Design of parameter-scheduled state-feedback controllers using shifting specifications

In this paper,the problem of designing aparameter-scheduled state-feedback controller is investigated. The paper presents an extension of the classical regional pole placement, H2 control and H1 control problems, so as to satisfy new specifications, that will be referred to as shifting pole placement control, shifting H2 control and shifting H1 control, respectively. By introducing some parameters, or using the existing ones, the controller can be designed in such away that different values of the separameters imply different regions where the closed-loop poles are situated, or different performances in the H2 or H1 sense. The proposed approach is derived within the so-called Lyapunov Shaping Paradigm, where a single quadratic Lyapunov function is used for ensuring stability and desired performances in spite of arbitrary parameter time variation. The problem is analyzed in the continuous-time LPV case, oventhough the developed theory could be applied to LTI systems in cases when it is desired to vary the control system performances online. Results obtained in simulation demonstrate the effectiveness and the relevant features of the proposed approach.Peer ReviewedPostprint (published version

A shifting pole placement approach for the design of performance-varying multivariable PID controllers via BMIs

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper, the design of a performance-varying multivariable Proportional-Integral-Derivative (PID) controllers is presented. The main objective is to provide a framework for changing online the closed-loop behavior of the controlled system using the shifting pole placement approach. In order to carry out this target, the PID design problem is transformed into a static output feedback design problem which is analyzed through the linear parameter-varying (LPV) paradigm. An academic example is used to demonstrate the effectiveness of the proposed approach.Peer ReviewedPostprint (author's final draft

LMI-based design of state-feedback controllers for pole clustering of LPV systems in a union of -regions

This paper introduces an approach for the design of a state-feedback controller that achieves pole clustering in a union of DR-regions for linear parameter varying systems. The design conditions, obtained using a partial pole placement theorem, are eventually expressed in terms of linear matrix inequalities. In addition, it is shown that the approach can be modified in a shifting sense. Hence, the controller gain is computed such that different values of the varying parameters imply different regions of the complex plane where the closed-loop poles are situated. This approach enables the online modification of the closed-loop performance. The effectiveness of the proposed method is demonstrated by means of simulations.Peer ReviewedPostprint (author's final draft

LMI-based design of state-feedback controllers for pole clustering of LPV systems in a union of DR-regions

This paper introduces an approach for the design of a state-feedback controller that achieves pole clustering in a union of DR-regions for linear parameter varying systems. The design conditions, obtained using a partial pole placement theorem, are eventually expressed in terms of linear matrix inequalities. In addition, it is shown that the approach can be modified in a shifting sense. Hence, the controller gain is computed such that different values of the varying parameters imply different regions of the complex plane where the closed-loop poles are situated. This approach enables the online modification of the closed-loop performance. The effectiveness of the proposed method is demonstrated by means of simulations.acceptedVersio

D-stable controller design for Lipschitz NLPV system

This paper addresses the design of a state-feedback controller for a class of nonlinear parameter varying (NLPV) systems in which the nonlinearity can be expressed as a parameter-varying Lipschitz term. The controller is designed to satisfy a D-stability specification, which is akin to imposing constraints on the closed-loop pole location in the case of LTI and LPV systems. The design conditions, obtained using a quadratic Lyapunov function, are eventually expressed in terms of linear matrix inequalities (LMIs), which can be solved efficiently using available solvers. The effectiveness of the proposed method is demonstrated by means of a numerical example.Postprint (author's final draft

Design of state-feedback controllers for linear parameter varying systems subject to time-varying input saturation

All real-world systems are affected by the saturation phenomenon due to inherent physical limitations of actuators. These limitations should be taken into account in the controller’s design to prevent a possibly severe deterioration of the system’s performance, and may even lead to instability of the closed-loop system. Contrarily to most of the control strategies, which assume that the saturation limits are constant in time, this paper considers the problem of designing a state-feedback controller for a system affected by time-varying saturation limits with the objective to improve the performance. In order to tie variations of the saturation function to changes in the performance of the closed-loop system, the shifting paradigm is used, that is, some parameters scheduled by the time-varying saturations are introduced to schedule the performance criterion, which is considered to be the instantaneous guaranteed decay rate. The design conditions are obtained within the framework of linear parameter varying (LPV) systems using quadratic Lyapunov functions with constant Lyapunov matrices and they consist in a linear matrix inequality (LMI)-based feasibility problem, which can be solved efficiently using available solvers. Simulation results obtained using an illustrative example demonstrate the validity and the main characteristics of the proposed approach.Peer ReviewedPostprint (published version

