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1.
This paper addresses the optimal control problem for a linear system with respect to a Bolza–Meyer criterion with a non-quadratic non-integral term. The optimal solution is obtained as a sliding mode control, whereas the conventional linear feedback control fails to provide a causal solution. Performance of the obtained optimal controller is verified in the illustrative example against the conventional LQ regulator that is optimal for the quadratic Bolza–Meyer criterion. The simulation results confirm an advantage in favor of the designed sliding mode control.  相似文献   

2.
This paper presents the sliding mode mean-square and mean-module controllers for linear stochastic systems with unknown parameters. In both cases, the controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. Performance of the obtained controllers is verified in the illustrative example against the sliding mode mean-square and sliding mode controllers that are optimal for linear systems with known parameters. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.  相似文献   

3.
This paper describes the design and implementation of digital controllers for a flywheel energy storage device that incorporates a radial flux hybrid permanent magnetic bearing. Although the uncontrolled device is asymptotically stable, active control is required to: (i) ensure that a finite radial air gap is maintained at all times, and (ii) attenuate the oscillations of the flywheel which reduce the efficiency of the motor generator. The paper presents the design of gain scheduled discrete time linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controllers for this rotordynamic system. Real time experiments are conducted to investigate the performance of the controllers. The result indicates that the LQR controller with approximate system velocities is easier to implement than the LQG controller, and also provides superior performance.  相似文献   

4.
This paper presents the optimal regulator for a linear system with state delay and a quadratic criterion. The optimal regulator equations are obtained using the maximum principle. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulator available for linear systems without delays. Simulation graphs demonstrating better performance of the obtained optimal regulator are included. The paper then presents a robustification algorithm for the obtained optimal regulator based on integral sliding mode compensation of disturbances. The general principles of the integral sliding mode compensator design are modified to yield the basic control algorithm oriented to time-delay systems, which is then applied to robustify the optimal regulator. As a result, the sliding mode compensating control leading to suppression of the disturbances from the initial time moment is designed. The obtained robust control algorithm is verified by simulations in the illustrative example.  相似文献   

5.
This paper presents the optimal LQG controller for linear systems with unknown parameters. The optimal controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. Performance of the obtained optimal controller is verified in the illustrative example against the conventional LQG controller that is optimal for linear systems with known parameters. Simulation graphs verifying overall performance and computational accuracy of the designed optimal controller are included.  相似文献   

6.
This paper proposes a framework for the design of sparsely distributed output feedback discrete-time sliding mode control (ODSMC) for interconnected systems. The major target here is to develop an observer based discrete-time sliding mode controller employing a sparsely distributed control network structure in which local controllers exploit some other sub-systems’ information as well as its own local information. As the local controllers/observers have access to some other sub-systems’ states, the control performance will be improved and the applicability region will be widened compared to the decentralised structure. As the first step, a stability condition is derived for the overall closed-loop system obtained from applying ODSMC to the underlying interconnected system, by assuming a priori known structure for the control/observer network. The developed LMI based controller design scheme provides the possibility to employ different information patterns such as fully distributed, sparsely distributed and decentralised patterns. In the second step, we propose a methodology to identify a sparse control/observer network structure with the least possible number of communication links that satisfies the stability condition given in the first step. The boundedness of the obtained overall closed-loop system is analysed and a bound is derived for the augmented system state which includes the closed-loop system state and the switching function.  相似文献   

7.
This paper presents the optimal control problem for a non-linear polynomial system with respect to a Bolza-Meyer criterion with a non-quadratic non-integral term. The optimal solution is obtained as a sliding mode control, whereas the conventional polynomial-quadratic regulator does not lead to a causal solution and, therefore, fails. Performance of the obtained optimal controller is verified in the illustrative example against the conventional polynomial-quadratic regulator that is optimal for the quadratic Bolza-Meyer criterion. The simulation results confirm an advantage in favor of the designed sliding mode control.  相似文献   

8.
This paper investigates the problem of sliding mode control (SMC) for discrete-time two-dimensional (2-D) systems subject to external disturbances. Given a 2-D Fornasini–Marchesini (FM) local state space model, attention is focused on designing the 2-D sliding surface and sliding mode controller, which guarantees the resultant closed-loop system to be asymptotically stable. Particularly, this problem is solved using the model transformation based method. First of all, sufficient conditions are formulated for the existence of a linear sliding surface guaranteeing the asymptotic stability of the equivalent sliding mode dynamics. Based on this, a sliding mode controller is synthesized to ensure that the associated 2-D FM system satisfies the reaching condition. The efficiency of the proposed 2-D SMC law design is shown by a numerical example. This paper extends the idea of model transformation to the 2-D systems and solves the SMC problem of a more general 2-D model in FM type for the first time.  相似文献   

