Prof. Dr. Hitay Özbay danışmanlığındaki tezler
20 tez · İhsan Doğramacı Bilkent University
Sonlu boyutlu filtreler ile gürbüz smith öngörücüsü tasarımı
The time delay is a widely recognized inherent phenomenon present in practical control systems, and it has been a subject of extensive research over the past century. Unless managed appropriately, even a minor delay can deteriorate performance and potentially lead to instability. Therefore, incorporating a model for time delay and designing the controller to mitigate its effects are crucial steps to attain the desired robustness and performance criteria in control theory. Additionally, owing to its infinite-dimensional structure, the majority of predictor-based controllers comprise finite impulse response filters, necessitating approximation with finite-dimensional transfer functions for seamless integration into physical systems. Controller designs based on the Smith predictor can effectively cancel out the impact of dead-time delay. This study introduces an extension of the Smith predictor to formulate stabilizing controllers for LTI SISO systems with multiple unstable modes and time delay. The main contribution of this approach lies in the streamlining of previous predictor-based control designs intended for unstable plants. The main contribution of this methodology lies in the simplification of previous predictor-based control designs tailored for unstable plants. The predictor filters are crafted by solving a Nevanlinna-Pick interpolation problem to attain optimal robust stability. The process also upholds the fundamental essence of the Smith predictor scheme, allowing the design of a controller based on the non-delayed nominal plant. Despite the susceptibility of Smith predictor-based designs to uncertain delays, the robustness of the proposed configuration surpasses that of the H-infinity optimal controller design, as demonstrated in the relevant section. The proposed design is also extensible to a category of distributed parameter SISO systems and MIMO plants. For distributed parameter SISO systems, it is assumed that the plant's transfer function can be expressed through coprime factorization. The fundamental idea underlying this approach is treating the infinite-dimensional inner factor of the plant as a "time delay", and, in turn, determining the predictor structure accordingly. The modeling and controller design steps expounded here are exemplified using a flexible beam model. Regarding MIMO systems, provided specific conditions are met, the tangential Nevanlinna-Pick interpolation technique can be employed to derive the controller and filters according to the proposed configuration. While numerous studies have addressed model order reduction in the context of H-infinity-norm error, achieving optimal H-infinity approximation remains a challenging and unresolved problem. This study introduces an alternative model reduction method that seeks to minimize the H-infinity norm of the difference between the reduced model and the original FIR structure. The proposed method essentially reduces the order of a given function by one with the minimum H-infinity-norm error, employing a high-order Padé approximation of the time-delay term. As the method reduces the order by one, an iterative algorithm is devised to recursively decrease the order of a given plant from n to a desired order of m, repeating the procedure (n-m) times following the outlined steps. The main contribution of the proposed technique is that it provides a new perspective against H-infinity-norm approximation by using Chebyshev equioscillation theorem on rational functions. Various examples are provided to elucidate the methodology of the suggested controller design and the robust stability condition in the context of approximating the infinite-dimensional predictor structure. Furthermore, the proposed model order reduction method is compared with the most recent state-of-the-art techniques within the literature. Finally, potential avenues for further research are deliberated, encompassing both the controller structure and H-infinity approximation.
İki bağlantılı robotik sistemler için güçlü stabilizasyon sağlayan kontrolcü tasarımı
Strong stabilization is defined as finding a stable controller that stabilizes the feedback system for a given plant. This study addresses the strong stabilization of a robotic system called the ``acrobot", which is a two-linked underactuated planar robot system. The linearized system is fourth-order, with two poles and one zero in the right half-plane. In this thesis, stable second-order controllers designed with different methods have been investigated for this system. The stability margins are analyzed with respect to various free parameters. In addition, the time-domain transient response analysis is illustrated through simulations. Furthermore, the effects of nonlinearities are studied by estimating the region of attraction for each linear controller considered.
