A pointwise constrained version of the Liapunov convexity theorem for vectorial linear first-order control systems

We generalize the Liapunov convexity theorem's version for vectorial control systems driven by linear ODEs of first-order p = 1 , in any dimension d ∈ N , by including a pointwise state-constraint. More precisely, given a x ‾ ( ⋅ ) ∈ W p , 1 ( [ a , b ] , R d ) solving the convexified p-th order differential inclusion L p x ‾ ( t ) ∈ co { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e., consider the general problem consisting in finding bang-bang solutions (i.e. L p x ˆ ( t ) ∈ { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e.) under the same boundary-data, x ˆ ( k ) ( a ) = x ‾ ( k ) ( a ) & x ˆ ( k ) ( b ) = x ‾ ( k ) ( b ) ( k = 0 , 1 , … , p − 1 ); but restricted, moreover, by a pointwise state constraint of the type 〈 x ˆ ( t ) , ω 〉 ≤ 〈 x ‾ ( t ) , ω 〉 ∀ t ∈ [ a , b ] (e.g. ω = ( 1 , 0 , … , 0 ) yielding x ˆ 1 ( t ) ≤ x ‾ 1 ( t ) ). Previous results in the scalar d = 1 case were the pioneering Amar & Cellina paper (dealing with L p x ( ⋅ ) = x ′ ( ⋅ ) ), followed by Cerf & Mariconda results, who solved the general case of linear differential operators L p of order p ≥ 2 with C 0 ( [ a , b ] ) -coefficients. This paper is dedicated to: focus on the missing case p = 1 , i.e. using L p x ( ⋅ ) = x ′ ( ⋅ ) + A ( ⋅ ) x ( ⋅ ) ; generalize the dimension of x ( ⋅ ) , from the scalar case d = 1 to the vectorial d ∈ N case; weaken the coefficients, from continuous to integrable, so that A ( ⋅ ) now becomes a d × d -integrable matrix; and allow the directional vector ω to become a moving AC function ω ( ⋅ ) . Previous vectorial results had constant ω, no matrix (i.e. A ( ⋅ ) ≡ 0 ) and considered: constant control-vertices (Amar & Mariconda) and, more recently, integrable control-vertices (ourselves).

Modeling, control and field tests on an experimental irrigation canal

Irrigation canals are complex hydraulic systems difficult to control. Many models and control strategies have already been developed using linear control theory. In the present study, a PI controller is developed and implemented in a brand new prototype canal and its features evaluated experimentally. The base model relies on the linearized Saint-Venant equations which is compared with a reservoir model to check its accuracy. This technique will prove its capability and versatility in tuning properly a controller for this kind of systems.

Plataforma interactiva para edifícios inteligentes com controlo preditivo

Esta dissertação desenvolve uma plataforma de controlo interactiva para edifícios inteligentes através de um sistema SCADA (Supervisory Control And Data Acquisition). Este sistema SCADA integra diferentes tipos de informações provenientes das várias tecnologias presentes em edifícios modernos (controlo da ventilação, temperatura, iluminação, etc.). A estratégia de controlo desenvolvida implementa um controlador em cascada hierárquica onde os "loops" interiores são executados pelos PLC's locais (Programmable Logic Controller), e o "loop" exterior é gerido pelo sistema SCADA centralizado, que interage com a rede local de PLC's. Nesta dissertação é implementado um controlador preditivo na plataforma SCADA centralizada. São apresentados testes efectuados para o controlo da temperatura e luminosidade de salas com uma grande área. O controlador preditivo desenvolvido tenta optimizar a satisfação dos utilizadores, com base nas preferências introduzidas em várias interfaces distribuídas, sujeito às restrições de minimização do desperdício de energia. De forma a executar o controlador preditivo na plataforma SCADA foi desenvolvido um canal de comunicação para permitir a comunicação entre a aplicação SCADA e a aplicação MATLAB, onde o controlador preditivo é executado. ABSTRACT: This dissertation develops an operational control platform for intelligent buildings using a SCADA system (Supervisory Control And Data Acquisition). This SCADA system integrates different types of information coming from the several technologies present in modem buildings (control of ventilation, temperature, illumination, etc.). The developed control strategy implements a hierarchical cascade controller where inner loops are performed by local PLCs (Programmable Logic Controller), and the outer loop is managed by the centralized SCADA system, which interacts with the entire local PLC network. ln this dissertation a Predictive Controller is implemented at the centralized SCADA platform. Tests applied to the control of temperature and luminosity in huge­area rooms are presented. The developed Predictive Controller tries to optimize the satisfaction of user explicit preferences coming from several distributed user-interfaces, subjected to the constraints of energy waste minimization. ln order to run the Predictive Controller at the SCADA platform a communication channel was developed to allow communication between the SCADA application and the MATLAB application where the Predictive Controller runs.