An integrated control strategy to solve the disturbance decoupling problem for max-plus linear systems with applications to a high throughput screening system

International audienceThis paper presents the new investigations on the disturbance decoupling problem (DDP) for the geometric control of max-plus linear systems. The classical DDP concept in the geometric control theory means that the controlled outputs will not be changed by any disturbances. In practical manufacturing systems, solving for the DDP would require further delays on the output parts than the existing delays caused by the system breakdown. The new proposed modified disturbance decoupling problem (MDDP) in this paper ensures that the controlled output signals will not be delayed more than the existing delays caused by the disturbances in order to achieve the just-in-time optimal control. Furthermore, this paper presents the integration of output feedback and open-loop control strategies to solve for the MDDP, as well as for the DDP. If these controls can only solve for the MDDP, but not for the DDP, an evaluation principle is established to compare the distance between two output signals generated by controls solving for the MDDP and DDP, respectively. This distance can be interpreted as the number of tokens or firings that are needed in order for the controls to solve for the DDP. Moreover, another alternative approach is finding a new disturbance mapping in order to guarantee the solvability of the DDP by the same optimal control for the MDDP. The main results of this paper are illustrated by using a timed event graph model of a high throughput screening system in drug discovery.</p

Multivariable PID control by decoupling

This paper presents a new methodology to design multivariable PID controllers based on decoupling control. The method is presented for general n×n processes. In the design procedure, an ideal decoupling control with integral action is designed to minimize interactions. It depends on the desired open loop processes that are specified according to realizability conditions and desired closed loop performance specifications. These realizability conditions are stated and three common cases to define the open loop processes are studied and proposed. Then, controller elements are approximated to PID structure. From a practical point of view, the windup problem is also considered and a new anti-windup scheme for multivariable PID controller is proposed. Comparisons with other works demonstrate the effectiveness of the methodology through the use of several simulation examples and an experimental lab process

Learning-Based Controller Design with Application to a Chiller Process

In this thesis, we present and study a few approaches for constructing controllers for uncertain systems, using a combination of classical control theory and modern machine learning methods. The thesis can be divided into two subtopics. The first, which is the focus of the first two papers, is dual control. The second, which is the focus of the third and last paper, is multiple-input multiple-output (MIMO) control of a chiller process. In dual control, the goal is to construct controllers for uncertain systems that in expectation minimize some cost over a certain time horizon. To achieve this, the controller must take into account the dual goals of accumulating more information about the process, by applying some probing input, and using the available information for controlling the system. This is referred to as the exploration-exploitation trade-off. Although optimal dual controllers in theory can be computed by solving a functional equation, this is usually intractable in practice, with only some simple special cases as exceptions. Therefore, it is interesting to examine methods for approximating optimal dual control. In the first paper, we take the approach of approximating the value function, which is the solution of the functional equation that can be used to deduce the optimal control, by using artificial neural networks. In the second paper, neural networks are used to represent and estimate hyperstates, which contain information about the conditional probability distributions of the system uncertainties. The optimal dual controller is a function of the hyperstate, and hence it should be useful to have a representation of this quantity when constructing an approximately optimal dual controller. The hyperstate transition model is used in combination with a reinforcement learning algorithm for constructing a dual controller from stochastic simulations of a system model that includes models of the system uncertainties. In the third paper, we suggest a simple reinforcement learning method that can be used to construct a decoupling matrix that allows MIMO control of a chiller process. Compared to the commonly used single-input single-output (SISO) structures, these controllers can decrease the variations in some system signals. This makes it possible to run the system at operating points closer to some constraints, which in turn can enable more energy-efficient operation

Observer-Based Controller for Disturbance Decoupling of Max-plus Linear Systems with Applications to a High Throughput Screening System in Drug Discovery

Max-plus linear systems are often used to model timed discrete-event systems, which represent system operations as discrete sequences of events in time. This paper presents the observer-based controller to solve the disturbance decoupling problem for max-plus linear systems where only estimations of system states are available for the controller. This observer-based controller leads to a greater control input than the one obtained with the output feedback strategy based on just-in-time criterion. A high throughput screening system in drug discovery illustrates this main result by showing that the scheduling obtained from the observer-based controller solving the disturbance decoupling problem is better than the scheduling obtained from the output feedback controller

Multiobjective Robust Control with HIFOO 2.0

Multiobjective control design is known to be a difficult problem both in theory and practice. Our approach is to search for locally optimal solutions of a nonsmooth optimization problem that is built to incorporate minimization objectives and constraints for multiple plants. We report on the success of this approach using our public-domain Matlab toolbox HIFOO 2.0, comparing our results with benchmarks in the literature