Zamanla değişen sistemlerin gözlemleyici tasarımı ve çıktı geribeslemesi
We study observer design and output feedback stabilization of switched and nonlinear time varying systems. To establish the stability of feedback switched systems with delay, we develop a new extension of a recently proposed trajectory based approach which is fundamentally different from classical Lyapunov function based methods. This new extension of trajectory based approach, which is of interest for its own sake, can be applied to a wide range of time varying systems with time varying delays and it tackles the issue of finding appropriate Lyapunov functions to establish stability results. Our stabilization methodology does not require stabilizability and detectability of all of the subsystems of the switched system and we do not impose any constraint on the derivative of the time varying delay. For nonlinear time varying systems, we build a new type of finite-time smooth observer in the case where a state dependent disturbance affects the linear approximation. We combine this finite time observer design and a switched systems approach to develop stabilizing feedbacks for nonlinear time varying systems whose outputs are only available on some finite time intervals. Again, we use an extension of the trajectory based approach to conclude the stability of the closed-loop system. Motivated by the fact that the measured components of the state do not need to be estimated, we also construct reduced order finite time observers for a broad class of nonlinear time varying systems. We show how these reduced order finite time observers can be used to solve dynamic output feedback stabilization problem for multiple input, multiple output nonlinear time varying systems. Finally, we design a finite time observer to estimate the exact state of a continuous-time linear time varying system from sampled output in the presence of a piecewise continuous disturbance.
Sonsuz boyutlu sistemler için düşük dereceli gürbüz ve güçlü denetleyici tasarımı
This thesis deals with the robust stabilization of infinite dimensional systems by stable and low order controllers. The close relation between the Nevanlinna-Pick interpolation problem and the robust stabilization is well known in the literature. In order to utilize this relation, we propose a new optimal solution strategy for the Nevanlinna-Pick interpolation problem. Differently from the known suboptimal solutions, our method includes no mappings or transformations, it directly solves the problem in the right half plane. We additionally propose a method via suboptimal solutions of an associated Nevanlinna-Pick interpolation problem to robustly and strongly stabilize a set of plants which include the linearized models of two well known under actuated robots around their upright equilibrium points. In the literature, it is shown that the robust stabilization of an infinite dimensional system by stable controllers can be reduced to a bounded unit interpolation problem. In order to use this approach to design a finite dimensional controller, we propose a predetermined structure for the solution of the bounded unit interpolation problem. Aforementioned structure reduces the problem to a classical Nevanlinna-Pick interpolation problem which can be solved by the optimal solution strategy of this thesis. Finally, by combining the finite dimensional solutions of the bounded unit interpolation problem with the finite dimensional approximation techniques, we propose a method to design finite dimensional and stable controllers to robustly stabilize a given plant. Since time delay systems are one of the best examples of infinite dimensional systems, we provide numerical examples of various time delay systems for each proposed method.
Zaman gecikmeli sistemler için karışık H_2/H_inf kontrolör tasarımı
This study discusses mixed H_2/H_inf controller design problem for uncertain Linear Time-Invariant (LTI) systems with a time delay. More precisely, the goal is to find an internally stabilizing controller that minimizes the H_2 performance measure subject to robust stability condition which bounds the H_inf norm of the weighted closed loop transfer function. Two different methods are used to find the optimal H_2 controller. The first method is inspired from the H_inf control design to reduce the two block problem into one block. Second method, however is the implementation of the Mirkin's formula. These methods are compared and their pros and cons are discussed. The key point in the optimal controller is that, it is in Smith predictor form that includes an internal feedback in the form of an Finite Impulse Response (FIR) filter. These types of controllers are easy to implement and programmed in physical systems. A case study is considered to show the exact way to controller design. The simulation results and the effects of delay term on the performance measure are also provided.
