Stability and performance comparison analysis for linear active disturbance rejection control–based system

This paper investigates the stability and performance of the linear active disturbance rejection control (LADRC)–based system with uncertainties and external disturbance via transfer functions and a frequency-domain view. The performance of LADRC is compared with the state-observer-based state feedback control (SOSFC) and state feedback control (SFC). First, the transfer functions and the error transfer functions for LADRC, SOSFC, and SFC are studied using the state-space method. It is proven that the LADRC-, SOSFC-, and SFC-based closed-loop systems have the same transfer function from the reference input to the output and achieve the same control effects for the nominal system. Then, it is proven for the first time that the LADRC has a better anti-interference ability than the SOSFC and SFC. Besides, the asymptotic stability condition of LADRC-based closed-loop system considering large parameter perturbations is given first. Moreover, the sensitivity analysis of the closed-loop system is carried out. The results show that the LADRC has stronger robustness under parameter perturbations. According to the results, we conclude that the LADRC is of great disturbance rejection ability and strong robustness.

Prescribed Performance Tracking Control for High-Order Uncertain Nonlinear Systems

This paper considers the prescribed performance tracking control for high-order uncertain nonlinear systems. For any initial system condition, a state feedback control is designed, which guarantees the prescribed tracking performance and the boundedness of closed-loop signals. The proposed controller can be implemented without using any approximation techniques for estimating unknown nonlinearities. In this respect, a significant advantage of this article is that the explosion of complexity is avoided, which is raised by backstepping-like approaches that are typically employed to the control of uncertain nonlinear systems, and a low-complexity controller is achieved. Moreover, contrary to the existing results in existing literature, the restrictions on powers of high-order nonlinear systems are relaxed to make the considered problem having stronger theoretical and practical values. The effectiveness of the proposed scheme is verified by some simulation results.

Reliable Centralized Control of PMSM

In this paper, we introduce the development methodology of a reliable centralized control applied to a synchronous permanent magnet machine. The proposed system is nonlinear, we linearize around a point of application. The resulting model will then be used to reproduce the dynamic behavior of the machine for a reliable control. The controller is based on the standard h infinite to increase performance, reduce measurement noise, and to tolerate the outage of certain sensors. To illustrate the results, we made a comparison between a standard state feedback control and reliable h infinite robust control. The simulation results shows, that the system in case of technical placements poles loses classic performance in the presence of an outage, that the reliable centralized robust control remain satisfactory performance even in the presence of outage.

Necessary and Sufficient Dissipativity-Based Conditions for Feedback Stabilization

Using the notion of exponential QSR-dissipativity, this work presents necessary and sufficient conditions for exponential stabilizability of nonlinear systems by linear static output feedback (SOF). It is shown that, under mild assumptions, the exponential stabilization of the closed-loop system around the origin is equivalent to the exponential QSR-dissipativity of the plant. Furthermore, whereas strict QSR-dissipativity is only sufficient for SOF asymptotic stabilization, it is proved to be necessary and sufficient for full state feedback control. New necessary and sufficient conditions for SOF stabilizability of linear systems are presented as well, along with a linear and noniterative semidefinite strategy for controller design. Necessary linear matrix inequality (LMI) conditions for stabilization are also introduced. Some examples illustrate the usefulness of the proposed approach.

Necessary and Sufficient Dissipativity-Based Conditions for Feedback Stabilization

Using the notion of exponential QSR-dissipativity, this work presents necessary and sufficient conditions for exponential stabilizability of nonlinear systems by linear static output feedback (SOF). It is shown that, under mild assumptions, the exponential stabilization of the closed-loop system around the origin is equivalent to the exponential QSR-dissipativity of the plant. Furthermore, whereas strict QSR-dissipativity is only sufficient for SOF asymptotic stabilization, it is proved to be necessary and sufficient for full state feedback control. New necessary and sufficient conditions for SOF stabilizability of linear systems are presented as well, along with a linear and noniterative semidefinite strategy for controller design. Necessary linear matrix inequality (LMI) conditions for stabilization are also introduced. Some examples illustrate the usefulness of the proposed approach.

Integral State Feedback Control Using Linear Quadratic Gaussian in DC-drive System

The electric motor is one of the technological developments which can support the production process. DC motor has some advantages compared to AC motor especially on the easier way to control its speed or position as well as its widely adjustable range. The main issue in the DC motor is controlling the angular speed with uncertainty and disturbance. The alternative solution of a control method with simple, easy to design, and implementable in a multi-input multi-output system is integral state feedback such as linear quadratic Gaussian (LQG). It is a combination between linear quadratic regulator and Kalman filter. One of the advantages of this method is the usage of fewer sensors compared with the original linear quadratic regulator method which uses sensors as many as the state in the system model. The design, simulation, and experimental study of the application of LQG as state feedback control in a DC-drive system have been done. Both performance and energy were analyzed and compared with conventional proportional integral derivative (PID). The gain of LQG was determined by trial whereas the PID gain is determined from MATLAB autotuning without fine-tuning. The load test and tracking test were carried out in the experiment. Both simulation and hardware tests showed the same result which LQG is superior in integral absolute error (IAE) by up to 74.37 % in loading test compared to PID. On the other side, LQG needs more energy, it consumes higher energy by 6.34 % in the load test.

Constrained stochastic LQ control on infinite time horizon with regime switching

This paper is concerned with a stochastic linear-quadratic (LQ) optimal control problem on infinite time horizon, with regime switching, random coefficients, and cone control constraint. To tackle the problem, two new extended stochastic Riccati equations (ESREs) on infinite time horizon are introduced. The existence of the nonnegative solutions, in both standard and singular cases, is proved through a sequence of ESREs on finite time horizon. Based on this result and some approximation techniques, we obtain the optimal state feedback control and optimal value for the stochastic LQ problem explicitly. Finally, we apply these results to solve a lifetime portfolio selection problem of tracking a given wealth level with regime switching and portfolio constraint.

Research on automobile four-wheel steering control system based on yaw angular velocity and centroid cornering angle

In order to improve the handling stability of four-wheel steering (4WS) cars, a two-degree-of-freedom 4WS vehicle dynamics model is constructed here, and the motion differential equation of the system model is established. Based on the quadratic optimal control theory, the optimal control of 4WS system is proposed in this paper. When running at low speed and high speed, through yaw rate feedback control, state feedback control, and optimal control, the 4WS cars are controlled based on yaw rate and centroid cornering angle with MATLAB/Simulink simulation. The result indicates that 4WS control based on the optimal control can improve the displacement of the cars. And, the optimal control of 4WS proposed in this paper can eliminate centroid cornering angle completely compared with other two traditional optimal control methods. Besides, the optimal control enjoys faster response speed and no overshoot happens. In conclusion, the optimal control method proposed in the paper represents better stability, moving track and stability, thereby further enhancing the handling property of cars.

Robust Exponential Stabilization for a Class of Nonlinear Uncertain Systems with Time-varying Delays

This paper is concerned with the problem of robust exponential stabilization for a class of nonlinear uncertain systems with time-varying delays. By using appropriately chosen Lyapunov-Krasovskii functional, together with the Finsler’s lemma, sufficient conditions for exponential stability of nonlinear uncertain systems with time-varying delays are proposed in terms of linear matrix inequality (LMI). Then, novel sufficient conditions are developed to ensure the nonlinear uncertain system with time-varying delay is robust exponentially stabilizable in terms of linear matrix inequality with state feedback control. Finally, a numerical example is given to illustrate the efficiency of proposed methods.