Control
Zahra Shabani; Haleh Tajadodi
Abstract
In this paper, a numerical technique is proposed to solve optimal control problems (OPCs) of Volterra integral equations (VIEs). We apply the linear B-spline polynomials to solve OPCs by VIEs. The B-spline function divides the interval into sub-intervals and then built a different approximating polynomial ...
Read More
In this paper, a numerical technique is proposed to solve optimal control problems (OPCs) of Volterra integral equations (VIEs). We apply the linear B-spline polynomials to solve OPCs by VIEs. The B-spline function divides the interval into sub-intervals and then built a different approximating polynomial on each sub-interval. In this method, optimal trajectory and control functions are expanded in terms of B-spline functions. The linear B-spline operational matrix of integration and multiplication are utilized in the proposed method.The main characteristic this method is that by using the suggested numerical technique and the related operational matrices, optimal control problem governed by Volterra integral equations is converted to a system of equations. Suffice it to say that this scheme simplifies The main problems and also makes to obtain a good approximate solution for them. In the end, there are two illustrative examples which numerical results show the validity and applicability of our method.
Control
Mohamad Hosein Shafiei; Nasrollah Azam Baleghi
Abstract
This paper considers the stability problem of discrete-time switched linear systems in the presence of parametric uncertainties. Parametric uncertainty is sometimes called structured uncertainty because of the structure of the model is known, but some of the parameters are uncertain. From the practical ...
Read More
This paper considers the stability problem of discrete-time switched linear systems in the presence of parametric uncertainties. Parametric uncertainty is sometimes called structured uncertainty because of the structure of the model is known, but some of the parameters are uncertain. From the practical viewpoint, it is important to investigate the robust stability conditions of uncertain switched systems. Therefore, under the assumption of knowing the structure of the uncertainty matrix and based on the common Lyapunov function for the nominal switched system, sufficient conditions for robust exponential stability of the discrete-time uncertain switched system (under any switching signal) are derived. Sufficient conditions are formulated in terms of matrix inequalities for fixed values of some parameters which may be solved via LMI techniques based on numerical methods. Moreover, a procedure is proposed to determine the maximum admissible bounds of the uncertain parameters which characterize the exponential stability of the uncertain switched system. Finally, numerical examples are provided to verify the theoretical results.
Control
Shoorangiz Shams shamsabad Farahani; Siavash Fakhimi Derakhshan
Abstract
In this paper buffer dynamic modeling for wireless sensor networks (WSNs) as a highly nonlinear system is accomplished in discrete time and the overall model is gained by blending subsystems obtained based on delay. Based on queue utilization and channel estimation algorithm, congestion is detected and ...
Read More
In this paper buffer dynamic modeling for wireless sensor networks (WSNs) as a highly nonlinear system is accomplished in discrete time and the overall model is gained by blending subsystems obtained based on delay. Based on queue utilization and channel estimation algorithm, congestion is detected and a suitable rate is selected by an adaptive back-off interval selection. In this paper, a new approach is proposed for controller synthesis of our system based on non-quadratic Lyapunov functions, and a controller is designed to stabilize each subsystem. The controller synthesis results are expressed as a set of Linear Matrix Inequalities (LMIs). Moreover, the performance is considered and decay rate is guaranteed. Finally, a set of new LMI-based congestion control schemes (LCC) is obtained for WSNs. The closed-loop systems are globally asymptotically stable (GAS) in case of delay changes resulted from queue size changes. The simulation results using MATLAB and OPNET simulator confirm the effectiveness of our proposed schemes.
Control
Saeed Tavakoli; Hamid Fasih; Jafar Sadeghi; Hamed Torabi
Abstract
In this paper, a novel centralized controller is presented to control multi-input multi-output industrial processes with heavy interactions and significant time-delays. The system model equations are represented in a non-minimal stochastic state-space form. Also, the state and measurement equations respectively ...
Read More
In this paper, a novel centralized controller is presented to control multi-input multi-output industrial processes with heavy interactions and significant time-delays. The system model equations are represented in a non-minimal stochastic state-space form. Also, the state and measurement equations respectively use smoothed random walk model and finite impulse response model of the plant. To design the controller, a quadratic cost function is considered. A standard Kalman filter algorithm is used to estimate the state vector of the controller and solve to the discrete algebraic Riccati equation simultaneously. By using the smoothing parameter, the controller behavior can be changed between the Kalman filter random walk controller and the Kalman filter integrated random walk controller. To evaluate the effect of the smoothing parameter the proposed controller is first applied to a single input single output system. Then an industrial-scale polymerization reactor which has the two-input and two-output system is used to investigate the performance of the designed controller. The simulation results indicate that the controller has a good performance in tracking the set point and robust due to changing the system parameters.
Control
Gholamreza Bidari; Naser Pariz; Ali Karimpour
Abstract
This paper investigates the stabilization problem of an autonomous Linear Time Invariant (LTI) switched system with interval uncertainty and unstable subsystems. It is proved that the system would be stable by using a common Lyapanov function whose derivative is negative and bounded by a quadratic function ...
