Flat systems, equivalence and trajectory generation

Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector field. After recalling the definition of a Lie-Backlund mapping, we say that two systems are equivalent if they are related by a Lie-Backlund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft

Kinetic Intersections as a Source of Information on Rate Coefficients

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A survey of differential flatness-based control applied to renewable energy sources

Conference ProceedingsThis paper presents an overview of various methods used to minimize the fluctuating impacts of power generated from renewable energy sources. Several sources are considered in the study (biomass, wind, solar, hydro and geothermal). Different control methods applied to their control are cited, alongside some previous applications. Hence, it further elaborates on the adoptive control principles, of which includes; Load ballast control, dummy load control, proportional integral and derivative (PID) control, proportional integral (PI) control, pulse-width modulation (PWM) control, buck converter control, boost converter control, pitch angle control, valve control, the rate of river flow at turbine, bidirectional diffuser-augmented control and differential flatnessbased controller. These control operations in renewable energy power generation are mainly based on a steady-state linear control approach. However, the flatness based control principle has the ability to resolve the complex control problem of renewable energy systems while exploiting their linear properties. Using their flatness properties, feedback control is easily achieved which allows for optimal/steady output of the system components. This review paper highlights the benefits that range from better control techniques for renewable energy systems to established robust grid (or standalone generations) connections that can bring immense benefits to their operation and maintenance costs

Flat systems, equivalence and trajectory generation

3rd cycleIntroduction : Control systems are ubiquitous in modern technology. The use of feedback control can be found in systems ranging from simple thermostats that regulate the temperature of a room, to digital engine controllers that govern the operation of engines in cars, ships, and planes, to flight control systems for high performance aircraft. The rapid advances in sensing, computation, and actuation technologies is continuing to drive this trend and the role of control theory in advanced (and even not so advanced) systems is increasing..

A SURVEY ON CONTROL TECHNIQUES OF A BENCHMARKED CONTINUOUS STIRRED TANK REACTOR

The study carried out in this paper unveils a survey on issues related to modelling problems control strategies of a Continuous Stirred Tank Reactor (CSTR), a highly nonlinear plant containing numbers of stable and unstable operating points is considered. The issues discussed are categorised into regulation, feedback linearization, flatness, observation and estimation as well as challenges related to equilibrium points concerning CSTR. In this study, the limited capability of a conventional PID controller is discussed based on preliminary description and a dynamic modelling of the nonlinear plant. Moreover, the limitations of the conventional PID is illustrated through a simulation using nonlinear model of CSTR carried out under input constraint and the presence of bounded disturbances. The result shows that a fixed PID will not guarantee consistent performance throughout operating set points. The feedback linearization formalism is presented to prove that only regulation in the neighbourhood of operating point is possible. Non-minimum phase property exhibited by a CSTR is investigated as well. Flatness control is demonstrated as one of the possible linearization control technique achieving the objective of the trajectory trackin

Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction

Considering the competitive and strongly regulated pharmaceutical industry, mathematical modeling and process systems engineering might be useful tools for implementing quality by design (QbD) and quality by control (QbC) strategies for low-cost but high-quality drugs. However, a crucial task in modeling (bio)pharmaceutical manufacturing processes is the reliable identification of model candidates from a set of various model hypotheses. To identify the best experimental design suitable for a reliable model selection and system identification is challenging for nonlinear (bio)pharmaceutical process models in general. This paper is the first to exploit differential flatness for model selection problems under uncertainty, and thus translates the model selection problem to advanced concepts of systems theory and controllability aspects, respectively. Here, the optimal controls for improved model selection trajectories are expressed analytically with low computational costs. We further demonstrate the impact of parameter uncertainties on the differential flatness-based method and provide an effective robustification strategy with the point estimate method for uncertainty quantification. In a simulation study, we consider a biocatalytic reaction step simulating the carboligation of aldehydes, where we successfully derive optimal controls for improved model selection trajectories under uncertainty

Funnel control for a moving water tank

We study tracking control for a moving water tank system, which is modelled using the Saint-Venant equations. The output is given by the position of the tank and the control input is the force acting on it. For a given reference signal, the objective is to achieve that the tracking error evolves within a prespecified performance funnel. Exploiting recent results in funnel control we show that it suffices to show that the operator associated with the internal dynamics of the system is causal, locally Lipschitz continuous and maps bounded functions to bounded functions. To show these properties we consider the linearized Saint-Venant equations in an abstract framework and show that it corresponds to a regular well-posed linear system, where the inverse Laplace transform of the transfer function defines a measure with bounded total variation.Comment: 11 page

Disturbance observer design for nonlinear systems represented by input-output models

A new approach to the design of nonlinear disturbance observers for a class of nonlinear systems described by inputoutput differential equations is presented in this paper. In contrast with established forms of nonlinear disturbance observers, the most important feature of this new type of disturbance observer is that only measurement of the output variable is required, rather than the state variables. An inverse simulation model is first constructed based on knowledge of the structure and parameters of a conventional model of the system. The disturbance can then be estimated by comparing the output of the inverse model and the input of the original nonlinear system. Mathematical analysis demonstrates the convergence of this new form of nonlinear disturbance observer. The approach has been applied to disturbance estimation for a linear system and a new form of linear disturbance observer has been developed. The differences between the proposed linear disturbance observer and the conventional form of frequency-domain disturbance observer are discussed through a numerical example. Finally, the nonlinear disturbance observer design method is illustrated through an application involving a simulation of a jacketed continuous stirred tank reactor syste