State Feedback Control Technique Research Articles

State-Feedback Control Design for the Cannon Stability System

Abstract— Tanks have an important role in protecting a region in the event of a battle. The tank's cannon is a very reliable weapon in warfare. However, the cannon's precision while aiming and firing targets is a concern. A control system must be created to increase the cannon's stability and precision. The state feedback control technique with a full-state observer is the control system that can manage cannon disturbances. The control system is built around three DC motors, each of which operates the cannon’s x, y, and z axes. Then performed tests for each axis at an angle of 90 degrees, The state feedback control with a full state observer can produce outstanding performance, with the time required for the cannon to reach the target angle was 0.51 seconds, and the cannon system had 0% overshoot.

Asymptotic pinning synchronization of nonlinear multi-agent systems: Its application to tunnel diode circuit

This work proposes a pinning state-feedback control technique for synchronizing non-linear multi-agent systems (MASs) with time delays. A collection of switching-directed graphs describes the communication exchanges between all of the agents. The challenge of asymptotic stability analysis for some error systems is translated into the construction of a leader-following synchronization of the relevant MASs. The closed-loop system could be acquired by building a convenient Lyapunov–Krasovskii functional (LKF) that has two integral terms, and by using Kronecker product qualities combined with matrix inequality techniques. When these conditions are met, a state-feedback pinning controller can be built with linear matrix inequalities (LMIs), which can be derived easily from a number of efficient optimization algorithms. Further, the performance of the proposed control design system is verified based on a tunnel diode circuit (TDC) by numerical simulations.

A Decentralized Event-Triggered State-Feedback Control Technique for Continuous-Time Linear Systems

In this article, a decentralized event-triggered technique is developed to effectively implement the state-feedback controllers for a class of linear systems. Toward this end, the system dynamics is represented in its Jordan canonical form, and the system states are sorted based on their time constants. Then, for any Jordan block, an event-triggered mechanism is designed to determine the execution times for sampling and sending its corresponding state variable(s) to the controller. In this way, each Jordan block has a mechanism to decide whether or not its data should be transmitted to the controller. Using the proposed technique, event-triggered policies can be designed such that the fast dynamics are sampled with short interevent intervals, while the slower dynamics are simultaneously permitted to send their data with relatively long interevent intervals. The proposed technique decreases both the number and the size of transmitted packets. The boundedness of the closed-loop system is guaranteed under the suggested event-triggered technique. Moreover, it is proved that the Zeno behavior is avoided. In comparison with ordinary event-triggered methods, the proposed decentralized event-triggered technique leads to better performance due to its extra degrees of freedom in sending the data from the system to the controller. Numerical simulations are presented to illustrate the promising features of the suggested event-triggered controller.

Fault tolerant control of a permanent magnet synchronous machine using multiple constraints Takagi-Sugeno approach

Introduction. Fault diagnosis, and fault tolerant control issues are becoming very important to ensure a good supervision of systems and guarantee the safety of human operators and equipments even if system complexity increases. Problem. In fact, the presence of faults in actuators, sensors and processes can lead to system performance degradation, system breakdown, economic loss, and even disastrous situations. Furthermore, Actuator saturation or control input saturation is probably the most usual nonlinearity encountered in control engineering because of the physical impossibility of applying unlimited control signals and/or safety constraints. Purpose. This article is dedicated to the problem of fault tolerant control for constrained nonlinear systems described by a Takagi-Sugeno model. One of the interests of this type of models is the possibility of extend some tools and methods from linear system case to the nonlinear one. The novelty of the work consists in developing a fault tolerant control algorithm for a nonlinear Permanent Magnet Synchronous Machine model using an observer based state-feedback control technique in order to enhance fault and state estimation despite actuator saturation and system disturbances. Methods. Indeed a sensor fault detection observer based residual generator is synthesized with a guaranteed L2 performance to attenuate the external disturbances effect from one side and to maximize the residual sensitivity to faults from the other side. Based on Lyapunov function, design conditions are formulated in terms of Linear Matrix Inequalities to ensure stability of the global system. Practical value. A detailed study concerning nonlinear permanent magnet synchronous machine model, which is consolidated by simulation results, is conducted to show the used algorithm’s effectiveness guarantying fault estimation and reconfiguration of the control law to maintain stable performance even in the presence of actuator faults, external perturbation and the phenomenon of actuator saturation.

Bifurcations and chaos control in a discrete-time prey–predator model with Holling type-II functional response and prey refuge

In this paper, we study the complex dynamical behavior in a discrete prey–predator model with Holling type II functional response with prey refuge. It is exhibited that the system shows different types of bifurcations viz. flip bifurcation, transcritical bifurcation and Neimark–Sacker bifurcation(NSB) by using center manifold theorem and bifurcation theory. Moreover, the chaos occurred in the system has been controlled by deploying control strategies viz. state feedback, pole placement and hybrid control techniques. The certain conditions have been determined under which chaos and bifurcation can be stabilized. The extensive numerical simulation is performed to demonstrate the analytical findings.

