Browsing by Subject "Control theory."

Now showing 1 - 20 of 24

Open Access
Algebraic theory of linear multivariable control systems
(1998) Çetin, Sevgi Babacan
The theory of linear multivariable systems stands out as tlie most developed and sophisticated among the topics of system theory. In the literature, many different solutions are presented to the linear midtivariable control problems using three main approaches : geometric approacli, fractional approach and polynomial model based approach. This thesis is a first draft for a textbook on linear multivariable control which contains a description of solutions to the most of the standard algebraic feedback control problems using simple linear algebra and a minimal amount of polynomial algebra. These problems are internal stabilization, disturbance decoupling by state feedback and measurement feedback, output stabilization, tracking with regulation in a scalar system, regulator problem with a single output channel and decentralized stabilization.
Open Access
Application of Gauss-Seidel method and singular value decomposition techniques to recursive least squares algorithm
(1991) Malaş, Atilla
System identification algorithms are utilized in many practical and theoretical applications such as parameter estimation of sj'stems, adaptive control and signal processing . Least squares algorithm is one of the most popular algorithms in system identification, but it has some drawbacks such as large time consumption and small convergence rates. In this thesis, Gauss-Seidel method is implemented on recursive least squares algorithm and convergence behaviors of the resultant algorithms are analyzed. .Also in standard recursive least squares algorithm the excitation of modes are monitored using data matrices and this algorithm is accordingly altered. A parallel scheme is proposed in this analysis for efficient computation of the modes. The simulation results are also presented.
Open Access
Approximate dynamic programming approach for sequential change diagnosis problem
(2013) Akbulut, Elif
We study sequential change diagnosis problem which is the combination of change diagnosis and multi-hypothesis testing problem. One observes a sequence of independent and identically distributed random variables. At a sudden disorder time, the probability distribution of the random variables change. The disorder time and its cause are unavailable to the observer. The problem is to detect this abrupt change in the distribution of the random process as quickly as possible and identify its cause as accurately as possible. Dayanık et al. [Dayanık, Goulding and Poor, Bayesian sequential change diagnosis, Mathematics of Operations Research, vol. 45, pp. 475-496, 2008] reduce the problem to a Markov optimal stopping problem and provide an optimal sequential decision strategy. However, only a small subset of the problems is computationally feasible due to curse of dimensionality. The subject of this thesis is to search for the means to overcome the curse of dimensionality. To this end, we propose several approximate dynamic programming algorithms to solve large change diagnosis problems. On several numerical examples, we compare their performance against the performance of optimal dynamic programming solution.
Open Access
Computation of the optimal H∞ controller for a fractional order system
(2014) Karagül, Abidin Erdem
This work investigates the H∞ 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 e −hs and a rational function of √ s, where h > 0 represents the delay. Recently in a paper by Ozbay, a formulation is given to design the ¨ H∞ 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∞ optimal controller for the fractional order system considered, and it is compared to alternative computation methods for H∞ 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.
Open Access
Controller design for haptic systems under delayed position and velocity feedback
(2012) Koru, Ahmet Taha
This thesis 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 quasipolynomials. 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∞ and stability margin optimization) optimal choice for the controller gains is proposed. H∞ optimization minimizes tracking error between devices while avoiding large control action inputs. H∞ 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 a 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
Open Access
Effects of endogenous depreciation on the optimal timing of technology adoption
(2006) Karaşahin, Ramazan
In this thesis, we use two stage optimal control techniques to analyze optimal timing of technology adoption under embodied technical change taking into account the endogenous nature of depreciation. We show that a more efficient maintenance service reducing the depreciation rate postpones the optimal timing of technology adoption. In this respect, we study to what extent can maintenance of the existing capital stock be a substitute for adoption of new technologies.
Open Access
Exact and approximate decoupling and noninteracting control problems
(1989) Akar, Nail
In this thesis, we consider “exact” and “approximate” versions of the disturbance decoupling problem and the noninteracting control problem for linear, time-invariant systems. In the exact versions of these problems, we obtain necessary and sufficient conditions for the existence of an internally stabilizing dynamic output feedback controller such that prespecified interactions between certain sets of inputs and certain sets of outputs are annihilated in the closed-loop system. In the approximate version of these problems we require these interactions to be quenched in the ‘Hoo sense, up to any degree of accuracy. The solvability of the noninteracting control problems are shown to be equivalent to the existence of a common solution to two linear matrix equations over a principal ideal domain. A common solution to these equations exists if and only if the equations each have a solution and a bilateral matrix equation is solvable. This yields a system theoretical interpretation for the solvability of the original noninteracting control problem.