9.
This paper presents the optimal quadratic-Gaussian controller for uncertain stochastic polynomial systems with linear control input and a quadratic criterion over linear observations. The optimal closed-form controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. As intermediate results, the paper gives closed-form solutions of the optimal regulator and controller problems for stochastic polynomial systems with linear control input and a quadratic criterion. Performance of the obtained optimal controller is verified in the illustrative example against the conventional quadratic-Gaussian controller that is optimal for stochastic polynomial systems with known parameters. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.  相似文献   

10.
In this paper, the observer-based sliding mode control (SMC) problem is investigated for a class of uncertain nonlinear neutral delay systems. A new robust stability condition is proposed first for the sliding mode dynamics, then a sliding mode observer is designed, based on which an observer-based controller is synthesized by using the SMC theory combined with the reaching law technique. Then, a sufficient condition of the asymptotic stability is proposed in terms of linear matrix inequality (LMI) for the overall closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability problem is also discussed. It is shown that the proposed SMC scheme guarantees the reachability of the sliding surfaces defined in both the state estimate space and the state estimation error space, respectively. Finally, a numerical example is given to illustrate the feasibility of the proposed design scheme.  相似文献   

11.
The present paper deals with an optimal boundary control problem in which the process of systems under consideration is governed by a linear parabolic partial differential equation over an infinite time interval. The objective of the paper is to determine the optimal boundary control that minimize a given energy-based performance measure. The performance measure is specified as a quadratic functional of displacement and a suitable penalty term involving the boundary controls. In order to determine the optimal boundary controls, the problem with boundary controls are converted into a problem with distributed controls. The modal space technique is then used to reduce the system into the optimal control of time invariant lumped parameter system. The associated system of uncoupled first order initial value problems is solved in terms of controllers. Next step deals with the computation of the control and trajectory of the linear time-invariant lumped parameter. For this we approximate the controllers by a finite number of orthogonal exponential zero-interpolants over the interval [0,∞). The resultant performance index after using the optimality condition leads to a system of linear algebraic equations. The suggested technique is easy to implement on digital computer. We provide a numerical example to demonstrate the applicability and efficiency of the proposed approach.  相似文献   

12.
This paper presents the design of a hysteresis band controller to regulate the switching frequency in a sliding mode controlled nonlinear Boost power converter. The proposed architecture relies on a piecewise linear modeling of the switching function behavior within the hysteresis band, and consists of a continuous-time integral-type controller that modifies the amplitude of the hysteresis band of the comparator in accordance with the error between the desired and the actually measured switching period. The study provides the dynamical models of the converter operating in sliding mode and the switching frequency control loop. Moreover, the design of the parameters of both the sliding mode control and the switching frequency controller guarantee the fulfilment of the desired output voltage regulation of the Boost converter and the steady state setting of the switching frequency with a known, taylored dynamics. A Boost power converter prototype has been built to validate the proposal. Experimental results confirm the predicted good performance of the controllers, as well as the robustness with respect to changes in the switching frequency reference and the system parameters.  相似文献   

13.
A sliding mode controller is developed for optimal transient operation of a continuous bioreactor. The sliding mode is the singular arc from the solution of an optimal control problem. The proposed controller is applied through simulations to an anaerobic digester and its performance is evaluated in terms of optimality and robustness properties.  相似文献   

14.
The recent transition in power generation and consumption is based on the integration of renewable energy sources using DC microgrids. To facilitate this integration, a multi-source DC microgrid structure with wind, photovoltaics, fuel cell and hybrid energy storage system including battery and supercapacitor is presented in this paper. These sources are linked to a DC-bus via DC-DC converters. A hierarchical control strategy with a device and a system-level control for coordinated control between energy sources and their storage devices is proposed. In the device-level control, a variable structure based sliding mode control is applied to regulate the DC bus voltage and to ensure global asymptotic stability. Whereas, the system-level control compensates for the supply and demand mismatches by using a rule-based fuzzy system. To verify the effectiveness of the proposed scheme and the superiority of one controller over another, the proposed controllers are simulated and compared in the MATLAB/Simulink environment under varying load and weather data conditions. Results show that super twisting sliding mode control had negligible chattering as well as better convergence as compared to controllers. Furthermore, the efficiency of the developed scheme is validated by controller hardware in loop experiments.  相似文献   

