The current article presents a design procedure for obtaining robust multiple-input and multiple-output (MIMO) fractional-order controllers using μ-synthesis with D–K iteration. uses the generalized Robust Control framework in order to find controller which meets stability performance criteria family of plants. Because this control problem is NP-hard, it usually solved an approximation, most common being iteration algorithm, but, approximation leads high-order controllers, are not...

μ-synthesis is a NP-hard optimization problem based on the generalized Robust Control framework which manages to find controller fulfills both robust stability and performance. In order solve such problems, nonsmooth techniques are employed nearly-optimal parameters values. However, free available for tuning must be involved only in classical arithmetic operations, leads fractional-order operator or its integer-order approximation, exponential operations being involved. The main goal of...

Abstract This article proposes an optimization‐based approach to selecting the sampling periods for classes of linear time‐invariant (LTI) regulators in a cascaded multi‐rate control structure, account practical implementation on numeric systems. Starting from Shannon‐Nyquist theorem, which minimum required frequency completely recovering original analog signal its discrete samples, scope process, viewed perspective, is ensure asymptotic stability closed‐loop system, with smallest possible...

The current article presents the design, implementation, validation, and use of a Computer-Aided Control System Design (CACSD) toolbox for nonlinear hybrid system uncertainty modeling, simulation, control using μ synthesis. Remarkable features include generalization classical interconnection operations to systems, automatic computation equilibrium points optimization least conservative bounds, with direct applicability A unified approach is presented step-down (buck), step-up (boost),...

This paper presents an end-to-end method to design passivity-based controllers (PBC) for a class of input-affine nonlinear systems, named quasi-linear affine. The approach is developed using Krasovskii’s Lyapunov function studying the asymptotic stability, and sufficient condition construct storage given, along with supply-rate function. linear fractional transformation interconnection between system Krasovskii PBC (K-PBC) results in which manages follow provided input trajectory. However,...

Fractional order calculus in modelling and control applications has been increasingly popular every scientific field due to its versatility superiority various instances. However, the main issue of fractional elements is related their implementation. Usually, integer are used through different approximation methods implement such elements. None existing discuss introduction a element fixed-structure robust synthesis method. MATLAB realp objects do not allow use other than classical...

The current paper proposes a cascade structure controller for use with finite-order input-affine nonlinear sys-tems polytopic linear time-invariant (LTI) bounds. is comprised of Krasovskii-passivity based component, designed systems, which guarantees closed-loop asymptotic stability the plant irrespective operating point, followed by robust path-planning component transient and steady-state performance, through <tex xmlns:mml="http://www.w3.org/1998/Math/MathML"...

This paper proposes a comparative study of uncertainty modelling approaches for inverted-pendulum type mechanical systems with input-output derivative behaviour to be directly used robust controller synthesis. Besides three from the literature obtain mathematical model parametric uncertainties, we propose an additional nonlinear optimization-based approach, which manages maintain reduced-order structure convex optimization fit, but better performance and robustness attainable through less...

The current paper proposes a set of theoretical results regarding the closed-loop control continuous linear time-invariant (LTI) physical processes using fixed-point discrete-time LTI regulators, interfaced uniform data converters, by providing necessary and sufficient conditions to quantify stability up worst-case computable bound. Additionally, are then gathered in an algorithmic manner such that engineer can specify desired performance for numerical system, starting from satisfactory...

The current paper proposes an extension for two controller design procedures a two-axis positioning mechatronic system, followed by comparison between them. As such, the first method consists in formulating optimization problem terms of linear matrix inequalities (LMIs) order to impose location closed-loop poles, considering uncertain model such system. is treated using various forms differential inclusions (LDIs), namely, polytopic LDI (PLDI) and diagonal norm-bound (DNLDI). Additionally,...

The inherent problem with continuous-time robust control synthesis is that it returns a controller which cannot directly be implemented on numeric device. discrete-time does not fully solve this problem, as the sampling rate considered an input hyperparameter, without explicitly performing selection, and quantization of coefficients encompassed in procedure. aim paper to provide rigorous means efficiently compute step for given continuous regulator order maintain stability performance...

This paper proposes an alternative nonconvex approach to fit single-input and single-output transfer function models on magnitude frequency-based response measurements, with additional constraints such as upper boundness, stability, minimum phase validity respect provided data. The proposed solution presents improvement over the established Log-Chebyshev convex which is used a well-placed starting point refines optimization become less conservative feasible in cases where (near)...