Improved LQR Control Using PSO Optimization and Kalman Filter Estimator

The electric motor is a device that converts electrical power into mechanical power. The DC motor has some advantages compared to the AC motor on its easier way to control the speed or position and wide adjustable range. However, it still has some issues, such as uncertainty and disturbance; most existing controllers still provide bad system performance or have major drawbacks in solving these issues. The alternative solution for a control method with simple, easy to design, and can be implemented in a multi-input multi-output system is the integral state feedback control technique, such as in Linear Quadratic Regulator (LQR). The weakness of LQR control is that there is no exact method to determine the best value of matrix Q and R used to calculate the state feedback gain; trial or manual tuning method is mostly used. Therefore, this paper proposed an improved LQR control using Particle Swarm Optimization (PSO) method and the Kalman filter estimator. The PSO was used to find optimal Q and R-value, while the Kalman filter reduced the number of sensors used to measure the system state. Both performance and energy consumption were compared using the Integral of Absolute Error (IAE) and total energy consumption. The simulation results showed that the proposed method is superior in performance and energy compared to manually-tuned LQR. However, based on the hardware implementation, although the manually-tuned LQR was found to have the smallest energy consumption, the proposed method has the smallest IAE, which can reduce the IAE by 11.28% with only 1% higher energy compared to manually-tuned LQR.

New results on finite-/fixed-time synchronization of delayed memristive neural networks with diffusion effects

<abstract><p>In this paper, we further investigate the finite-/fixed-time synchronization (FFTS) problem for a class of delayed memristive reaction-diffusion neural networks (MRDNNs). By utilizing the state-feedback control techniques, and constructing a general Lyapunov functional, with the help of inequality techniques and the finite-time stability theory, novel criteria are established to realize the FFTS of the considered delayed MRDNNs, which generalize and complement previously known results. Finally, a numerical example is provided to support the obtained theoretical results.</p></abstract>

State feedback control for stabilization of PMSM ‐based servo‐drive with parametric uncertainty using interval analysis

For a class of multivariable uncertain dynamic systems, the parametric uncertainties are belonging to a closed interval with lower and upper boundaries a priori known. Thereby, these systems can be analyzed based on interval structures and interval matrices. In this article, a fully interval analysis–based method is developed and applied to the state feedback control of permanent magnet synchronous motor (PMSM) in order to design a stabilized servo-drive. Indeed, the parametric uncertainties are investigated in state space representation, which represents a simplified and effective way to analyze the robust stability for the interval system. Firstly, a robust state feedback control technique, dedicated to an uncertain system is introduced. For that, the robust controllability test is performed for the interval system by using the linear independency condition of column interval vectors. It is proven that there is a direct correlation between the controllability test and the existence of a robust modal P-regulator for the correction of the uncertain system. It is also shown that it invariably relies on each input's controllability indices and thus their effect on the uncertain system's state variables. In order to ensure stability in a closed loop, the modal P-regulator is designed with possibility of incorporation of an integral action. The modified modal PI regulator has the ability to reject disturbance and guarantee zero-steady-state error for step inputs. In fact, the stability is achieved by placing all coefficients of the system characteristic polynomial within assigned intervals based on Kharitonov's Theorem. The technique provides a matrix gain with interval coefficients for the stabilizing regulator. Finally, the developed approach is applied to position control of linearized model of the PMSM-based servo-drive, presenting parametrical uncertainties. To demonstrate the efficiency of the proposed method, a numerical and graphical comparison of conventional LQR and pole placement, state feedback controllers for the PMSM servo-drive with the robust interval controller is provided. In order to verify the feasibility of the whole proposed technique, calculations and simulations are performed by using Matlab/Intlab toolbox. Real-time simulation is also investigated using Lab-View Compact-RIO.

L₁-Adaptive Robust Control Design for a Pressurized Water-Type Nuclear Power Plant

This work proposes adaptive control-based design strategies to control a pressurized water reactor (PWR) nuclear power plant (NPP). An L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -adaptive-based state-feedback control technique is proposed using the linear quadratic Gaussian control and projection-based adaptation laws. The control scheme possesses good robustness capabilities in handling disturbances and uncertainties. A robust L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -adaptive control technique is also proposed by combining the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -adaptive control with the loop transfer recovery (LTR) technology. The framework hence gives the strengthened robust set-point tracking performance given the matched and unmatched uncertainties and disturbances. The NPP model employed in this article is defined by five inputs, five outputs, and 38 state variables. A linear model for controller design is obtained by linearizing the nonlinear NPP model at operating conditions. Various simulations are carried out on subsystems of the NPP to verify the effectiveness of the proposed scheme. Numerical and statistical measures are computed for quantitative analysis of the controllers' performance. Several classical control design techniques are also implemented, and their performance is compared with the proposed adaptive control techniques.

