Sand cat swarm optimization-based feedback controller design for nonlinear systems

The control of the open loop unstable systems with nonlinear structure is challenging work. In this paper, for the first time, we present a sand cat swarm optimization (SCSO) algorithm-based state feedback controller design for open-loop unstable systems. The SCSO algorithm is a newly proposed metaheuristic algorithm with an easy-to-implement structure that can efficiently find the optimal solution for optimization problems. The proposed SCSO-based state feedback controller can successfully optimize the control parameters with efficient convergence curve speed. In order to show the performance of the proposed method, three different nonlinear control systems such as an Inverted pendulum, a Furuta pendulum, and an Acrobat robot arm are considered. The control and optimization performances of the proposed SCSO algorithm are compared with well-known metaheuristic algorithms. The simulation results show that the proposed control method can either outperform the compared metaheuristic-based algorithms or have competitive results.

High-performance state feedback controller for permanent magnet synchronous motor

Due to the outstanding characteristics of permanent magnet synchronous motor (PMSM), such as fast response speed, high torque and power density, it has been widely used in the automation industry. However, it remains a challenge to obtain high control performance caused by its dynamic complexity. In order to achieve favorable control performance, a novel state feedback control algorithm and parameter tuning method for permanent magnet synchronous motor is proposed in this paper. The development of the presented control method starts with the analyses of current state-space equation in rotor reference frame and then provides the design procedure of state feedback controller from the first-order to third-order system. An enhanced Proportional-Integral (PI) plus state feedback controller is designed, which includes the information of current, the error of current and the integral of the current error. The stability and convergence of the proposed control approach, as the extension of the conventional PI regulator, is mathematically justified in state feedback theory. The simulation and experimental results compared with the classical state feedback control method illustrate that the proposed PI plus state feedback control scheme can obtain better control performance in the presence of parameter changes and disturbance.

Application of quadratic linearization state feedback control with hysteresis reference reformer to improve the dynamic response of interior permanent magnet synchronous motors

Interior Permanent Magnet Synchronous Motors (IPMSMs) offer excellent features, however, the dynamic complexity of these motors has always caused a challenge to control them. In addition, Field Oriented Control (FOC) method developed using Proportional-Integral (PI) regulators, which is the most implemented approach to control the IPMSM, is associated with slow dynamic response and saturation in the controller. This paper presents a novel control algorithm based on State Feedback (SF) regulator for IPMSM drives. The focus of the paper is on simplifying the dynamic of the IPMSM using nonlinear analysis methods and enhancing the response of the designed control approach. The development of the control system starts with linearizing the dynamics of the IPMSM. A linearization approach based on Quadratic Linearization Method (QLM) is proposed and then the linear model is used for designing a state feedback controller optimized by Linear Quadratic Regulator (LQR) method. Applying control constraints is a challenge in systems controlled by state feedback theory. Hence, the proposed control method offers a novel solution based on hysteresis control theory. The proposed hysteresis technique offers several advantages such as lowering overshoot in speed step response in addition to applying constraints and it eliminates all drawbacks of hysteresis controllers. To control the IPMSM in the whole speed range (constant torque and constant power regions), the proposed approach adopts Maximum Torque per Ampere (MTPA) and Voltage Constraint Tracking (VCT) control strategies. Finally, simulations are carried out in MATLAB/SIMULINK environment to compare the performance of the proposed controller with the conventional FOC method.

Improved results on state feedback stabilization for a networked control system with additive time-varying delay components' controller

This paper investigates the problems of stability and stabilization for a networked control system (NCS) with additive time-varying delay components' controller. Firstly, stability of a NCS with additive time-varying delays is investigated. A novel approach with free parameters is proposed. By constructing a new Lyapunov-Krasovskii functional (LKF) with two free parameters, stability criteria are obtained. The obtained stability criteria depend not only on upper bounds of delays but also free parameters. In addition, input-output method is extended to study the stability problem for the NCS. Compared with other approaches such as input-output method, the free-parameter approach is more flexible and effective in reducing the conservatism. Then, based on the stability results, a state feedback controller is designed to guarantee the asymptotically stable of the closed-loop systems. Finally, numerical examples are provided to show the effectiveness and less conservatism of the proposed results.

