Reduced-Order Observer-Based LQR Controller Design for Rotary Inverted Pendulum

The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Despite the implementation of various control strategies to maintain equilibrium,optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive.Existing methods frequently rely on extensive experimental data or the designer’s expertise,presenting a notable drawback.This paper proposes a novel tracking control approach for RIP,utilizing a Linear Quadratic Regulator(LQR)in combination with a reduced-order observer.Initially,the RIP system is mathematically modeled using the Newton-Euler-Lagrange method.Subsequently,a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states.This approach enhances the controller’s robustness by eliminating differential terms from the observer,thereby attenuating unknown disturbances.Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below50Hz and achieve precise tracking below1.4 rad,validating the effectiveness of the proposed control scheme.

Practical bipartite consensus for multi-agent systems:A barrier function-based adaptive sliding-mode control approach

This paper is concerned with bipartite consensus tracking for multi-agent systems with unknown disturbances.A barrier function-based adaptive sliding-mode control(SMC)approach is proposed such that the bipartite steady-state error is converged to a predefined region of zero in finite time.Specifically,based on an error auxiliary taking neighboring antagonistic interactions into account,an SMC law is designed with an adaptive gain.The gain can switch to a positive semi-definite barrier function to ensure that the error auxiliary is constrained to a predefined neighborhood of zero,which in turn guarantees practical bipartite consensus tracking.A distinguished feature of the proposed controller is its independence on the bound of disturbances,while the input chattering phenomenon is alleviated.Finally,a numerical example is provided to verify the effectiveness of the proposed controller.

IGBT Temperature Field Monitoring Based on Reduced-order Model

With the rapid development of the world economy,IGBT has been widely used in motor drive and electric energy conversion.In order to timely detect the fatigue damage of IGBT,it is necessary to monitor the junction temperature of IGBT.In order to realize the fast calculation of IGBT junction temperature,a finite element method of IGBT temperature field reduction is proposed in this paper.Firstly,the finite element calculation process of IGBT temperature field is introduced and the linear equations of finite element calculation of temperature field are derived.Temperature field data of different working conditions are obtained by finite element simulation to form the sample space.Then the covariance matrix of the sample space is constructed,whose proper orthogonal decomposition and modal extraction are carried out.Reasonable basis vector space is selected to complete the low dimensional expression of temperature vector inside and outside the sample space.Finally,the reduced-order model of temperature field finite element is obtained and solved.The results of the reduced order model are compared with those of the finite element method,and the performance of the reduced-order model is evaluated from two aspects of accuracy and rapidity.

Distributed Secondary Control of AC Microgrids With External Disturbances and Directed Communication Topologies:A Full-Order Sliding-Mode Approach

This paper addresses the problem of distributed secondary control for islanded AC microgrids with external disturbances.By using a full-order sliding-mode(FOSM)approach,voltage regulation and frequency restoration are achieved in finite time.For voltage regulation,a distributed observer is proposed for each distributed generator(DG)to estimate a reference voltage level.Different from some conventional observers,the reference voltage level in this paper is accurately estimated under directed communication topologies.Based on the observer,a new nonlinear controller is designed in a backstepping manner such that an FOSM surface is reached in finite time.On the surface,the voltages of DGs are regulated to the reference level in finite time.For frequency restoration,a distributed controller is further proposed such that a constructed FOSM surface is reached in finite time,on which the frequencies of DGs are restored to a reference level in finite time under directed communication topologies.Finally,case studies on a modified IEEE 37-bus test system are conducted to demonstrate the effectiveness,the robustness against load changes,and the plug-and-play capability of the proposed controllers.