State feedback control of advanced static var compensator using a five-level NPC inverter topology

This paper deals with the modeling and control of an advanced static var compensator (ASVC) using a five-level neutral point-clamped (NPC) voltage source inverter (VSI). The nonlinear state space model of the five-level ASVC is obtained from the d-q axis frame. The effectiveness of this compensator highly depends on the choice of the control strategy. The proposed state feedback control (SFC) technique is applied to adjust the ASVC Var flow with the AC transmission network and achieve DC voltage capacitor balance. The dynamic performance of the ASVC based SFC controller is evaluated under several operating conditions. The simulation results demonstrate that the proposed SFC control strategy is highly robust compared to the conventional Proportional-Integral (PI) control.

Decentralized Voltage Control of Autonomous DC Microgrids With Robust Performance Approach

In this article, we propose an optimal decentralized robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> control system for the voltage control problem of autonomous uncertain dc microgrids consisting of multiple distributed generations (DGs) with general topology. The one-degree-of-freedom (DoF) structure of the developed control system guarantees the robust performance of the system as well as its robust stability against various sources of uncertainty, such as plug-and-play (PnP) operation of the DGs, topology changes, large load perturbations, different subsequent system changes, and the presence of constant power loads (CPLs). To that end, the uncertain dc microgrid is modeled as a Linear Time-Invariant (LTI) polytopic state-space system. Then, a state-feedback control technique based on linear matrix inequality (LMI) with linearly parameter-dependent (LPD) Lyapunov matrices is implemented on the uncertain dc microgrids. The proposed controller does not require any sort of communications, and the robust performance property of the controller eliminates the need for prefilter design. The efficiency of the proposed controller is analyzed by simulating different case studies through SimPowerSystems Toolbox in MATLAB. Finally, the performance of the proposed control method is validated via experimental studies.

An LMI Approach to Nonlinear State-Feedback Stability of Uncertain Time-Delay Systems in the Presence of Lipschitzian Nonlinearities

This article proposes a new nonlinear state-feedback stability controller utilizing linear matrix inequality (LMI) for time-delay nonlinear systems in the presence of Lipschitz nonlinearities and subject to parametric uncertainties. Following the Lyapunov–Krasovskii stabilization scheme, the asymptotic stability criterion resulted in the LMI form and the nonlinear state-feedback control technique was determined. Due to their significant contributions to the system stability, time delays and system uncertainties were taken into account while the suggested scheme was designed so that the system’s stabilization was satisfied in spite of time delays and system uncertainties. The benefit of the proposed method is that not only is the control scheme independent of the system order, but it is also fairly simple. Hence, there is no complexity in using the proposed technique. Finally, to justify the proficiency and performance of the suggested technique, a numerical system and a rotational inverted pendulum were studied. Numerical simulations and experimental achievements prove the efficiency of the suggested control technique.

Reachable set synthesis of singular Markovian jump systems

The reachable set synthesis problem of singular Markovian jump systems (SMJSs) is investigated in this paper. Both state reachable set and output reachable set are considered for SMJSs without delay and with distributed delay. By utilizing proportional and derivative state feedback control technique, sufficient conditions for delay-free SMJSs are proposed to guarantee the reachable set of closed-loop systems to be mean-square bounded by a prescribed ellipsoid firstly. Then the result is extended to SMJSs with distributed delay. Numerical examples are given to demonstrate the effectiveness of the obtained result.

Fixed-Time Synchronization of Delayed Fractional-Order Memristor-Based Fuzzy Cellular Neural Networks

In this article, we discussed the fixed-time synchronization of fractional-order memristor-based fuzzy cellular neural networks (FMFCNNs) with time-varying delays. Based on the differential inclusion theory and discontinuous state feedback control technique, some useful novel criteria of the fixed-time synchronization for FMFCNNs are derived by constructing appropriate Lyapunov function. The results in our paper improve and generalize current literature research results significantly. Finally, the effectiveness of our control schemes for the fixed-time synchronization is demonstrated through numerical simulations.

Synchronization of stochastic multi-weighted complex networks with Lévy noise based on graph theory

This paper addresses the synchronization problem of stochastic multi-weighted complex networks with Lévy noise. Based on the drive-response concept and graph theory, global Lyapunov function of the error network between drive-response networks is obtained by the weighted summation of Lyapunov functions of vertex systems. According to the stochastic analysis and state feedback control technique, the rigorous synchronization analysis of drive-response networks in the pth moment and probability sense is presented. The obtained synchronization criteria are closely related with multi-weights and the intensity of Lévy noise. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.