Design and Implementation of Control Techniques of Power Electronic Interfaces for Photovoltaic Power Systems

The aim of this thesis is to scrutinize and develop four state-of-the-art power electronics converter control techniques utilized in various photovoltaic (PV) power conversion schemes accounting for maximum power extraction and efficiency. First, Cascade Proportional and Integral (PI) Controller-Based Robust Model Reference Adaptive Control (MRAC) of a DC-DC boost converter has been designed and investigated. Non-minimum phase behaviour of the boost converter due to right half plane zero constitutes a challenge and its non-linear dynamics complicate the control process while operating in continuous conduction mode (CCM). The proposed control scheme efficiently resolved complications and challenges by using features of cascade PI control loop in combination with properties of MRAC. The accuracy of the proposed control system’s ability to track the desired signals and regulate the plant process variables in the most beneficial and optimised way without delay and overshoot is verified. The experimental results and analysis reveal that the proposed control strategy enhanced the tracking speed two times with considerably improved disturbance rejection. Second, (P)roportional Gain (R)esonant and Gain Scheduled (P)roportional (PR-P) Controller has been designed and investigated. The aim of this controller is to create a variable perturbation size real-time adaptive perturb and observe (P&O) maximum power point tracking (MPPT) algorithm. The proposed control scheme resolved the drawbacks of conventional P&O MPPT method associated with the use of constant perturbation size that leads to a poor transient response and high continuous steady-state oscillations. The prime objective of using the PR-P controller is to utilize inherited properties of the signal produced by the controller’s resonant path and integrate it to update best estimated perturbation that represents the working principle of extremum seeking control (ESC) to use in a P&O algorithm that characterizes the overall system learning-based real time adaptive (RTA). Additionally, utilization of internal dynamics of the PR-P controller overcome the challenges namely, complexity, computational burden, implantation cost and slow tracking performance in association with commonly used soft computing intelligent systems and adaptive control strategies. The experimental results and analysis reveal that the proposed control strategy enhanced the tracking speed five times with reduced steady-state oscillations around maximum power point (MPP) and more than 99% energy extracting efficiency.Third, the interleaved buck converter based photovoltaic (PV) emulator current control has been investigated. A proportional-resonant-proportional (PR-P) controller is designed to resolve the drawbacks of conventional PI controllers in terms of phase management which means balancing currents evenly between active phases to avoid thermally stressing and provide optimal ripple cancellation in the presence of parameter uncertainties. The proposed controller shows superior performance in terms of 10 times faster-converging transient response, zero steady-state error with significant reduction in current ripple. Equal load sharing that constitutes the primary concern in multi-phase converters has been achieved with the proposed controller. Implementing of robust control theory involving comprehensive time and frequency domain analysis reveals 13% improvement in the robust stability margin and 12-degree bigger phase toleration with the PR-P controller. Fourth, a symmetrical pole placement Method-based Unity Proportional Gain Resonant and Gain Scheduled Proportional (PR-P) Controller has been designed and investigated. The proposed PR-P controller resolved the issues associated with the use of the PI controller which are tracking repeating control input signal with zero steady-state and mitigating the 3rd order harmonic component injected into the grid for single-phase PV systems. Additionally, the PR-P controller has overcome the drawbacks of frequency detuning in the grid and increase in the magnitude of odd number harmonics in the system that constitute the common concerns in the implementation of conventional PR controller. Moreover, the unprecedented design process based on changing notch filter dynamics with symmetrical pole placement around resonant frequency overcomes the limitations that are essentially complexity and dependency on the precisely modelled system. The verification and validation process of the proposed control schemes has been conducted using MATLAB/Simulink and implementing MATLAB/Simulink/State flow on dSPACE Real-time-interface (RTI) 1007 processor, DS2004 High-Speed A/D and CP4002 Timing and Digital I/O boards

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Modelling and LPV control of an electro-hydraulic servo system

This paper aims to show the modelling and control of an hydraulic servo system, targeting at frequency domain based controller design and the implementation of a LPV controller. The actual set-up consists of a mass, moved by a hydraulic cylinder and an electro-hydraulic servo valve. A nonlinear parametric model of the system, a number of fitted linear black box models as well as a LPV model combining these fits have been determined. In discretization of the control strategies for implementation on a digital control system, a new discretization algorithm is derived for LPV structures. Simulations and experimental results indicate the potential benefits of a position dependent controller over a classical controller, but show the limitations as well