Vision-based Stabilization of Nonholonomic Mobile Robots by Integrating Sliding-mode Control and Adaptive Approach

Vision-based pose stabilization of nonholonomic mobile robots has received extensive attention. At present, most of the solutions of the problem do not take the robot dynamics into account in the controller design, so that these controllers are difficult to realize satisfactory control in practical application. Besides, many of the approaches suffer from the initial speed and torque jump which are not practical in the real world. Considering the kinematics and dynamics, a two-stage visual controller for solving the stabilization problem of a mobile robot is presented, applying the integration of adaptive control, sliding-mode control, and neural dynamics. In the first stage, an adaptive kinematic stabilization controller utilized to generate the command of velocity is developed based on Lyapunov theory. In the second stage, adopting the sliding-mode control approach, a dynamic controller with a variable speed function used to reduce the chattering is designed, which is utilized to generate the command of torque to make the actual velocity of the mobile robot asymptotically reach the desired velocity. Furthermore, to handle the speed and torque jump problems, the neural dynamics model is integrated into the above mentioned controllers. The stability of the proposed control system is analyzed by using Lyapunov theory. Finally, the simulation of the control law is implemented in perturbed case, and the results show that the control scheme can solve the stabilization problem effectively. The proposed control law can solve the speed and torque jump problems, overcome external disturbances, and provide a new solution for the vision-based stabilization of the mobile robot.

Adaptive sliding-mode path following control system of the underactuated USV under the influence of ocean currents

The path-following control of the asymmetry underactuated unmanned surface vehicle(USV) under external disturbances such as unknown constant and irrational ocean currents is discussed, and an adaptive sliding-mode path-following control system is proposed, which comprises a path-variable updated law,a modified integral line-of-sight(ILOS) guidance law based on a time-varying lookahead distance and adaptive feedback linearizing controllers combined with sliding-mode technique. A more accurate USV model without the assumption of having diagonal inertia and damping matrices is first presented, aiming at improving the performance of the path-following control. Next, the coordinate transformation is adopted to decouple the sway dynamic from the rudder angle, and the path-following errors dynamics without non-singular problem are presented in the moving Frenet-Serret frame. Then, based on the cascaded theorem and the adaptive sliding-mode method, the adaptive control law of position errors and course error are designed, among which the lookahead distance and integral gain are all computed as different functions of cross-track error to estimate and compensate the sideslip angle caused by external disturbances adaptively. Finally, according to the Lyapunov and cascaded theorem, the control system proposed is proved to be uniform globally asymptotic stability(UGAS) and uniform semiglobal exponential stability(USGES) when the control objectives are all achieved. Simulation results illustrate the precision and high-quality performance of this new controller.

Adaptive Sliding-Mode Control of an Automotive Electronic Throttle in the Presence of Input Saturation Constraint

In modern vehicles, electronic throttle(ET) has been widely utilized to control the airflow into gasoline engine. To solve the control difficulties with an ET, such as strong nonlinearity,unknown model parameters and input saturation constraints,an adaptive sliding-mode tracking control strategy for an ET is presented. Compared with the existing control strategies for an ET, input saturation constraints and parameter uncertainties are adequately considered in the proposed control strategy. At first, the nonlinear dynamic model for control of an ET is described. According to the dynamical model, the nonlinear adaptive sliding-mode tracking control method is presented,where parameter adaptive laws and auxiliary design system are employed. Parameter adaptive law is given to estimate the unknown parameter with an ET. An auxiliary system is designed,and its state is utilized in the tracking control method to handle the input saturation. Stability proof and analysis of the adaptive sliding-mode control method is performed by using Lyapunov stability theory. Finally, the reliability and feasibility of the proposed control strategy are evaluated by computer simulation.Simulation research shows that the proposed sliding-mode control strategy can provide good control performance for an ET.

Sliding-mode observers for systems with unknown inputs and measurement disturbances

The method to design sliding-mode observers for systems with unknown inputs and measurement disturbances is presented in the paper. An augmented system is constructed by viewing the measurement disturbances as unknow inputs. For such an augmented system, the so-called observer matching condition is not satisfied. Based on the construction of auxiliary outputs, the observer matching condition may be satisfied. High-order sliding-mode differentiators are developed to obtain the estimates of those unmeasurable variables contained in the auxiliary output vector. Employing the estimate of auxiliary output vector, a sliding-mode observer is designed. The simulation results to a real model show that the proposed method is effective.

Sliding-mode control for a rolling-missile with input constraints

This paper investigates the overload stabilization problem of the rolling-missile subject to parameters uncertainty and actuator saturation. In order to solve this problem, a sliding-mode control(SMC) scheme is technically employed by using the backstepping approach to make the dynamic system stable. In addition,SMC with the tanh-type switching function plays an important role in reducing intrinsic vibration. Furthermore, an auxiliary system(AS) is developed to compensate for nonlinear terms arising from input saturation. Finally, the simulation results provide a solution to demonstrate that the suggested SMC and the AS methodology have advantages of strong tracking capability, anti-interference ability and anti-saturation performance.