Open Access
High-gain sampled-data control of interconnected systems
(2002) Altunel, Haluk
Stabilization of interconnected systems using adaptive, decentralized, high-gain, sampled-data controllers is considered. Main applications of high-gain methodology to various systems under modeling uncertainties are reviewed. Then, sampled-data, high-gain and decentralized control techniques are combined to nd a solution to stabilization of interconnected systems, while satisfying the overall synchronization of the whole system. It is shown that overall system can be stabilized in continuous and discrete time domains by applying an adaptation mechanism for perturbations with unknown bounds.
Open Access
Identification of some nonlinear systems by using least-squares support vector machines
(2010) Yavuzer, Mahmut
The well-known Wiener and Hammerstein type nonlinear systems and their various combinations are frequently used both in the modeling and the control of various electrical, physical, biological, chemical, etc... systems. In this thesis we will concentrate on the parametric identification and control of these type of systems. In literature, various identification methods are proposed for the identification of Hammerstein and Wiener type of systems. Recently, Least Squares-Support Vector Machines (LS-SVM) are also applied in the identification of Hammerstein type systems. In the majority of these works, the nonlinear part of Hammerstein system is assumed to be algebraic, i.e. memoryless. In this thesis, by using LS-SVM we propose a method to identify Hammerstein systems where the nonlinear part has a finite memory. For the identification of Wiener type systems, although various methods are also available in the literature, one approach which is proposed in some works would be to use a method for the identification of Hammerstein type systems by changing the roles of input and output. Through some simulations it was observed that this approach may yield poor estimation results. Instead, by using LS-SVM we proposed a novel methodology for the identification of Wiener type systems. We also proposed various modifications of this methodology and utilized it for some control problems associated with Wiener type systems. We also proposed a novel methodology for identification of NARX (Nonlinear Auto-Regressive with eXogenous inputs) systems. We utilize LS-SVM in our methodology and we presented some results which indicate that our methodology may yield better results as compared to the Neural Network approximators and the usual Support Vector Regression (SVR) formulations. We also extended our methodology to the identification of Wiener-Hammerstein type systems. In many applications the orders of the filter, which represents the linear part of the Wiener and Hammerstein systems, are assumed to be known. Based on LS-SVR, we proposed a methodology to estimate true orders
Open Access
Inverse optimal control and positive real systems
(1997) Ünal Yılmaz
In this thesis an inverse optimal control problem for constant output feedbacks is investigated. Necessary and sufficient conditions for optimality of an output feedback are derived for single-input, single-output systems. The class of systems with members for which any constant positive output feedback is optimal turns out to be precisely the class of positive real systems. It is also shown that for a class of minimum phase systems all “large” positive gains are optimal.
Open Access
Linear quadratic control for harmonic signals
(2001) Köroğlu, Hakan
Open Access
On the s-procedure and some variants
(2004) Derinkuyu, Kürşad
In this thesis, we deal with the S-procedure that corresponds to verifying that the minimum of a quadratic function over constraints consisting of quadratic functions is positive. S-procedure is an instrumental tool in control theory and robust optimization analysis. It is also used in linear matrix inequality (or semi definite programming) reformulations and analysis of quadratic programming. We improve an error bound in the Approximate S-Lemma used in establishing levels of conservatism results for approximate robust counterparts. Moreover we extend the S-procedure and obtain some general results in this field. Finally, we get a bound similar to Nesterov’s bound for trust region subproblem, which consists in minimizing an indefinite quadratic function subject to a norm-1 constraint by using the Approximate S-Lemma.
Open Access
An optimal solution for the multi-agent rendezvous problem appearing in cooperative control
(2008) Kölmek, Fatih
The multi-agent rendezvous problem appearing in cooperative control is considered in this thesis. There are various approaches to this topic as the objectives and problem set-ups vary in real-life rendezvous problems. Some of the applications can be given as the coordination of autonomous mobile robots or unmanned air vehicles (UAVs) for joint tasks, and motion planning for vehicle convoys. The problem is basically on providing a rendezvous for mobile agents at a specified or unspecified destination. What makes the topic interesting is maintaining a coordination between the mobile 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. Imperfect road conditions, obstacles, internal problems of the agents or similar disturbances are also tried to be handled. As these factors are included in the problem, it is assumed that the agents communicate between each other at specified time instants exchanging information about their expected arrival times in order to maintain a common rendezvous time among the team. The solution is initially derived for rendezvous in one-dimensioned space. Then, the problem configuration is altered for two-dimensioned motions, and the target point is assumed to be moving in order to extend the solution to possible practical applications. The effect of increasing disturbance on the control input and time delays in the communication are also discussed.
