Patrick Lanusse

Robust Control of LTI Square Mimo Plants Using Two Crone Control Design Approaches

Abstract A multi-SISO or a MIMO design approach is proposed for the robust control of uncertain LTI square MIMO plants, depending on the extent of the plant’s diagonal nature. For the multi-SISO approach, new multivariable frequency uncertainty domains are defined using the Gershgorin and the small gains theorems. These domains are based both on the structured frequency uncertainty domains related to the diagonal elements of the plant transfer matrix, and on the Gershgorin circles related to the corresponding column elements. Each element of the diagonal controller can be thus designed independently of the others using the SISO Crone design method. The totally MIMO approach is based on the optimization of an open-loop diagonal transfer matrix to minimize the stability margin variations of the perturbed diagonal elements of the closed-loop transfer matrix.

CRONE control system design toolbox for the control engineering community: tutorial and case study

Fractional-order differentiation offers new degrees of freedom that simplify the design of high-performance dynamic controllers. The CRONE control system design (CSD) methodology proposes the design of robust controllers by using fractional-order operators. A software toolbox has been developed based on this methodology and is freely available for the international scientific and industrial communities. This paper presents both the CRONE CSD methodology and its implementation using the toolbox. The design of two robust controllers for irrigation canals shows how to use the toolbox.

Fractional Control-System Design for a Hydraulic Actuator

Abstract The robust control of a hydraulic actuator that is part of an evaluation system for mechanical structures is presented. The dynamic model of the system, defmed from the common laws of physics, is nonlinear. An initial input-output linearization is achieved for the nominal plant, and then a set of tangent linearized models of the input-output linearized system is computed for perturbed plants. Then the robust control-system design approach is based on Crone control.

Extension of PID to fractional orders controllers: a frequency-domain tutorial presentation

Abstract This paper presents how common PID controllers have been generalized to fractional order PID controllers and how the additional tuning parameters can be used to meet more requirements. It is shown that the first generation CRONE control-system design methodology is able to provide robust fractional order PID for uncertain gain perturbed plants.

Bode optimal loop shaping with CRONE compensators

Ideal Bode Characteristics give a classical answer to optimal loop design for LTI feedback control systems, in the frequency domain. This work recovers 4-parameters and 8-parameters Bode optimal loop gains, providing a useful and simple theoretical reference for the best possible loop shaping from a practical point of view. The main result of the paper is to use CRONE compensators to make a good approximation to the Bode optimal loop. For that purpose, a special loop structure based on second and third generation CRONE compensators is used. As a result, simple design relationships will be obtained for tuning the proposed CRONE compensator.

Fractional Order PID and First Generation CRONE Control System Design

This chapter presents the design of controllers for Single Input/Single Output (SISO) systems, that is to say only one signal to control only one measured output. The fractional order controller is presented as a generalization of the common PID controller. Then, it is shown how the first generation of the CRONE methodology is able to design robust controllers for a class of gain-like perturbed systems.

Additional optimization parameter for a simplified design of third generation CRONE controllers

Although the CRONE Control System Design toolbox for Matlab makes it possible to optimize the parameters of robust controllers, it appears that the performance of the optimized controllers depends on the users experience. New optimization criteria facilitating the CRONE design of controllers that are as robust and as efficient as possible have therefore been proposed. This paper proposes to optimize an additional design parameter that simplifies the choice of the required nominal model of the plant. A high dynamic Engine-Dynamometer test-bed MIMO control problem is used to show the efficiency of this modified third generation CRONE design.

State space modeling of fractional systems using block pulse functions

Abstract In this paper, an algebraic method for the approximation of fractional commensurable state space models with classical reduced one is presented. The block pulse functions and their generalized operational matrices fitted to the Rieamann-Liouville definition of fractional differentiation are used to transform the non integer differential state equation into a matrix problem which can be solved numerically with the nonlinear optimization techniques in Matlab. A discussion of the resolution is led through the variation of parameters of the considered orthogonal basis. Examples and simulations are exhibited to prove the validity of the proposed developments.

Discrete-time robust control with an anticipative action for preview systems

A discrete-time robust controller design method is proposed for optimal tracking of future references in preview systems. In the context of preview systems, it is supposed that future values of the reference signal are available a number of time steps ahead. The objective is to design a control algorithm that minimizes a quadratic error between the reference and the output of the system and at the same time achieves a good level of the control signal. The proposed solution combines a robust feedback controller with a feedforward anticipative filter. The feedback controllers purpose is to assure robust-ness of the closed-loop system to model uncertainties. Any robust control methodology can be used (such as µ-synthesis, QFT, or CRONE control). The focus of this paper will be on the design of the feedforward action in order to introduce the anticipative effect with respect to known future values of the reference signal without hindering the robustness achieved through the feedback controller. As such, the model uncertainties are taken into account also in the design of the feedforward anticipative filter. The proposed solution is validated in simulation and on an experimental water tank level control system.

Gen eralized predictive controller performances in an anticipative context

An existing method for tuning a generalized predictive control (GPC) law using desired closed-loop transfer functions is applied to preview systems. In the context of preview systems, it is supposed that future values of the reference signal are available a number of time steps ahead. This information can be used to reduce the error between the reference signal and the measured output by adding an anticipative action to the controller. This paper evaluates the performances of GPC in this context. Although the design method used provides good robust performances in an non-anticipative context, it is shown that unwanted behaviour can occur when anticipation is introduced. First the performances and robustness of the obtained GPC controller are validated in an non-anticipative context. Then, it is shown that an equivalent feedforward filter appears when anticipation is added, which can have bad effects on the system performances. An academic simulated example is used to validate our conclusions.