On the use of inversion formulae for the synthesis of discrete PID controllers

This paper presents a new set of formulae for the design of discrete proportional-integral-derivative (PID) controllers under requirements on steady-state performance and robustness specifications, such as the phase and the gain margins, as well as the gain crossover frequency. The proposed technique has the advantage of avoiding trial-and error procedures or approximations connected to an a posteriori discretisation. This method can also be implemented as a graphical design procedure in the Nyquist plane

Direct digital design of PIDF controllers with ComPlex zeros for DC-DC buck converters

This paper presents a new direct digital design method for discrete proportional integral derivative PID + filter (PIDF) controllers employed in DC-DC buck converters. The considered controller structure results in a proper transfer function which has the advantage of being directly implementable by a microcontroller algorithm. Secondly, it can be written as an Infinite Impulse Response (IIR) digital filter. Thirdly, the further degree of freedom introduced by the low pass filter of the transfer function can be used to satisfy additional specifications. A new design procedure is proposed, which consists of the conjunction of the pole-zero cancellation method with an analytical design control methodology based on inversion formulae. These two methods are employed to reduce the negative effects introduced by the complex poles in the transfer function of the buck converter while exactly satisfying steady-state specifications on the tracking error and frequency domain requirements on the phase margin and on the gain crossover frequency. The proposed approach allows the designer to assign a closed-loop bandwidth without constraints imposed by the resonance frequency of the buck converter. The response under step variation of the reference value, and the disturbance rejection capability of the proposed control technique under load variations are also evaluated in real-time implementation by using the Arduino DUE board, and compared with other methods

Exact Tuning of PID Controllers in Control Feedback Design

In this study, the authors introduce a range of techniques for the exact design of PID controllers for feedback control problems involving requirements on the steady-state performance and standard frequency-domain specifications on the stability margins and crossover frequencies. These techniques hinge on a set of simple closed-form formulae for the explicit computation of the parameters of the controller in finite terms as functions of the specifications, and therefore they eliminate the need for graphical, heuristic or trial-and-error procedures. The relevance of this approach is (i) theoretical, since a closed-form solution is provided for the design of PID-type controllers with standard frequency-domain specifications; (ii) computational, since the techniques presented here are readily implementable as software routines, for example, using MATLAB®; (iii) educational, because the synthesis of the controller reduces to a simple exercise on complex numbers that can be solved with pen, paper and a scientific calculator. These techniques also appear to be very convenient within the context of adaptive control and self-tuning strategies, where the controller parameters have to be calculated online. Furthermore, they can be easily combined with graphical and first/second-order plant approximation methods in the cases where the model of the system to be controlled is not known

Plurilinear Modeling and discrete μ-Synthesis Control of a Hysteretic and Creeped Unimorph Piezoelectric Cantilever.

International audienceFirst, we present a survey on modeling and control of bending piezoelectric microactuators. Second, a simple model for nonlinear piezoelectric actuators (hysteresis and creep) is presented. It is based on the multilinear approximation. This model requires low computing power and is well adapted for embedded systems. Finally, a μ-synthesis controller is implemented. Experiments show that the obtained performances are compatible with the requirements of micromanipulation tasks

