Sharif Digital Repository

The averaged switch modeling approach is a powerful method for representing the behavior of a wide variety of converters through equivalent circuits. The model is not linear and it is common to perform a small signal linearization about an operating point and design a linear controller. Models obtained with such method involve considerable approximation and produce results that are limited for high performance controller designs. In this paper a piecewise affine approximation technique is introduced for modeling PWM converters. This model is much more precise in predicting the dynamic response of averaged nonlinear model comparing the linear model. This paper also presents a piecewise linear... 

Recently, moment dual approach of sums of squares relaxations developed for polynomial optimization problems was successfully extended to optimization problems with polynomial matrix inequality constraints. In this paper, we first derive an efficient polynomial formulization for matrix rank minimization problem which does not add any slack variable or additional equality or inequality constraint. Using the aforementioned theory, then we propose a hierarchy of convex LMI relaxations to provide a sequence of increasingly tight lower bounds on the global minimum rank of an arbitrary matrix under linear and polynomial matrix inequality constraints. Surprisingly enough, these lower bounds are... 

An application of a new controller order reduction technique with stability and performance preservation based on linear matrix inequality optimization to an active suspension system is presented. In this technique, the rank of the residue matrix of a proper rational approximation of a high-order H∞controller subject to the H∞-norm of a frequency-weighted error between the approximated controller and the high-order H∞ controller is minimized. However, because solving this matrix rank minimization problem is very difficult, the rank objective function is replaced with a nuclear-norm that can be reduced to a semidefinite program so that it can be solved efficiently. Application to the active... 

The practicality of robust model predictive control of systems with model uncertainties depends on the time consumed for solving a defined optimization problem. This paper presents a method for the computational complexity reduction in a robust model predictive control. First a scaled state vector is defined such that the objective function contours in the defined optimization problem become vertical or horizontal ellipses or circles, and then the control input is determined at each sampling time as a state feedback that minimizes the infinite horizon objective function by solving some linear matrix inequalities. The simulation results show that the number of iterations to solve the problem... 

This paper presents a new robust control strategy for an islanded microgrid in the presence of load unmodeled dynamics. The microgrid consists of parallel connection of several electronically interfaced distributed generation units and a local load. The load is parametrically uncertain and topologically unknown and, thus, is the source of unmodeled dynamics. The objective is to design a robust controller to regulate the load voltage in the presence of unmodeled dynamics. To achieve the objective, the problem is first characterized by a two-degree-of-freedom (2DOF) feedback-feedforward controller. The 2DOF control design problem is then transformed to a nonconvex optimization problem.... 

This paper is concerned with the disturbance attenuation problem of fuzzy large-scale systems which consist of N interconnected subsystems which are represented by Takagi-Sugeno fuzzy models. Using Lyapunov function and linear matrix inequalities (LMIs), a criterion is proposed to have a prescribed level of disturbance attenuation. A numerical example is given to illustrate the control design procedure and its effectiveness  

Single-phase power factor correction (PFC) converter circuits are non-linear systems due to the contribution of their multiplier. This non-linearity causes difficulties in analysis and design. Models that reduce the system to a linear system involve considerable approximation, and produce results that are susceptible to instability problems. In this paper a piecewise affine (PWA) system is introduced for describing the nonlinear averaged model. Then robust output feedback controllers are established in terms of the linear matrix inequality (LMI). Simulation and experiments results show the effectiveness of the proposed control method  

In this paper, a new model reference adaptive controller (MRAC) for uncertain switched linear systems is developed. A class of uncertain switched linear systems with parametric mismatched and input matched uncertainties, control input effectiveness and unmodeled dynamics is studied in this paper. The difference in input matrix for different switching modes which means the input channel degradation is investigated through this paper. By using common Lyapunov function method and developing new linear matrix inequality based sufficient conditions, uniform ultimate boundedness of the reference tracking error is guaranteed by switched MRAC and by using a novel nonlinear controller term, the size... 

Using a non-linear model in model predictive control (MPC) changes the control problem from a convex quadratic programme to a non-convex non-linear problem, which is much more challenging to solve. In this study, we introduce an MPC algorithm for non-linear discrete-time systems. The systems are composed of a linear constant part perturbed by an additive state-dependent non-linear term. The control objective is to design a state-feedback control law that minimises an infinite horizon cost function within the framework of linear matrix inequalities. In particular, it is shown that the solution of the optimisation problem can stabilise the non-linear plants. Three extensions, namely,... 

Time-delay in sensor measurements can be a frequent cause of instability and performance degradation in a robotic system. In this paper, motion tracking of rigid manipulators in presence of constant and known delay in sensors is investigated. By using non-minimal model of a manipulator, a dynamically smooth controller based on the Linear Matrix Inequality (LMI) approach is proposed which guarantees asymptotic tracking of desired joint angles and velocities in presence of delayed measurements. For a given controller the maximum amount of delay that preserves system stability is computed by solving an LMI optimization and also by numerical simulations, and the results are compared. Finally, a... 