Observer based projective reduced-order synchronization of different chaotic systems

The projective reduced-order synchronization of two different chaotic systems with different orders is investigated based on the observer design in this paper.According to the observer theory,the reduced-order observer is designed.The projective synchronization can be realized by choosing the transition matrix of the observer as a diagonal matrix.Further,the synchronization between hyperchaotic Chen system(fourth order)and Rssler system(third order)is taken as the example to demonstrate the effectiveness of the proposed observer.Numerical simulations confirm the effectiveness of the method.

Reduced-Order Observer-Based Leader-Following Formation Control for Discrete-Time Linear Multi-Agent Systems

Formation control of discrete-time linear multi-agent systems using directed switching topology is considered in this work via a reduced-order observer, in which a formation control protocol is proposed under the assumption that each directed communication topology has a directed spanning tree. By utilizing the relative outputs of neighboring agents, a reduced-order observer is designed for each following agent. A multi-step control algorithm is established based on the Lyapunov method and the modified discrete-time algebraic Riccati equation. A sufficient condition is given to ensure that the discrete-time linear multi-agent system can achieve the expected leader-following formation.Finally, numerical examples are provided so as to demonstrate the effectiveness of the obtained results.

A reduced-order extrapolation algorithm based on CNLSMFE formulation and POD technique for two-dimensional Sobolev equations

A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equations is established. The error estimates of the reduced-order CNLSMFE solutions and the implementation for the reduced-order extrapolation algorithm are provided. A numerical example is used to show that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order extrapolation algorithm is feasible and efficient for seeking numerical solutions to 2D Sobolev equations.

Reduced-Order GPIO Based Dynamic Event-Triggered Tracking Control of a Networked One-DOF Link Manipulator Without Velocity Measurement

In networked robot manipulators that deeply integrate control, communication and computation, the controller design needs to take into consideration the limited or costly system resources and the presence of disturbances/uncertainties. To cope with these requirements, this paper proposes a novel dynamic event-triggered robust tracking control method for a onedegree of freedom(DOF) link manipulator with external disturbance and system uncertainties via a reduced-order generalized proportional-integral observer(GPIO). By only using the sampled-data position signal, a new sampled-data robust output feedback tracking controller is proposed based on a reduced-order GPIO to attenuate the undesirable influence of the external disturbance and the system uncertainties. To save the communication resources, we propose a discrete-time dynamic event-triggering mechanism(DETM), where the estimates and the control signal are transmitted and computed only when the proposed discrete-time DETM is violated. It is shown that with the proposed control method, both tracking control properties and communication properties can be significantly improved. Finally, simulation results are shown to demonstrate the feasibility and efficacy of the proposed control approach.

Reduced-order Kalman filtering for state constrained linear systems

This paper aims at solving the state filtering problem for linear systems with state constraints. Three classes of typical state constraints, i.e., linear equality, quadratic equality and inequality, are discussed. By using the linear relationships among different state variables, a reduced-order Kalman filter is derived for the system with linear equality constraints. Afterwards, such a solution is applied to the cases of the quadratic equality constraint and inequality constraints and the two constrained state filtering problems are transformed into two relative constrained optimization problems. Then they are solved by the Lagrangian multiplier and linear matrix inequality techniques, respectively. Finally, two simple tracking examples are provided to illustrate the effectiveness of the reduced-order filters.

Generalized reduced-order synchronization of chaotic system based on fast slide mode

A new kind of generalized reduced-order synchronization of different chaotic systems is proposed in this paper. It is shown that dynamical evolution of third-order oscillator can be synchronized with the canonical projection of a fourth-order chaotic system generated through nonsingular states transformation from a cell neural net chaotic system. In this sense, it is said that generalized synchronization is achieved in reduced-order. The synchronization discussed here expands the scope of reduced-order synchronization studied in relevant literatures. In this way, we can achieve generalized reduced-order synchronization between many famous chaotic systems such as the second-order Drifting system and the third-order Lorenz system by designing a fast slide mode controller. Simulation results are provided to verify the operation of the designed synchronization.

