C. Mañoso

IIR approximations to the fractional differentiator/integrator using Chebyshev polynomials theory

This paper deals with the use of Chebyshev polynomials theory to achieve accurate discrete-time approximations to the fractional-order differentiator/integrator in terms of IIR filters. These filters are obtained using the Chebyshev-Padé and the Rational Chebyshev approximations, two highly accurate numerical methods that can be computed with ease using available software. They are compared against other highly accurate approximations proposed in the literature. It is also shown how the frequency response of the fractional-order integrator approximations can be easily improved at low frequencies.

Fractional-Order Generalized Predictive Control: Formulation and some properties

This paper deals with the formal formulation of Fractional-Order Generalized Predictive Control, a generalization of GPC that makes use of fractional-order operators in its cost function. A thorough mathematical description of FGPC is given and the main similarities and differences between GPC and FGPC are highlighted.

Fractional-Order Generalized Predictive Control: Application for Low-Speed Control of Gasoline-Propelled Cars

There is an increasing interest in using fractional calculus applied to control theory generalizing classical control strategies as the PID controller and developing new ones with the intention of taking advantage of characteristics supplied by this mathematical tool for the controller definition. In this work, the fractional generalization of the successful and spread control strategy known as model predictive control is applied to drive autonomously a gasoline-propelled vehicle at low speeds. The vehicle is a Citroen C3 Pluriel that was modified to act over the throttle and brake pedals. Its highly nonlinear dynamics are an excellent test bed for applying beneficial characteristics of fractional predictive formulation to compensate unmodeled dynamics and external disturbances.

A survey of Fractional-Order Generalized Predictive Control

This work describes the fractional generalization of GPC, known as Fractional-Order Generalized Predictive Control (FGPC). Based on a real-order fractional cost function, FGPC combines valuable characteristics of fractional calculus and predictive control. The mathematical fundamentals of FGPC as well as a possible tuning algorithm are reviewed. We also present application examples where FGPC has proved to be a versatile and valuable control strategy to control real plants.

Low speed hybrid generalized predictive control of a gasoline-propelled car.

Low-speed driving in traffic jams causes significant pollution and wasted time for commuters. Additionally, from the passengers׳ standpoint, this is an uncomfortable, stressful and tedious scene that is suitable to be automated. The highly nonlinear dynamics of car engines at low-speed turn its automation in a complex problem that still remains as unsolved. Considering the hybrid nature of the vehicle longitudinal control at low-speed, constantly switching between throttle and brake pedal actions, hybrid control is a good candidate to solve this problem. This work presents the analytical formulation of a hybrid predictive controller for automated low-speed driving. It takes advantage of valuable characteristics supplied by predictive control strategies both for compensating un-modeled dynamics and for keeping passengers security and comfort analytically by means of the treatment of constraints. The proposed controller was implemented in a gas-propelled vehicle to experimentally validate the adopted solution. To this end, different scenarios were analyzed varying road layouts and vehicle speeds within a private test track. The production vehicle is a commercial Citroën C3 Pluriel which has been modified to automatically act over its throttle and brake pedals.

Robust stability analysis of GPC and CRHPC using the theory of extreme point results

Most stability results in model predictive control (MPC) are based on the assumption that the model describes the real plant perfectly. But in reality, the model is always different to the process. In this paper it is shown how the nominal stability results (mean level, constrained receding horizon predictive control, CRHPC, etc.) fail due to the presence of uncertainties, making it necessary to analyse the robust stability. This work provides tools which are easy to use and with low computational cost in order to study the robust stability of the systems under structured uncertainties. These tools are the extreme point results.

NEW DIRECT DISCRETIZATION OF THE FRACTIONAL-ORDER DIFFERENTIATOR/INTEGRATOR BY THE CHEBYSHEV-PADÉ APPROXIMATION

Abstract This paper deals with the use of the Chebyshev-Pade approximation (CP) in order to achieve accurate direct discrete-time approximations to the fractional-order differentiator/integrator. It is shown how, for a given order of the transfer functions, CP is much more accurate at low frequencies than the continued fraction expansion (CFE). Furthermore, CP can be more accurate than a CFE approximation of a higher order.

GPC with Structured Perturbations: The Influence of Prefiltering and Terminal Equality Constraints

It is widely accepted that in order to improve the robust stability of generalized predictive control (GPC), the use of a prefilter and terminal equality constraints plays a fundamental role. In this work it is shown with straightforward counterexamples how, in the presence of structured uncertainties, neither the prefilter nor the equality constraints guarantee that the robust stability is improved. In fact, it can even worsen compared with “conventional” GPC.

Robust Stability of GPC: The Influence of Prefiltering and Terminal Equality Constraints

Abstract In this work it will be considered the model-process mismatch of a GPC controller represented by structured perturbations. In this framework, it will be analysed the influence of the polynomial T and the effect of the consideration of the equality constraints on the system stability.

F.M.S.C. An Adaptive Sampling System

Abstract The aim of this paper is to present a new sampling system of those named adaptives. This system presents at its main characteristic two grades of freedom for its configuration and immunity to the noises present in the system.