Control of an industrial polymerization reactor using flatness

Petit, Nicolas; Rouchon, Pierre; Boueilh, Jean-Michel; Guerin, Frédéric; Pinvidic, Philippe

doi:10.1007/bfb0110305

Cited by 3 publications

(4 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let ξ j − (x, s) and ξ j + (x, s) be the general solutions to (12) and (13), respectively, and denote their inverse Laplace transforms by ξ j − (x, t) and ξ j + (x, t). The solution to (9) can be written as…”

Section: Control Design Based On Zero-dynamics Inverse and Differentimentioning

confidence: 99%

See 1 more Smart Citation

In-Domain Control of a Heat Equation: An Approach Combining Zero-Dynamics Inverse and Differential Flatness

Zheng

Zhu

2015

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This paper addresses the set-point control problem of a heat equation with in-domain actuation. The proposed scheme is based on the framework of zero dynamics inverse combined with flat system control. Moreover, the set-point control is cast into a motion planing problem of a multiple-input, multiple-out system, which is solved by a Green's function-based reference trajectory decomposition. The validity of the proposed method is assessed through the convergence and solvability analysis of the control algorithm. The performance of the developed control scheme and the viability of the proposed approach are confirmed by numerical simulation of a representative system. functional analytic setting based on semigroup and other related tools can be applied (see, e.g., [1,2,3,4]). It is interesting to note that in recent years, some methods that were originally developed for the control of finite-dimensional systems have been successfully extended to the control of parabolic PDEs, such as backstepping (see, e.g., 10[5, 6, 7]), flat systems (see, e.g., [8,9, 10,11,12,13,14]), as well as their variations (see, e.g., [15,16,17]).This paper addresses the in-domain (or interior point) control problem of a heat equation, which may arise in application related concerns for, e.g., the enhancement of control efficiency. Integrating a number of control inputs acting in the domain will lead 15 to non-standard inhomogeneous PDEs [1,18], which should be treated differently than the standard boundary control problem. The control scheme developed in the present work is based-on the framework of zero-dynamics inverse (ZDI), which was introduced by Byrnes and his collaborators in [19] and has been exploited and developed in a series of work [20,21,22,23,24]. It is pointed out in [23] that "for certain boundary control 20 systems it is very easy to model the system's zero dynamics, which, in turn, provides a simple systematic methodology for solving certain problems of output regulation."Indeed, the construction of zero dynamics for output regulation of certain in-domain controlled PDEs is also straightforward (see, e.g., [22]) and hence, the control design can be carried out in a systematic manner. A main issue related to the ZDI design is that 25 the computation of dynamic control laws requires resolving the corresponding zero dynamics, which may be very difficult for generic regulation problems, such as set-point control. To overcome this difficulty, we leverage one of the fundamental properties of flat systems, that is if a lumped or distributed parameter system is differentially flat (or flat for short), then its states and inputs can be explicitly expressed by the so-called flat 30 output and its time-derivatives [25,13]. In the context of ZDI design, the control can be derived from the flat output without explicitly solving the zero dynamics. Moreover, in the framework of flat systems, set-point control can be cast into a problem of motion planning, which can also be carried out in a systematic manner.The system model used in this ...

show abstract

Section: Control Design Based On Zero-dynamics Inverse and Differentimentioning

confidence: 99%

“…[5, 6, 7]), flat systems (see, e.g., [8,9, 10,11,12,13,14]), as well as their variations (see, e.g., [15,16,17]).…”

mentioning

confidence: 99%

In-Domain Control of a Heat Equation: An Approach Combining Zero-Dynamics Inverse and Differential Flatness

Zheng

Zhu

2015

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…The design of tracking controls has gained more and more attention. For instance, the growing demands on product quality and production efficiency, which require to turn away from the pure stabilization of an operating point towards tracking task as can be seen in some industrial applications, see for instance [15,21,5]. In that line, a potential application of the tracking of the State of Charge might be related with the dynamic pricing.…”

Section: Introductionmentioning

confidence: 99%

A tracking problem for the state of charge in an electrochemical Li-ion battery model

Hernández

Prieur

Cerpa

2022

MCRF

View full text Add to dashboard Cite

<p style='text-indent:20px;'>In this paper the Single Particle Model is used to describe the behavior of a Li-ion battery. The main goal is to design a feedback input current in order to regulate the State of Charge (SOC) to a prescribed reference trajectory. In order to do that, we use the boundary ion concentration as output. First, we measure it directly and then we assume the existence of an appropriate estimator, which has been established in the literature using voltage measurements. By applying backstepping and Lyapunov tools, we are able to build observers and to design output feedback controllers giving a positive answer to the SOC tracking problem. We provide convergence proofs and perform some numerical simulations to illustrate our theoretical results.</p>

show abstract

“…In the present work, we employ the method of flatness-based control, which has been applied to a variety of infinitedimensional systems (see, e.g., [18], [20], [21], [22], [23], [24], [25], [26], [27]). Nevertheless, applying this tool to systems controlled by multiple in-domain actuators leads essentially to a multiple-input multiple-output (MIMO) problem, which still remains a challenging topic.…”

Section: Introductionmentioning

confidence: 99%

Flatness‐based deformation control of an Euler–Bernoulli beam with in‐domain actuation

Badkoubeh

Zheng

Zhu

2016

IET Control Theory & Applications

View full text Add to dashboard Cite

This paper addresses the problem of deformation control of an Euler-Bernoulli beam with in-domain actuation. The proposed control scheme consists in first relating the system model described by an inhomogeneous partial differential equation to a target system under a standard boundary control form. Then, a combination of closed-loop feedback control and flatness-based motion planning is used for stabilizing the closed-loop system around reference trajectories. The validity of the proposed method is assessed through well-posedness and stability analysis of the considered systems. The performance of the developed control scheme is demonstrated through numerical simulations of a representative micro-beam.

show abstract

Control of an industrial polymerization reactor using flatness

Cited by 3 publications

References 9 publications

In-Domain Control of a Heat Equation: An Approach Combining Zero-Dynamics Inverse and Differential Flatness

In-Domain Control of a Heat Equation: An Approach Combining Zero-Dynamics Inverse and Differential Flatness

A tracking problem for the state of charge in an electrochemical Li-ion battery model

Flatness‐based deformation control of an Euler–Bernoulli beam with in‐domain actuation

Contact Info

Product

Resources

About