Computationally efficient direction finding using polynomial rooting with reduced-order and real-valued computations

The root multiple signal classification（root-MUSIC） algorithm is one of the most important techniques for direction of arrival（DOA） estimation. Using a uniform linear array（ULA） composed of M sensors, this method usually estimates L signal DOAs by finding roots that lie closest to the unit circle of a（2M-1）-order polynomial, where L 〈 M. A novel efficient root-MUSIC-based method for direction estimation is presented, in which the order of polynomial is efficiently reduced to 2L. Compared with the unitary root-MUSIC（U-root-MUSIC） approach which involves real-valued computations only in the subspace decomposition stage, both tasks of subspace decomposition and polynomial rooting are implemented with real-valued computations in the new technique,which hence shows a significant efficiency advantage over most state-of-the-art techniques. Numerical simulations are conducted to verify the correctness and efficiency of the new estimator.

Sliding-Mode Control Based on Index control Law for MPPT in Photovoltaic Systems

A novel maximum power point tracking method based on sliding mode control and average state model of PV generation systems is developed.This method consists of two parts:term of constant control and term of index control.It is different from the conventional sliding mode control which uses a constant speed control law.The developed method uses a controllable sliding mode switching function which can automatically adjust the approaching speed,so as to enable the photovoltaic system to achieve fast dynamic response and stable output power.System simulations using MATLAB are performed.Compared with conventional methods,simulation results show that maximum power point tracking times for the novel method both in start-up phase and in cases of environmental changes can be shorten by more than 50%.A experimental platform of 150W PV system has been established to conduct tests.Experimental results show that the maximum power point tracking times both in start-up phase and in load stepping phase including the illumination change phase,can be significantly decreased.These results indicate that the developed method owns better dynamic response than constant speed control law.It can be used in photovoltaic generation system.

Nonlinear Control of an Induction Motor Using a Reduced-Order Extended Sliding Mode Observer for Rotor Flux and Speed Sensorless Estimation

This article proposes an innovative strategy to the problem of non-linear estimation of states for electrical machine systems. This method allows the estimation of variables that are difficult to access or that are simply impossible to measure. Thus, as compared with a full-order sliding mode observer, in order to reduce the execution time of the estimation, a reduced-order discrete-time Extended sliding mode observer is proposed for on-line estimation of rotor flux, speed and rotor resistance in an induction motor using a robust feedback linearization control. Simulations results on Matlab-Simulink environment for a 1.8 kW induction motor are presented to prove the effectiveness and high robustness of the proposed nonlinear control and observer against modeling uncertainty and measurement noise.

Research of influence of reduced-order boundary on accuracy and solution of interior points

The flow field with a high order scheme is usually calculated so as to solve complex flow problems and describe the flow structure accurately. However, there are two problems, i.e., the reduced-order boundary is inevitable and the order of the scheme at the discontinuous shock wave contained in the flow field as the supersonic flow field is low. It is questionable whether the reduced-order boundary and the low-order scheme at the shock wave have an effect on the numerical solution and accuracy of the flow field inside. In this paper, according to the actual situation of the direct numerical simulation of the flow field, two model equations with the exact solutions are solved, which are steady and unsteady, respectively, to study the question with a high order scheme at the interior of the domain and the reduced-order method at the boundary and center of the domain. Comparing with the exact solutions, it is found that the effect of reduced-order exists and cannot be ignored. In addition, the other two model equations with the exact solutions, which are often used in fluid mechanics, are also studied with the same process for the reduced-order problem.

A Novel Sliding-mode Guidance Law Based on Lie-group Method

Although the channel-decoupling assumption is often used in design of three-dimensional guidance laws, it loses its rationality for aircrafts with strong kinematics coupling because body rotation arises. To overcome this trouble, a novel guiding method was proposed based on Lie-group. After a model of 3D guidance is formulated using vectors, the precision guidance with ending angular constraints can be transformed into a problem involving the relation between directional angles and rotational angular velocities of certain vectors. When the guidance model is imposed a SO(3)-based description, a novel 3D sliding mode guidance law with ending angular constraints can be developed via Lie-group control method and variable structure control theory. Finally, the feasibility and performance of the guidance law were shown by simulating the examples.