Due to adding the extra degree of freedom, fractional order PID controllers can achieve better control performance than integer controllers. The present paper proposes a novel controller design method, inspired by Kessler's optimum magnitude method. explicit tuning rules are accessible even less experienced users in calculus, taking only advantages and not disadvantage complex mathematical background. method demonstrated case study.

This paper presents an algorithm for the iterative refinement of matrix solutions algebraic Riccati equation in both continuous and discrete-time cases. It is based on Newton's method root-finding extended using Fréchet derivative framework. The improvement brought by considering complete structure equations, which typically consider input-state dependency to be zero. approach reasonable computing linear quadratic regulators estimators, but must treated field Robust Control, as equations...

This paper presents the mechanical, electrical, software, controller design and implementation for a two-wheeled robot, having goal of maintaining it's equilibrium by itself. In order to create this mechanical structure was designed, such than an exact replica could be constructed using 3D printer laser cutting machine. Having robot created mathematical state-space model defined, system's parameters were identified validated. Then, linear quadratic regulator (LQR) which would achieve...

In a distributed energy system, the optimal scheduling of use resources is important to reduce cost and can become critical meeting needs in an isolated system. This paper presents general framework that allows formulate management problem linear programming with inequality constraints. order solve thus formulated, classical simplex or mixed-integer algorithms have been replaced two interior point methods, which are polynomial-time complexity.

The current journal paper proposes an end-to-end analysis for the numerical implementation of a two-degrees-of-freedom (2DOF) control structure, starting from sampling rate selection mechanism via quasi-optimal manner, along with estimation worst-case execution time (WCET) specified controller. For selection, classical Shannon–Nyquist theorem is replaced by optimization problem that encompasses trade-off between fidelity controllers’ representation, resulting closed-loop systems, and...

This paper presents the design of a passivity-based controller for nonideal DC-DC boost converter containing parasitic terms (NPBC). The PBC ideal case circuit leads to current and voltage offsets which are not tolerated in high-performance systems. All results have been obtained by simulation on both state-space averaging model using more realistic hybrid system model. NPBC functions keeping prescribed inductor at desired value irrespective output load. With an appropriate computation...

The current paper proposes a state feedback approach to design cascade controller for an augmented model of Computer Numerical Control (CNC) machine. main objective is obtain the position and velocity controllers based on optimal matrix computed using solution provided by solving set linear inequalities (LMIs). problem formulated corresponding LMIs which characterize certain region needs contain closed-loop poles in order ensure stability desired time-response performance. Additionally, case...

The current paper proposes an approach to adequately select optimal sampling period for linear time-invariant (LTI) regulators targeted practical implementation on microprocessor-based systems. Although the classical Shannon-Nyquist theorem solution in order completely recover original analog signal from its discrete samples, scope of process, viewed a control perspective, is ensure asymptotic stability closed-loop system, with as small degradation initially-proposed performance indices...

In the domain of passivity theory, there were major contributions in last decade, most recent notion being so-called Krasovskii passivity. This framework offers possibility designing a controller which ensures resulting closed-loop system. The current paper proposes solution to design parameters passivity-based controllers (K-PBCs) order ensure small sensitivity systems. As such, after initial construction output, are designed impose dominant eigenvalues Jacobian system with smallest...

Fractional order (FO) calculus in modelling and control applications has been increasingly popular every scientific field due to its versatility superiority various instances. Moreover, the models' parameters present uncertainties, called intervals. However, main issue of fractional elements is related their implementation. Usually, integer are used through different approximation methods implement such elements. None existing discuss introduction a element fixed-structure robust synthesis...

This paper presents a white-box implementation of three-phase induction machine model with short-circuited rotor using MATLAB/Simulink®. It can be used as computer-aided design (CAD) tool for understanding, designing and testing various control techniques this type machine. The is open-source available in the GitHub platform. Besides model, project supports space vector modulation PWM function to command stator motor, constant voltage over frequency ratio added feedforward load compensation...

The paper focuses on the analysis of sensitivity and robustness for linear dynamical systems. A variation Kharitonov theorem is presented to provide a simple visual quantitative measurement system performances given parameter modifications. method applied in tutorial approach determine component tolerance influences two commonly-used notch filter topologies. frequency responses filters are correlated pole-zero placement complex plane.