Design of Low-Order Controllers using Optimization Techniques

In many applications, especially in the process industry, low-level controllers are the workhorses of the automated production lines. The aim of this study has been to provide simple tuning procedures, either optimization-based methods or tuning rules, for design of low-order controllers. The first part of this thesis deals with PID tuning. Design methods or both SISO and MIMO PID controllers based on convex optimization are presented. The methods consist of solving a nonconvex optimization problem by deriving convex approximations of the original problem and solving these iteratively until convergence. The algorithms are fast because of the convex approximations. The controllers obtained minimize low-frequency sensitivity subject to constraints that ensure robustness to process variations and limitations of control signal effort. The second part of this thesis deals with tuning of feedforward controllers. Tuning rules that minimize the integrated-squared-error arising from measurable step disturbances are derived for a controller that can be interpreted as a filtered and possibly time-delayed PD controller. Using a controller structure that decouples the effects of the feedforward and feedback controllers, the controller is optimal both in open and closed loop settings. To improve the high-frequency noise behavior of the feedforward controller, it is proposed that the optimal controller is augmented with a second-order filter. Several aspects on the tuning of this filter are discussed. For systems with PID controllers, the response to step changes in the reference can be improved by introducing set-point weighting. This can be interpreted as feedforward from the reference signal to the control signal. It is shown how these weights can be found by solving a convex optimization problem. Proportional set-point weight that minimizes the integrated-absolute-error was obtained for a batch of over 130 different processes. From these weights, simple tuning rules were derived and the performance was evaluated on all processes in the batch using five different feedback controller tuning methods. The proposed tuning rules could improve the performance by up to 45% with a modest increase in actuation

Several new designs for PID, IMC, Decoupling and Fuzzy Control

Ph.DDOCTOR OF PHILOSOPH

Real-time Feedback of B0 Shimming at Ultra High Field MRI

Magnetic resonance imaging(MRI) is moving towards higher and higher field strengths. After 1.5T MRI scanners became commonplace, 3T scanners were introduced and once 3T scanners became commonplace, ultra high field (UHF) scanners were introduced. UHF scanners typically refer to scanners with a field strength of 7T or higher. The number of sites that utilise UHF scanners is slowly growing and the first 7T MRI scanners were recently CE certified for clinical use. Although UHF scanners have the benefit of higher signal-to-noise ratio (SNR), they come with their own challenges. One of the many challenges is the problem of inhomogeneity of the main static magnetic field(B0 field). This thesis addresses multiple aspects associated with the problem of B0 inhomogeneity. The process of homogenising the field is called "shimming". The focus of this thesis is on active shimming where extra shim coils drive DC currents to generate extra magnetic fields superimposed on the main magnetic field to correct for inhomogeneities. In particular, we looked at the following issues: algorithms for calculating optimal shim currents; global static shimming using very high order/degree spherical harmonic-based (VHOS) coils; dynamic slice-wise shimming using VHOS coils compared to a localised multi-coil array shim system; B0 field monitoring using an NMR field camera; characterisation of the shim system using a field camera; and designing a controller based on the shim system model for real-time feedback

Modelling, control and analysis of a voltage source converter

The present thesis describes the modelling and control of a three-phase voltage source converter for electrochemical storage systems and renewable energy generation connected to the grid by means of a simplified averaged model. Open and closed-loop control structures based on lineal classical controllers are explored. Control scheme, including PLL, inner current loop and outer loops (active and reactive power and DC voltage), is detailed and parametrisation of the controllers is carried out. The dynamic model is implemented and its simulations are used to further study the converter’s response. Voltage dip faults, capability curves and current limitation and voltage stability under different grid impedance are analytically discussed and in depth analyzed through simulationsLa present tesi descriu la modelització i el control d’un convertidor trifàsic de font de voltatge per a sistemes d’emmagatzematge electroquímic i generació d’energia renovable con- nectats a la xarxa mitjançant un model simplificat mitjà. Es fan exploracions de les estructures de control en llaç obert i tancat basades en controladors clàssics lineals. Es detalla el sistema de control, incloent el PLL, el llaç de corrent intern i els llaços externs (potència activa i reactiva i voltatge DC) i es realitza la parametrització dels controladors. El model dinàmic s’implementa i les simulacions s’utilitzen per aprofundir en l’estudi de la resposta del convertidor. Les faltes de caiguda de tensió, les corbes de capacitat i les limitacions de corrent i la estabilitat de voltatge envers diferents impedàncies de xarxa primer es discuteixen analíticament i després s’analitzen a fons mitjançant simulacionsLa presente tesis describe la modelización y control de un convertidor trifásico de fuente de voltaje para sistemas de almacenamiento electroquímico y generación de energía renovable conectados a la red mediante un modelo simplificado promedio. Se exploran estructuras de control en lazo abierto y cerrado basadas en controladores clásicos lineales. Se detalla el sistema de control, incluyendo el PLL, el lazo de corriente interno y los lazos externos (potencia activa y reactiva y voltaje DC) y se realiza la parametrización de los controladores. El modelo dinámico se implementa y las simulaciones se utilizan para profundizar en el estudio de la respuesta del convertidor. Las faltas de caída de tensión, las curvas de capacidad y las limitaciones de corriente y la estabilidad de voltaje bajo diferentes impedancias de red se discuten primero analíticamente y luego se analizan en profundidad mediante simulacione