Open Access
Optimal timing of an energy saving technology adoption
(2011) Harmankaya, Mehmet Fatih
In this thesis, we use two stage optimal control techniques to analyze the optimal timing of energy saving technology adoptions. We assume that the physical capital goods sector is relatively more energy intensive than consumption goods sector. First, we solve a benchmark problem without exogenously growing energy saving technology frontier. In such a case, the economy sticks either to the initial technology or immediately switches to a new technology, depending on the growth rate advantage compared to the obsolescence and adjustment costs. In the second step, we introduce exogenously growing energy saving technology frontier. The anticipated level of the technology provides incentives to delay the adoption and generates an interior switching time. Finally, we analyze numerically the e§ects of the speed of adjustment to the new technology, growth rate of technology, subjective time preference and planning horizon on the optimal timing of technology adoption.
Open Access
Output regulation for all-pole and minimum phase LTI
(2010) Saldı, Naci
In this thesis, the problem of enabling the output of a system to track the reference signals and reject the disturbances created by the same exogenous system is considered. This problem is widely known as Output Regulation Problem. Firstly, we propose a method for all-pole LTI systems by using relative degree property and then we apply the same method for minimum phase LTI systems along with some modifications. In order to obtain controllers for a minimum phase LTI case, the system is converted into an all-pole system by employing the inverse system as the first part of the controller. Then using the method that we used in all-pole cases, we obtain the second part of the controller. Combining these two controllers gives us an overall controller which solves the output regulation problem. This method for LTI systems is then extended to all-pole and minimum phase LTV systems. However, in order to apply the same methodology we have to make some assumptions on LTV systems. For minimum phase cases, the normal form is obtained by applying certain Lyapunov transformations and then minimum phaseness is defined in accordance with the normal form. Furthermore we show that, similar to minimum phase LTI cases, pole / zero cancelations occur between the inverse system and the original system in minimum phase LTV cases. The method that we develop depends on analytical calculation of the controller and gives a certain degree of freedom to change the transient behavior of the system by only changing some controller parameters.
Open Access
Parameter optimized controller design based on frequency domain identification
(1995) Köroğlu, Hakan
Recently, there has been a great tendency towards the development of iterative design methodologies combining identification with control in a mutually supportive fashion. In this thesis, we develop such an algorithm utilizing nonparametric frequency domain identification methods in order to realize the online iterative design of parameter optimized controllers for a system of unknown dynamics. The control design is based on the minimization of LQG (Linear Quadratic Gaussian) cost criterion with a two-degree of freedom control system. This is achieved by the approximation of an optimality relation, which is derived for a particular parametrization of one of the controllers, using the frequency domain transfer function estimates and application of this together with a numerical optimization algorithm. It is shown that, if the first controller is a FIR filter of length greater than or equal to two times the number of frequencies present in the reference input, the designed control system is optimal independent of the stabilizing second controller.
Open Access
PID controller design for first order unstable time delay systems
(2009) Arslan, Gül Ezgi
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 of [39] 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.
Open Access
Ripple-free deadbeat control of sampled-data systems
(1990) Mumcuoğlu, Erkan Ünal
In this thesis, we consider the ripple-free deadbeat control problem for linear, multivariable sampled-data systems represented by state-space models. Existing results concerning the deadbeat/ripple-free deadbeat regulation and tracking problems are based on controller configurations of either constant state-feedback or discrete dynamic output feedback. In the thesis, the problem is analyzed for two new sampled-data controllers, namely, generalized sampled-data hold functions and multirate-output controllers. Some necessary and sufficient solvability conditions for the problem are stated by theorems in time-domain and frequency domain in terms of the open-loop system parameters. Several special cases are also considered as corollaries.
Open Access
Robust sampled data control
(1990) Ocalı, Ogan
Robust control of uncertain plants is a major area of interest in control theory. In this thesis, robust stabilization of plants under a class of structural perturbations using sampled-data controllers is considered. It is shown that a controllable system under bounded perturbations that satisfy matching conditions can be stabilized using high-gain sampled-data control, provided that the sampling period is sufficiently small. This result is then applied to robust stabilization of interconnected systems using decentralized sampled-data control, where both single-rate and multi-rate sampling schemes are considered.
Open Access
Robust sampled-data control
(1995) Ocalı, Ogan
Robust control of uncertain plants is a major area of interest in control theory. In this dissertation, robust stabilization of plants under various classes of structural perturbations using sampled-data controllers is considered. It is shown that a controllable system under bounded perturbations that satisfy certain structural conditions can be stabilized using high-gain sampled-data state feedback control, provided that the sampling period is sufficiently small, with generalizations to decentralized control of interconnected systems. This result is then modified so as to enable adapting the gain and the sampling periods of controllers online. Finally another design methodology is given which enables the controllers to operate on the sampled values of output only, instead of full state measurements.