15.
This study investigates the passivity analysis of fractional-order Takagi-Sugeno (T-S) fuzzy systems subject to external disturbances and nonlinear perturbations under an adaptive integral sliding mode control (AISMC) methodology. To better accommodate the features of the T-S fuzzy dynamical model, a novel fractional-order memory-based integral-type sliding manifold function is defined, which is different from the existing sliding manifold function. With the help of Caputo fractional-order derivative properties and quadratic Lyapunov functional, some linear matrix inequality (LMI)-based sufficient criteria are derived to ensure the asymptotic stability conditions of resulting sliding mode dynamics with passive performance index. Besides that, an adaptive sliding mode control law is designed for the addressed systems to guarantee the system state variables onto the predefined integral sliding manifold. Finally, the effectiveness of the proposed controller is validated based on derived sufficient conditions with two practical models, such as fractional-order interconnected power systems and fractional-order permanent-magnet synchronous generator (PMSG) model, respectively.  相似文献   

16.
In the present paper, the problem of designing a global sliding mode control scheme based on fractional operators for tracking a quadrotor trajectory is investigated. The model of the quadrotor system is given with disturbances and uncertainties. To converge in short finite time of the sliding manifold, a classical quadratic Lyapunov function was used and also a global stabilization of the quadrotor system is ensured. The proposed controller can be ensured the robustness against external disturbances and model uncertainties. Some scenarios are illustrated in this paper. Finally, a comparative study to three other controllers is provided to show the validity and feasibility of the proposed method.  相似文献   

17.
A novel variable structure controller is investigated for satellite attitude control. This novel controller does not lead to a sliding mode, which avoids the chattering problem, making it suitable for practical implementation. Detailed formulation of the controller is presented along with analytical stability analysis for a second order system. The system having this nonlinear controller is homogeneous, which leads to a similar response at large and small deviations from the equilibrium. A procedure for tuning homogeneous controllers for all initial conditions is proposed. A detailed model of the satellite attitude dynamics, actuator dynamics, and delays in the system is utilized to optimize controller gains numerically. A comparative analysis shows the superiority of the proposed controller over a conventional PID controller in terms of better transients and lower energy consumption.  相似文献   

18.
This paper deals with the problem of delay-dependent dissipative control for a class of linear time-delay systems. We develop the design methods of dissipative static state feedback and dynamic output feedback controllers such that the closed-loop system is quadratically stable and strictly (Q,S,R)-dissipative. Sufficient conditions for the existence of the quadratic dissipative controllers are obtained by using linear matrix inequality (LMI) approach. Furthermore, a procedure of constructing such controllers from the solutions of LMIs is given. It is shown that the solvability of a dissipative controller design problem is implied by the feasibility of LMIs. The main results of this paper unify the existing results on H∞ control and passive control.  相似文献   

19.
This paper investigates sliding mode control of stochastic singular Markovian jump systems with nonlinearity. The unmatched nonlinearity satisfies one-sided Lipschitz condition and quadratically inner-boundedness. In term of a new technical variable transformation, sufficient conditions are developed for nonlinear stochastic singular Markovian jump systems constrained on sliding manifold to guarantee stochastic admissibility and uniqueness of solution based on implicit function theorem. The sliding mode control law by which the trajectories of system can be compelled to the predefined sliding surface in finite time no matter what initial state value is, is synthesized. The derivative singular matrix is fully considered in the whole design process such that the derived conditions can be checked easily.The technical treatment of the nonlinear matrix term avoids the classification discussion of sliding mode controller design. Convex optimization problems subject to linear matrix inequalities are formulated to optimize the desired indexes of interest. Finally, the effectiveness of the proposed approach is illustrated by a numerical example and a practical example.  相似文献   

20.
This paper is concerned with the global projective synchronization in fixed time for complex dynamical networks (CDNs) with nonidentical nodes in the presence of disturbances. Firstly, in order to realize the fixed-time projective synchronization of CDNs with matched disturbances, the second-order sliding mode is established, and the global fixed-time reachability of sliding manifolds is analyzed. The fixed-time stability of the sliding mode dynamics is also proved analytically based on Lyapunov stability theory. Moreover, the fixed convergence time of both reaching and sliding mode phases can be adjusted to any desired values in advance by the choice of the designable parameters. Secondly, in order to realize the fixed-time projective synchronization of CDNs with mismatched disturbances, a super-twisting-like (STL) controller, which does not require the information of the derivative of the sliding variable, is designed, and the synchronization condition is addressed in terms of linear matrix inequalities (LMIs). By the proposed controllers, continuous control signals can be provided to reduce the chattering effect and improve the control accuracy. Finally, two numerical examples are given to demonstrate the validity of the theoretical results and the the feasibility of the proposed approaches.  相似文献   

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