State feedback control design for Boolean networks

Background

Driving Boolean networks to desired states is of paramount significance toward our ultimate goal of controlling the progression of biological pathways and regulatory networks. Despite recent computational development of controllability of general complex networks and structural controllability of Boolean networks, there is still a lack of bridging the mathematical condition on controllability to real boolean operations in a network. Further, no realtime control strategy has been proposed to drive a Boolean network.

Results

In this study, we applied semi-tensor product to represent boolean functions in a network and explored controllability of a boolean network based on the transition matrix and time transition diagram. We determined the necessary and sufficient condition for a controllable Boolean network and mapped this requirement in transition matrix to real boolean functions and structure property of a network. An efficient tool is offered to assess controllability of an arbitrary Boolean network and to determine all reachable and non-reachable states. We found six simplest forms of controllable 2-node Boolean networks and explored the consistency of transition matrices while extending these six forms to controllable networks with more nodes. Importantly, we proposed the first state feedback control strategy to drive the network based on the status of all nodes in the network. Finally, we applied our reachability condition to the major switch of P53 pathway to predict the progression of the pathway and validate the prediction with published experimental results.

Conclusions

This control strategy allowed us to apply realtime control to drive Boolean networks, which could not be achieved by the current control strategy for Boolean networks. Our results enabled a more comprehensive understanding of the evolution of Boolean networks and might be extended to output feedback control design.

State feedback integral control for a rotary direct drive servo valve using a Lyapunov function approach

This paper concerns a state feedback integral control using a Lyapunov function approach for a rotary direct drive servo valve (RDDV) while considering parameter uncertainties. Modeling of this RDDV servovalve reveals that its mechanical performance is deeply influenced by friction torques and flow torques; however, these torques are uncertain and mutable due to the nature of fluid flow. To eliminate load resistance and to achieve satisfactory position responses, this paper develops a state feedback control that integrates an integral action and a Lyapunov function. The integral action is introduced to address the nonzero steady-state error; in particular, the Lyapunov function is employed to improve control robustness by adjusting the varying parameters within their value ranges. This new controller also has the advantages of simple structure and ease of implementation. Simulation and experimental results demonstrate that the proposed controller can achieve higher control accuracy and stronger robustness.

Stabilization strategies of a general nonlinear car-following model with varying reaction-time delay of the drivers

In this paper, the stabilization strategies of a general nonlinear car-following model with reaction-time delay of the drivers are investigated. The reaction-time delay of the driver is time varying and bounded. By using the Lyapunov stability theory, the sufficient condition for the existence of the state feedback control strategy for the stability of the car-following model is given in the form of linear matrix inequality, under which the traffic jam can be well suppressed with respect to the varying reaction-time delay. Moreover, by considering the external disturbance for the running cars, the robust state feedback control strategy is designed, which ensures robust stability and a smaller prescribed H∞ disturbance attenuation level for the traffic flow. Numerical examples are given to illustrate the effectiveness of the proposed methods.

Delay-range-dependent chaos synchronization approach under varying time-lags and delayed nonlinear coupling

This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies.

Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control

This paper investigates drive-response synchronization for a class of neural networks with time-varying discrete and distributed delays (mixed delays) as well as discontinuous activations. Strict mathematical proof shows the global existence of Filippov solutions to neural networks with discontinuous activation functions and the mixed delays. State feedback controller and impulsive controller are designed respectively to guarantee global exponential synchronization of the neural networks. By using Lyapunov function and new analysis techniques, several new synchronization criteria are obtained. Moreover, lower bound on the convergence rate is explicitly estimated when state feedback controller is utilized. Results of this paper are new and some existing ones are extended and improved. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.

Complex dynamic behavior in a viral model with state feedback control strategies

With the consideration of mechanism of prevention and control for the spread of viral diseases, in this paper, we propose two novel virus dynamics models where state feedback control strategies are introduced. The first model incorporates the density of infected cells (or free virus) as control threshold value; we analytically show the existence and orbit stability of positive periodic solution. Theoretical results imply that the density of infected cells (or free virus) can be controlled within an adequate level. The other model determines the control strategies by monitoring the density of uninfected cells when it reaches a risk threshold value. We analytically prove the existence and orbit stability of semi-trivial periodic solution, which show that the viral disease dies out. Numerical simulations are carried out to illustrate the main results.