Dağıtık parametreli sistemlerin eniyilik ölçütü odaklı yapısal kontrolü
This thesis proposes a complete procedure to obtain static output feedback (SOF) controllers for large scale discrete time linear time invariant (LTI) systems by considering two criteria: (1) use a small number of actuators and sensors, (2) calculate a SOF gain that minimizes a quadratic cost of the states and the input. If the considered system is observable and stabilizable, the proposed procedure leads to a SOF gain which has a performance comparable to the linear quadratic regulator (LQR) problem in terms of the $\mathcal{H}_2$ norm of the closed loop system. When the system is not observable but detectable, only the observable part is considered. Since the structure of input and output matrices for the LTI system have a significant importance for the success of the proposed algorithm, an optimal actuator/sensor placement problem is considered first. This problem is handled by taking the final goal of SOF stabilization into account. In order to formulate the actuator/sensor placement as an optimization problem, a method to calculate the generalized Gramians of unstable discrete time LTI systems is developed. The results are demonstrated on a large scale flexible system and a biological network model.
Sonsuz boyutlu sistemlerin frekans tepkisi versisinden indirgenmiş dereceli modellenmesi
In this thesis, a system identification method using frequency response data is studied. Identification method is applied to various types of distributed parameter systems, in particular flexible structures. One of the challenging tasks in the control of flexible structures is the estimation of the dominant modes (location of resonant frequencies and associated damping coefficients). In the literature, there are several studies where transfer functions of flexible structures are derived from PDEs (Partial Differential Equations); these are infinite dimensional models. In this study, a numerical method is proposed to identify the dominant flexible modes of a flexible structure with an input/output delay. The method uses a frequency domain approach (frequency response data) to estimate the resonating frequencies and damping coefficients of the flexible modes, as well as the amount of the time delay. A sequential NLLS (Non-Linear Least Squares) curve fitting procedure is adopted. Instead of optimizing over all available data collected on a frequency interval, a data selection scheme that increases the amount of data at each step is followed. Selecting relevant parts of data and optimizing sequentially increasing number of coefficients in every step is the essential part idea behind this approach. The optimization problem solved reduces to a curve fitting problem. It is illustrated that such a Newtonian optimization method has the capability of finding the parameters of a reduced order transfer function by minimizing a cost function involving nonlinearities such as exponential and rational terms. Further model reduction techniques can be applied by analyzing Hankel singular values of the resulting transfer function. Comparisons with other methods solving similar problems are illustrated with examples. Simulation results demonstrate efficiency of the proposed algorithm.
Kesirli dereceden bir sistem için h-infinity denetleç tasarimi
This work investigates the h-infinity optimal controller design for a fractional order system with time delay. For illustrative purposes, a magnetic suspension system model, derived by Knospe and Zhu is considered. The transfer function is infinite dimensional including exp(-hs) and a rational function of s^0.5, where h>0 represents the delay. Recently in a paper by Özbay, a formulation is given to design the h-infinity optimal controller for the mixed sensitivity minimization problem for unstable infinite dimensional plants with low order weights. This formulation is used to design the h-infinity optimal controller for the fractional order system considered, and it is compared to alternative computation methods for h-infinity control of infinite dimensional systems. To implement the controller, approximation methods are also investigated. Furthermore, finite dimensional rational approximation techniques of the fractional order integrator are evaluated for simulation purposes.
Sabi̇t di̇sk sürücülerde zaman geci̇kmeli̇ kafa konumlanması i̇çi̇n P ve PI kontrolcü tasarımı
In today's high performance positioning applications, due to stringent design objectives, it is very challenging to cope with input-output time delays. In Hard Disk Drive (HDD) servo system, the information flow between process and the controller is under a time delay. Typical state-space based modern control algorithms are not applicable to such in finite dimensional plants. In this thesis several control design objectives are considered and various types of stabilizing controllers are derived for this in nite dimensional plant. The objective of this thesis is to determine alternative simple (low order) controllers to the previously designed H1 controller and controllers designed from Pade approximations. For this purpose, six di erent P and PI controllers for the unstable in nite dimensional plant are obtained. Comparisons of the controllers with each other are done and advantages of every approach are demonstrated.
