There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

System Identification I

Solar power generation by PV (photovoltaic) technology: A review

Pulsewidth modulation (PWM) voltage source converters are becoming a popular interface to the power grid for many applications. Hence, issues related to the reduction of PWM harmonics injection in the power grid are becoming more relevant. The use of high-order filters like LCL filters is a standard solution to provide the proper attenuation of PWM carrier and sideband voltage harmonics. However, those grid filters introduce potentially unstable dynamics that should be properly damped either passively or actively. The second solution suffers from control and system complexity (a high number of sensors and a high-order controller), even if it is more attractive due to the absence of losses in the damping resistors and due to its flexibility. An interesting and straightforward active damping solution consists in plugging in, in cascade to the main controller, a filter that should damp the unstable dynamics. No more sensors are needed, but there are open issues such as preserving the bandwidth, robustness, and limited complexity. This paper provides a systematic approach to the design of filter-based active damping methods. The tuning procedures, performance, robustness, and limitations of the different solutions are discussed with theoretical analysis, selected simulation, and experimental results.

Filter-Based Active Damping of Voltage Source Converters With $LCL$ Filter

Data-driven discovery is revolutionizing the modeling, prediction, and control of complex systems. This textbook brings together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science. It highlights many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy. Aimed at advanced undergraduate and beginning graduate students in the engineering and physical sciences, the text presents a range of topics and methods from introductory to state of the art.

Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control

A stability analysis for a maximum power point tracking (MPPT) scheme based on extremum-seeking control is developed for a photovoltaic (PV) array supplying a dc-to-dc switching converter. The global stability of the extremum-seeking algorithm is demonstrated by means of Lyapunov's approach. Subsequently, the algorithm is applied to an MPPT system based on the "perturb and observe" method. The steady-state behavior of the PV system with MPPT control is characterized by a stable oscillation around the maximum power point. The tracking algorithm leads the array coordinates to the maximum power point by increasing or decreasing linearly with time the array voltage. Off-line measurements are not required by the control law, which is implemented by means of an analog multiplier, standard operational amplifiers, a flip-flop circuit and a pulsewidth modulator. The effectiveness of the proposed MPPT scheme is demonstrated experimentally under different operating conditions.

MPPT of photovoltaic systems using extremum - seeking control

A consistent framework for robust linear quadratic regulators (LQRs) control of power converters is presented. Systems with conventional LQR controllers present good stability properties and are optimal with respect to a certain performance index. However, LQR control does not assure robust stability when the system is highly uncertain. In this paper, a convex model of converter dynamics is obtained taking into account uncertainty of parameters. In addition, the LQR control for switching converters is reviewed. In order to apply the LQR control in the uncertain converter case, we propose to optimize the performance index by using linear matrix inequalities (LMIs). As a consequence, a new robust control method for dc-dc converters is derived. This LMI-LQR control is compared with classical LQR control when designing a boost regulator. Performance of both cases is discussed for load and line perturbations, working at nominal and non nominal conditions. Finally, the correctness of the proposed approach is verified with experimental prototypes.

/pdf/robust-lqr-control-for-pwm-converters-an-lmi-approach-3uteo6nxha.pdf

Robust LQR Control for PWM Converters: An LMI Approach

This work presents an analytical study and an experimental verification of a robust control design based on a linear matrix inequalities (LMI) framework for boost regulators. With the proposed LMI method, non-linearities and uncertainties are modelled as a convex polytope. Thus, the LMI constraints permit to robustly guarantee a certain perturbation rejection level and a region of pole location. With this approach, the multiobjective robust controller is computed automatically by a standard optimisation algorithm. The proposed method results in a state-feedback law efficiently implementable by operational amplifiers. PSIM simulations and experimental results obtained from a prototype are used to validate this approach. The results obtained are compared with a conventional PID controller.

LMI robust control design for boost PWM converters

https://homepages.laas.fr/queinnec/PDFpublis/automatica2008_NLsat.pdf

Isabelle Queinnec

Papers

MPPT of photovoltaic systems using extremum - seeking control

Robust LQR Control for PWM Converters: An LMI Approach

LMI robust control design for boost PWM converters

Brief paper: Control design for a class of nonlinear continuous-time systems

Robust optimal control of bilinear DC–DC converters