In this paper, a model-based fuzzy controller for attitude stabilization of a Quadrotor is proposed. To achieve this purpose first a Takagi-Sugeno fuzzy model for Quadrotor which is obtained from dynamic model is presented. Parallel Distributed Compensation (PDC) technique is utilized to design a state feedback controller. The purpose of control is to stabilize the Quadrotor while taking into account performance specifications such as decay rate and constraint on the input. Both of these conditions can be represented in term of linear matrix inequalities (LMIs). By simultaneously solving these LMIs a stabilizing fuzzy controller that achieves desired speed of response and small control... 

This paper presents a robust model predictive control algorithm with a time-varying terminal constraint set for systems with model uncertainty and input constraints. In this algorithm, the nonlinear system is approximated by a linear model where the approximation error is considered as an unstructured uncertainty that can be represented by a Lipschitz nonlinear function. A continuum of terminal constraint sets is constructed off-line, and robust stability is achieved on-line by using a variable control horizon. This approach significantly reduces the computational complexity. The proposed robust model predictive controller with a terminal constraint set is used in tracking set-points for... 

The turbine control system is one of the key control loops in the dynamic performance of steam power generation units. In this paper a multivariable PID controller is designed for the governing system of steam turbine power generators. The necessary and sufficient conditions for existence of a strong robust H ∞ dynamic compensator are established in terms of linear matrix inequality (LMI) approach. This controller is designed in succeeding to the existing proportional controller in a power plant. To reach to this goal, the complete dynamic model of an actual turbine-generator including the governor, turbine and generator, are derived. Simulation results show that proposed controller has good... 

This paper proposes a novel representation of uncertain LTI fractional order systems based on the state-space model which contains both interval and polytopic uncertainties. First, a set of linear matrix inequalities, which are sufficient conditions, are presented for analyzing the robust stability of the mentioned systems. Then, some sufficient conditions are obtained for designing a feedback gain matrix to tackle the robust stabilization of the considered systems. Note that the concluded conditions of this paper are valid for fractional systems with a given constant derivative order α in 1 ≤ α < 2 and also, can be employed conservatively for α in 0 < α < 1. Finally, through two numerical... 

This paper presents some computationally efficient algorithms for online tracking of set points in robust model predictive control context subject to state and input constraints. The nonlinear systems are represented by a linear model along with an additive nonlinear term which is locally Lipschitz. As an unstructured uncertainty, this term is replaced in the robust stability constraint by its Lipschitz coefficient. A scheduled control technique is employed to transfer the system to desired set points, given online, by designing local robust model predictive controllers. This scheme includes estimating the regions of feasibility and stability of the related equilibriums and online switching... 

In this paper, a decentralized model predictive control approach is proposed for discrete linear systems with a high number of inputs and states. The system is decomposed into several interacting subsystems. The interaction among subsystems is modeled as external disturbances. Then, using the concept of robust positively invariant ellipsoids, a robust model predictive control law is obtained for each subsystem solving several linear matrix inequalities. Maintaining the recursive feasibility while considering the attenuation of mutual coupling at each time step and the stability of the overall system are investigated. Moreover, an illustrative simulation example is provided to demonstrate the... 

This paper deals with the stabilization of the feasible equilibrium point of a special class of nonlinear quadratic systems known as Lotka-Volterra (LV) systems, in the presence of interval uncertainty via a fixed linear state feedback (FLSF). It is well known that for a linear time-invariant system with interval uncertainty, stability at the vertices of a polytope implies stability in the interior of the whole polytope. It has been shown that this idea can be extended to examine the stability of LV systems in the presence of interval uncertainty, recently. In fact, it has been proved that in spite of nonlinear nature of the system, stability at a special vertex guarantees stability at all... 

This paper considers the problem of high-performance global stabilization of an integrator chain via a bounded control at the presence of input disturbance. While nested saturated feedback (NSF) is known as the most inspiring existing solution in the literature, we shall highlight the inherent shortcomings of this approach which cause a poor performance in terms of convergence rate. Then, a novel dual-mode control scheme combining an improved NSF law with a linear matrix inequality (LMI)-based model predictive controller (MPC) is developed to overcome the weaknesses of pure NSF. By offline calculations, a set of nested robust invariant attraction regions and their attributed feedback gains... 

In this study, an auxiliary damping controller based on a robust controller considering the active and reactive power control loops for a doubly-fed induction generator for wind farms is proposed. The presented controller is able to improve the inter-area oscillation damping. In addition, the proposed controller applies only one accessible local signal as the input; however, it can improve the inter-area oscillation damping and, consequently the system stability for the various working conditions and uncertainties. The oscillatory modes of the system are appointed using the linear analysis. Then, the controller’s parameters are determined using the robust control approaches (H∞/ H2) with the...