Kararsız sonsuz boyutlu ve zaman gecikmeli modeller için PD kontrolcü tasarımı
In real life, everything is in movement so there are always continuous transfers, transmissions and transports of people, materials, information and energy to other places. These transfers, transmissions and transports occur with a time delay. In control theory, time delays are encountered very commonly as in real life. By considering this fact, four unstable plants with time delays are considered from di fferent application perspectives and five delay values are chosen. For stabilization of these infi nite dimensional plants, PD controllers are designed by three diff erent design methods: two of them give di fferent least fragile PD controllers and the other design method gives a gain margin optimizing PD controller. Designed PD controllers and equivalent plants are put in feedback loop and robust performance test results and step responses are obtained and compared.
Zaman gecikmeli ölçümler altında H∞ süzgeç tabanlı hedef izleme
In this thesis target tracking problem for time delayed linear systems is studied. The standard mixed sensitivity problem is considered with time delayed continous time processes. Using the duality between control and filtering methods, the H∞ control problem is converted to H∞ filtering problem and a new H∞ optimal filtering approach is proposed. To investigate state estimation for target tracking, a typical vehicle model moving in 1-D is used but the proposed method can be expanded for movements in 3-D. Delay in both process and measurement is considered. The estimation of states and their performances are analyzed under different scenarios including change in delay, input pattern, noise parameters etc. The results obtained by H2 filter and simulation results are shown.
Zaman gecikmeli esnek robot kolu için birinci dereceden kontrolör tasarımı
In an earlier work, Gündeş et al. (2007), stabilizing PID controllers for a class of unstable plants with time delays (I/O delays) are obtained. By utilizing this approach and methods given in Özbay and Gündeş (2007, 2014) we aim to investigate appropriate PI, PD and PID controllers by finding the maximum allowable boundaries for each controller parameter. A model of a flexible robot arm which includes a time delay and an integrator is considered as an application example. It is aimed to find the optimal coefficients for the derivative and integral gains such that the designs achieve a set of performance and robustness objectives. Stability and robustness properties of the closed-loop system are also investigated. Specifically, for PD controller design, optimal derivative action gain is determined under various performance objectives. For PI controller design, optimal P (proportional) and D (derivative) gains are determined to achieve the least fragile integral action gain. Moreover, system performance is compared with other PID designs considering different types of control objectives.
Zaman gecikmeli ve integral eylemli sistemler için integral yığılması düzenleyici
Being one of the most popular saturation compensator methods, anti-windup mechanism is commonly used in various control applications. The problems arising from the system nonlinearities are prone to change the behaviors of the system adversely in time such as performance degradation or instability. Anti-windup schemes including internal model structure with the robust compensator are crucial in terms of preserving the system stability and minimizing the tracking error when controller operates at the limits of the actuator. Saturation problem is further aggravated by the dead-time that appears frequently in the systems depending on processing of sensed signals or transferring control signals to plants. Smith predictor based controllers are efficient in the compensation of time delay, indeed the controller is designed by eliminating the delay element from the characteristic equation of the closed-loop system. We apply Smith predictor based controller design for the system incorporating time delay and integral action to achieve high performance sinusoidal tracking. This study extends an anti-windup scheme via Smith predictor based controller approach by redesigning the transfer functions within the anti-windup structure. We present simulation studies on the plant transfer function including time delay and integrator to illustrate that our extended structure successfully accomplish accurate tracking under the saturation nonlinearity.