On the finite-time boundedness of linear systems

This paper deals with the finite-time boundedness (FTB) of linear time-varying (LTV) systems; in this context, the novel contribution of our work goes in several directions. The first result is a sufficient condition for FTB when the plant input is generated by an exo-system; it is worth noting that constant, norm bounded signals, which most part of the previous literature has considered so far, belong to such class of inputs. To this regard, it is possible to compare our result with the existing literature, which shows that our approach yields less conservative conditions. The second result provided in the paper, is a sufficient condition for FTB when the input belongs to L2, the class of square integrable signals, which have never been considered so far. In both cases, the proposed results require the solution of a feasibility problem constrained by differential linear matrix inequalities (DLMIs). A third contribution of the paper proves that, from the system-theoretic point of view, the obtained FTB conditions can be interpreted in terms of the norm of a suitable input–output operator. As a consequence of this fact, we are able to find alternative and equivalent conditions for FTB, both for the exogenous and the L2 cases, which are based on the solution of differential Lyapunov equations (DLEs), which are much more efficient from the computational point of view. The DLMI-based condition, however, is fundamental to solve the design problem, which is also investigated in the paper. Some examples show that the proposed technique is less conservative with respect to the previous literature, when exogenous inputs are considered, and its effectiveness when L2 signals are considered. Moreover, one example is devoted to show that the analysis approach, based on the solution of DLE, is much more efficient from the computational point of view with respect to the one based on DLMIs; finally the last example investigates the application of the state feedback control technique.

Exponential synchronization of stochastic Cohen–Grossberg neural networks driven by G-Brownian motion

This paper investigates the problem of stochastic Cohen–Grossberg neural networks driven by G-Brownian motion (G-SCGNNs, in short). We establish the exponential synchronization of G-SCGNNs by applying inequality technique, kth vertex-G-Lyapunov functions, graph-theory and state feedback control technique. A concrete example is given to verify the obtained theory.

Exponential synchronization of stochastic complex networks with multi-weights: A graph-theoretic approach

This paper concerns the exponential synchronization problem of stochastic complex networks with multiple weights (SCNMW). By the method of network split, SCNMW can be modelled as stochastic coupled systems driven by Brownian motion. By combining graph theory, Lyapunov stability theory and state feedback control technique, drive-response synchronization criteria of SCNMW have been obtained. Two kinds of exponential synchronization criteria are obtained, one is given with Lyapunov functions of vertex systems, and the other is shown with the coefficients of SCNMW. The obtained synchronization principles are closely related to the coupling strength of multiple sub-networks and the intensity of noise perturbation. Finally, a numerical example with some simulations is presented to illustrate the theoretical results.

Implementation of Maximum Power Point Tracking Based on Variable Speed Forecasting for Wind Energy Systems

In order to precisely control the wind power generation systems under nonlinear variable wind velocity, this paper proposes a novel maximum power tracking (MPPT) strategy for wind turbine systems based on a hybrid wind velocity forecasting algorithm. The proposed algorithm adapts the bat algorithm and improved extreme learning machine (BA-ELM) for forecasting wind speed to alleviate the slow response of anemometers and sensors, considering that the change of wind speed requires a very short response time. In the controlling strategy, to optimize the output power, a state feedback control technique is proposed to achieve the rotor flux and rotor speed tracking purpose based on MPPT algorithm. This method could decouple the current and voltage of induction generator to track the reference of stator current and flux linkage. By adjusting the wind turbine mechanical speed, the wind energy system could operate at the optimal rotational speed and achieve the maximal power. Simulation results verified the effectiveness of the proposed technique.

Prescribed performance-barrier Lyapunov function for the adaptive control of unknown pure-feedback systems with full-state constraints

In this paper, an adaptive state-feedback control technique is proposed for a class of unknown pure-feedback systems. A remarkable feature is that not only the problem of full-state constraints and prescribed performance tracking is solved together, but also the design is an approximation-free control scheme for pure-feedback systems with completely unknown nonlinearities. These properties will lead to a difficult task for designing a stable controller. To this end, a novel prescribed performance-barrier Lyapunov function is developed to guarantee that all the state constraints are not violated and the tracking error is preserved within a specified prescribed performance bound at all times, simultaneously. Then, by utilizing the mean value theorem, Nussbaum gain technique, a low-pass filter and a novel bounded estimation approach at each step of back-stepping procedure, a novel adaptive dynamics surface control scheme is developed to remove the difficulties of pure-feedback characteristic, unknown nonlinearities, unknown control direction and “explosion of complexity”, which can guarantee that the proposed design is universal and low-complexity. Moreover, it is proved that all the signals in the closed-loop system are global uniformly bounded. Two simulation studies are worked out to illustrate the performance of the proposed approach.