Discrete-time optimal preview control

There are many situations in which one can preview future reference signals, or future disturbances. Optimal Preview Control is concerned with designing controllers which use this preview to improve closed-loop performance. In this thesis a general preview control problem is presented which includes previewable disturbances, dynamic weighting functions, output feedback and nonpreviewable disturbances. It is then shown how a variety of problems may be cast as special cases of this general problem; of particular interest is the robust preview tracking problem and the problem of disturbance rejection with uncertainty in the previewed signal. . (', The general preview problem is solved in both the Fh and Beo settings. The H2 solution is a relatively straightforward extension ofpreviously known results, however, our contribution is to provide a single framework that may be used as a reference work when tackling a variety of preview problems. We also provide some new analysis concerning the maximum possible reduction in closed-loop H2 norm which accrues from the addition of preview action. / Name of candidate: Title of thesis: I DESCRIPTION OF THESIS Andrew Hazell Discrete-Time Optimal Preview Control The solution to the Hoo problem involves a completely new approach to Hoo preview control, in which the structure of the associated Riccati equation is exploited in order to find an efficient algorithm for computing the optimal controller. The problem tackled here is also more generic than those previously appearing in the literature. The above theory finds obvious applications in the design of controllers for autonomous vehicles, however, a particular class of nonlinearities found in typical vehicle models presents additional problems. The final chapters are concerned with a generic framework for implementing vehicle preview controllers, and also a'case study on preview control of a bicycle.Imperial Users onl

A classification of techniques for the compensation of time delayed processes. Part 2: Structurally optimised controllers

Following on from Part 1, Part 2 of the paper considers the use of structurally optimised controllers to compensate time delayed processes

New Approaches in Automation and Robotics

The book New Approaches in Automation and Robotics offers in 22 chapters a collection of recent developments in automation, robotics as well as control theory. It is dedicated to researchers in science and industry, students, and practicing engineers, who wish to update and enhance their knowledge on modern methods and innovative applications. The authors and editor of this book wish to motivate people, especially under-graduate students, to get involved with the interesting field of robotics and mechatronics. We hope that the ideas and concepts presented in this book are useful for your own work and could contribute to problem solving in similar applications as well. It is clear, however, that the wide area of automation and robotics can only be highlighted at several spots but not completely covered by a single book

Design and Control of Power Converters 2019

In this book, 20 papers focused on different fields of power electronics are gathered. Approximately half of the papers are focused on different control issues and techniques, ranging from the computer-aided design of digital compensators to more specific approaches such as fuzzy or sliding control techniques. The rest of the papers are focused on the design of novel topologies. The fields in which these controls and topologies are applied are varied: MMCs, photovoltaic systems, supercapacitors and traction systems, LEDs, wireless power transfer, etc

Development of adaptive control methodologies and algorithms for nonlinear dynamic systems based on u-control framework

Inspired by the U-model based control system design (or called U-control system design), this study is mainly divided into three parts. The first one is a U-model based control system for unstable non-minimum phase system. Pulling theorems are proposed to apply zeros pulling filters and poles pulling filters to pass the unstable non-minimum phase characteristics of the plant model/system. The zeros pulling filters and poles pulling filters derive from a customised desired minimum phase plant model. The remaining controller design can be any classic control systems or U-model based control system. The difference between classic control systems and U-model based control system for unstable non-minimum phase will be shown in the case studies.Secondly, the U-model framework is proposed to integrate the direct model reference adaptive control with MIT normalised rules for nonlinear dynamic systems. The U-model based direct model reference adaptive control is defined as an enhanced direct model reference adaptive control expanding the application range from linear system to nonlinear system. The estimated parameter of the nonlinear dynamic system will be placement as the estimated gain of a customised linear virtual plant model with MIT normalised rules. The customised linear virtual plant model is the same form as the reference model. Moreover, the U-model framework is design for the nonlinear dynamic system within the root inversion.Thirdly, similar to the structure of the U-model based direct model reference adaptive control with MIT normalised rules, the U-model based direct model reference adaptive control with Lyapunov algorithms proposes a linear virtual plant model as well, estimated and adapted the particular parameters as the estimated gain which of the nonlinear plant model by Lyapunov algorithms. The root inversion such as Newton-Ralphson algorithm provides the simply and concise method to obtain the inversion of the nonlinear system without the estimated gain. The proposed U-model based direct control system design approach is applied to develop the controller for a nonlinear system to implement the linear adaptive control. The computational experiments are presented to validate the effectiveness and efficiency of the proposed U-model based direct model reference adaptive control approach and stabilise with satisfied performance as applying for the linear plant model