Yeni bir PI ve PID kontrolü tasarımı methodu ve TCP akışları için AQM tasarımı uygulaması
PID controllers are continuing to be used in many control applications due totheir simple structures. Design of such controllers for unstable systems with timedelays is an active research area. Recently, stabilizing PI and PD controllers fora class of unstable MIMO (multi-input multi-output) systems with input/outputdelays have been investigated and allowable controller gain intervals for suchcontrollers have been maximized. Motivated by these studies, this thesis proposesa new method for tuning the parameters of PI, PD and PID controllers forintegrating processes with time delays. The method is based on selecting thecenters of the maximized gain intervals as the controller gains for the purposeof obtaining optimal controllers. As an application of this method, controllersfor AQM (Active Queue Management) of TCP (Transmission Control Protocol)ï¬ows have been designed. AQM is a congestion control method used in computernetworks to increase link utilization with less queueing delays. The ï¬uid ï¬owmodel of TCP?s congestion avoidance mode based on delay diï¬erential equationssupplies the mathematical background for modelling the AQM as a feedbackcontrol system and designing diï¬erent control schemes accordingly. Firstly, theproposed controller design method has been applied to AQM for the case oftime invariant time delay and secondly the method has been supported withswitching control technique to obtain optimum system performance in the caseof time varying time delay. The performance of the designed controllers for bothcases has been illustrated by packet level simulations in ns-2.Keywords: PID control, time delay, Active Queue Management (AQM), switch-ing control, ns-2
İşbirlikli kontrolde görülen çok araçlı buluşma problemi için optimal bir çözüm
The multi-agent rendezvous problem appearing in cooperative control is considered in this thesis. There are variousapproaches to this topic as the objectives and problem set-ups vary in real-life rendezvous problems. Some of theapplications can be given as the coordination of autonomous mobile robots or unmanned air vehicles (UAVs) for jointtasks, and motion planning for vehicle convoys. The problem is basically on providing a rendezvous for mobile agentsat a specified or unspecified destination. What makes the topic interesting is maintaining a coordination between themobile agents so that the agents reach the rendezvous point simultaneously. Early or late arrivals are not desired.An energy optimal solution is obtained for the problem. Imperfectroad conditions, obstacles, internal problems of the agents or similar disturbancesare also tried to be handled. As these factors are included in the problem, it is assumed that theagents communicate between each other at specified time instants exchanginginformation about their expected arrival times in order to maintain a commonrendezvous time among the team.The solution is initially derived for rendezvous in one-dimensioned space. Then, the problemconfiguration is altered for two-dimensioned motions, and the target point is assumed to be moving in order to extend thesolution to possible practical applications. The effect of increasing disturbance on the control inputand time delays in the communication are also discussed.
Birinci dereceden zaman gecikmeli ve kararsız sistemler için PID denetleyici tasarımı
In this thesis, problem of designing P, PI and PD-like controllers for switched first order unstable systems with time delay is studied. For each type of controller, the problem is solved in two steps. First, the set of stabilizing controllers for the class of plants considered is determined using different approaches. Then, an appropriate controller inside this set is chosen such that the feedback systems satisfies a desired property, which is for example gain and phase margin maximization or the dwell time minimization. In the first part, we focus on PI controllers and tune the PI controller parameters in order to maximize the gain and phase margins. The observations in this part show that a P controller is adequate to maximize gain and phase margins. Then, we move on to the problem of tuning P, PI and PD-like (first order stable) controller parameters such that the switched feedback system is stabilized and the dwell time (minimum required time between consequent switchings to ensure stability) is minimized. For this purpose, a dwell-time based stability condition is used for the class of switched time delay systems. We show that a proportional controller can be found with this method, but a PI controller is not feasible. Finally, we focus on the design of PD-like controllers for switched first order unstable systems with time delays. The proposed method finds the values of PD-like (first order stable) controller parameters which minimize an upper bound of the dwell time. The conservatism analysis of this method is done by time domain simulations. The results show that the calculated upper bound for the dwell time is close to the lower bound of the dwell time observed by simulations. In addition, we compare the obtained PD-like controller results with some alternative PD and first order controller design techniques proposed in the literature.
Zaman gecikmeli geri bildirim içeren ısı denklemi için kararlılık analizi ve kontrolör tasarımı
In this thesis, the stability analysis for the system defined by the heat equation with time delayed feedback is performed. In the first part of the thesis, stability conditions in terms of LMI conditions which are obtained from the analysis in time domain, are explained. Necessary and sufficient conditions for stability are obtained using a frequency domain analysis. In the second part of the thesis, robust stability conditions are obtained for the system with parametric uncertainty. In the third part, an H? controller design procedure is given for this type of plants described by the heat equation with time delayed feedback. Finally, the results are illustrated with simulations.
