. The average dynamic output feedback control scheme is realized by a means of a generalized proportional integral (GPI) controller.

ON THE GENERALIZED-PROPORTIONAL-INTEGRAL MULTILEVEL SIGMA-DELTA SLIDING MODE CONTROL OF A “BUCK” INVERTER

This article considers the output feedback controller design for a multilevel dc-to-dc “buck” power converter structure, used as an inverter, in an arbitrary bounded output voltage reference signal trajectory tracking task. The multilevel output feedback controller design is accomplished via a suitable combination of the Generalized Proportional Integral (GPI) feedback controller design technique along with a multilevel generalization of the sliding mode based Sigma-Delta (SM – Δ) modulator. Simulations depict the feasibility of the proposed output feedback controller scheme.

Design of Generalized PI Observers for Descriptor Linear Systems

The new type of generalized proportional integral (GPI) observers for descriptor linear systems is proposed. Based on a complete parametric solution to a type of generalized Sylvester matrix equations, a parametric approach for the design of the GPI observers is established. The proposed approach gives parameterizations of all the observer gain matrices in terms of some free parameters which represent the degrees of design freedom. Moreover, the parametric expression of the corresponding finite left eigenvector matrix of the observer system is also presented. The proposed approach, which guarantees the regularity of the observer system, realizes the elimination of impulsive behaviors of the observer system. The proposed design method offers all the degrees of design freedom which can be further utilized to achieve additional specifications and performances. An illustrative example shows the effect of the proposed approach

ON THE GPI-PWM CONTROL OF A CLASS OF SWITCHED FRACTIONAL ORDER SYSTEMS

The control of a special class of Single Input Single Output (SISO) switched fractional order systems (SFOS), known as the relaxation-oscillation equation, is addressed from the viewpoints of the Generalized Proportional Integral (GPI) feedback control approach in combination with a Pulse-Width-Modulation (PWM) based Σ – Δ modulator implementation of an average model based designed feedback controller. An illustrative simulation example is presented.

Sliding Mode-Delta Modulation GPI Control of a DC Motor through a Buck Converter

In this article, one Generalized Proportional Integral (GPI) feedback control scheme is proposed for a smooth “ starter” for a DC motor based on a switch controlled DC-to-DC power converter of the “buck” type. The dynamic feedback controller is based on a suitable combination of GPI based control, flatness and a Σ – Δ modulator implementation of the average designed controller. The scheme proposes a direct regulation of the motor shaft speed. As a consequence, the proposed feedback controller, which are not based on asymptotic observers nor calculations based on samplings, use only an optical velocity sensor. The effectiveness of the proposed controller was verified by computer simulations using the P-Spice circuit simulation program.

CONTROL OF THE CHUA'S SYSTEM BASED ON A DIFFERENTIAL FLATNESS APPROACH

In this paper, we present a flatness based control approach for the stabilization and tracking problem, for the well-known Chua chaotic circuit, that includes an additional input. We introduce two feedback controller design options for the set-point stabilization and the trajectory tracking problem: a direct pole placement approach, and Generalized Proportional Integral (GPI) approach based only on measured inputs and outputs.

Regulation and tracking for the average boost converter circuit: A generalized proportional integral approach

In this article we examine, in the context of constant equilibrium stabilization and equilibrium-to-equilibrium reference trajectory tracking, the generalized proportional integral (GPI) control of a non-linear average model of a DC-to-DC power converter of the 'Boost' type. We particularly emphasize the links between differential flatness and GPI control in the state feedback controllers design and synthesis tasks, respectively. The design approach relies on the converter's tangent linearization models for each case. The performance of the feedback controlled non-linear system is evaluated by means of digital computer simulations including large, unmodelled, load parameter variations.