Read More
This paper investigates the stabilization problem of an autonomous Linear Time Invariant (LTI) switched system with interval uncertainty and unstable subsystems. It is proved that the system would be stable by using a common Lyapanov function whose derivative is negative and bounded by a quadratic function within activation regions of each subsystem. First, a sufficient condition for the stability of an Linear Time Invariant switched system with interval uncertainty, based on the convex analysis and interval set theoretical approach, is presented and proved. Moreover, conservatism in the stability robustness bound is obtained. Then, a switching control law is designed to shift the Linear Time Invariant switched system among subsystems to ensure the decrease of the Lyapanov function within the state space. Finally, in order to decrease the switching frequency and to avoid chattering, the switching law is modified. Two examples are included to demonstrate the effectiveness of the theoretical findings.
Control
Khadijeh Akbari; Behrooz Rezaie; Safa Khari
Abstract
In this paper, a full-order sliding mode controller, based on adaptive neuro-fuzzy inference system is proposed as approximator, for controlling nonlinear chaotic systems in presence of uncertainty. At first, the full-order sliding mode controller is designed for the system in the absence of uncertainty ...
Read More
In this paper, a full-order sliding mode controller, based on adaptive neuro-fuzzy inference system is proposed as approximator, for controlling nonlinear chaotic systems in presence of uncertainty. At first, the full-order sliding mode controller is designed for the system in the absence of uncertainty such that the system states are converged to the sliding surface. Then, adding uncertainty to system equations, convergence of the method is illustrated using simulations. By assuming that a part of the system dynamics is uncertain and only input-output data is partly available, adaptive neuro-fuzzy inference system is used in off-line mode to approximate the uncertain dynamics of the system based on input-output data. The proposed method can effectively solve the problems of the sliding-based methods, such as chattering phenomenon and singularity. The simulation results, applied to the well-known nonlinear systems namely PMSM and plasma torch systems when they behave in chaotic mode, demonstrate effectiveness and fidelity of the proposed control method.
Control
amin ramezani; Seyed Arash Pourhashemi Shahri; Mahdi Siahi
Abstract
This paper deals with the problem of synchronization (anti-synchronization) of fractional nonlinear systems. Here, due to the advantages of fractional calculus and sliding mode control, we provide a new fractional order sliding mode control for synchronization (anti-synchronization) problems. So, in ...
Read More
This paper deals with the problem of synchronization (anti-synchronization) of fractional nonlinear systems. Here, due to the advantages of fractional calculus and sliding mode control, we provide a new fractional order sliding mode control for synchronization (anti-synchronization) problems. So, in this paper a novel sliding surface is introduced and with and without the existence of uncertainties and external disturbances, finite-time synchronization is achieved by designing a new fractional sliding mode control. This method applied to the class of fractional order nonlinear systems and sufficient conditions for achieving synchronization/anti-synchronization are derived by the use of fractional Lyapunov theory. The method is perform on different fractional order nonlinear chaotic system which confirm the applicability of the method. Here, we bring two of them for confirmation. That is to say, to show the effectiveness and robustness of the proposal, we applied our method on two identical fractional order permanent magnet synchronous machine to verify the efficacy.
Control
Mir Mohammad Khalilipour; Farhad Shahraki; Jafar Sadeghi; kiyanoosh Razzaghi
Abstract
The paper presents the computer simulation of a multivariate control algorithm. Industrial relevance is given as the problem is derived from a real plant, an industrial athmospheric distillation column at Shiraz refinery. The control performance of the industrial column using relative gain array (RGA) ...
Read More
The paper presents the computer simulation of a multivariate control algorithm. Industrial relevance is given as the problem is derived from a real plant, an industrial athmospheric distillation column at Shiraz refinery. The control performance of the industrial column using relative gain array (RGA) and relative normalized gain array (RNGA) configurations has been examined for nominal operating capacity and 10% increase in capacity. The results show that RNGA structure remains stable and has an acceptable control performance for both nominal and increased capacity. RGA structure unlike RNGA changes at the increased capacity and has some difficulties in crude oil switch scenario. It has also been shown that the furnace duty will increase considerably in the case of using RGA for operating at increased capacity. The results indicate that RNGA represents better decision for loop pairing and control structure selection and can solve control issues of industrial distillation column specifically for uncertain feed condition.
Control
Saeed Tavakoli; Amir Afroomand
Abstract
For a two-input two-output distillation column with heavy interactions and long dead times, a two-by-two PI/PID controller is designed. The design objectives are good setpoint regulation and appropriate load disturbance rejection. The constraints are on degree of robust stability, control effort as well ...
Read More
For a two-input two-output distillation column with heavy interactions and long dead times, a two-by-two PI/PID controller is designed. The design objectives are good setpoint regulation and appropriate load disturbance rejection. The constraints are on degree of robust stability, control effort as well as peaks of the maximum singular value of sensitivity and complementary sensitivity matrices. As this set of design objectives and constraints is often conflicting, a more flexible control structure, a two-degree-of-freedom scheme, is proposed. The design problem is formulated as a constrained optimization problem and is solved by a powerful random-search optimization technique, the so-called vector-based swarm optimization. Next, the performance of the proposed method in controlling a Wood and Berry distillation column is evaluated and compared with that of several well-known design techniques. Because of using a flexible control structure, a powerful optimization algorithm and a comprehensive set of design requirements, the proposed control strategy performs well in coping with conflicting design objectives.