Zaman gecikmeli iki dönüşsel biyolojik sistem modelinin analizi
In this thesis, we perform the stability analysis of two types of cyclic biological processes involving time delays.We analyze the genetic regulatory network having nonlinearities with negative Schwarzian derivatives.Using preliminary results on Schwarzian derivatives, we present necessaryconditions implying the global stability and existence of periodic solutionsregarding the genetic regulatory network.We also analyze homogenous genetic regulatory network and prove some stability conditions which only dependon the parameters of the nonlinearity function.In the thesis, we also perform a local stability analysis of a dynamical model of erythropoiesis whichis another type of cyclic system involving time delay.We prove that the system has a unique fixed point which is locally stable if the time delay is less than a certain criticalvalue, which is analytically computed from the parameters of the model.By the help of simulations, existence of periodic solutions are shown for delays greater than this critical value.
Gecikmeli pozisyon ve hız gerbeslemesine sahip haptik sistemler için kontrolcü tasarımı
Thisthesis considers controller design for haptic systems under delayed position and velocity feedback. More precisely, a complete stability analysis of a haptic system, where local dynamics are described by some second-order mechanical dynamics, is presented. Characteristic equation of this system with time delays involves quasi-polynomials. By a change of variables in the characteristic equation, stability conditions are obtained analytically and regions are plotted by using Matlab.Next, using two optimization techniques (H_infinity and stability margin optimization) optimal choice for the controller gains is proposed. H_infinity optimization minimizes tracking error between devices while avoiding large control action inputs. H_infinity analysis requires high computational cost for accurate results due to its dependency to frequency domain. On the other hand, stability margin optimization defines a cost function that expresses the trade-off between system bandwidth and robustness with low computational cost. The derived results are tested on an three degree-of-freedom real-time experimental platform to illustrate the theoretical results. Finally robustness analysis is performed for optimal parameters to find allowable delay perturbations.
Gen düzenleyici ağ modelleri ve onların kararlılık analizi üzerine denemeler
Gene expression is one of the core areas in comprehending and assessing how biological cells work. Gene regulatory networks (GRNs), representing the intricate mechanism between genes and their regulatory modules, are instrumental in controlling gene expression and cell functions. These models shed light on how transcription factors interact with their regulatory modules within a cell. Despite the multitude of studies focusing on the analysis and enhancement of GRNs, there is still room for contributions. This thesis investigates a novel framework inspired by the gene networks constructed using synthetic biology, and presents stability analyses of the nonlinear infinite dimensional dynamical system models arising in this framework. In the first part of the thesis, we extend a previously studied benchmark GRN model including time delay, and present an analysis of the extended framework. We utilize unmodeled dynamics and possibly ignored interactions, including higher-order dynamics, in our system design. The stability of the extended system is analyzed by considering various nonlinearity functions and design parameters, and the results are compared with those of the benchmark original model. In the second part, we employ an extension of a gene network model using a multiplicative perturbation of the dynamical system. Each cascaded subsystem in this extended framework has an additional block, including a multiplicative term with a high-pass filter, and the effect of additional parameters on the robustness and delay margin of the system is investigated. Experiments with various design parameters yield that the stability characteristics of GRNs can be improved using the model pertaining to the extension under specific perturbations. Finally, the third part covers the analysis of nonlinear dynamics and chaos in GRNs, particularly focusing on the two-gene original and extended gene networks. Chaotic dynamics depend strongly on the inclusion of time delays, but the circuit motifs that show chaos differ when both original and extended models are considered. Our results suggest that for a particular higher-order extension of the gene network, it is possible to observe the chaotic dynamics in a two-gene system without adding any self-inhibition. This finding can be explained as a result of the modification of the original benchmark model induced by unmodeled dynamics. We argue that regulatory gene circuit models with additional parameters demonstrate non-periodic dynamics much more easily.