Backstepping-based Decentralized PID Controller Design for MIMO Processes

A novel decentralized PID controller design procedure based on backstepping principles is presented to operate multiple-input multiple-output(MIMO)dynamic processes.The first key feature of the design procedure is that a whole MIMO control system is decomposed into multiple control loops,therefore the sub-controllers can be efficiently flexibly designed in parallel prototype. The second key feature is that the decentralized controller has equivalency to those designed by backstepping approach.As a complementary support to the design procedure,the sufficient condition of the whole closed-loop system stability is analyzed via the small gain theorem and it can be proven that the process tracking performance is improved.The simulation results of the Shell benchmark control problem are provided to verify the effectiveness and practicality of the proposed decentralized PID control.     

An adaptive fuzzy design for fault-tolerant control of MIMO nonlinear uncertain systems

This paper presents a novel control method for accommodating actuator faults in a class of multiple-input multiple-output (MIMO) nonlinear uncertain systems.The designed control scheme can tolerate both the time-varying lock-in-place and loss of effectiveness actuator faults.In each subsystem of the considered MIMO system,the controller is obtained from a backstepping procedure;an adaptive fuzzy approximator with minimal learning parameterization is employed to approximate the package of unknown nonlinear functions in each design step.Additional control effort is taken to deal with the approximation error and external disturbance together.It is proven that the closed-loop stability and desired tracking performance can be guaranteed by the proposed control scheme.An example is used to show the effectiveness of the designed controller.     

Optimal decentralized control of large scale systems

This paper presents a new optimized decentralized controller design method for solving the tracking and disturbance rejection problems for large-scale linear time-invariant systems, using only low-order decentralized controllers. To illustrate the type of results which can be obtained using the new optimized decentralized control design method, the control of a large flexible space structure is studied and compared with the standard centralized LQR-observer controller. The order of the resultant decentralized controller is much smaller than that of the standard centralized LQR-observer controller. The proposed controller also has certain fail-safe properties and, in addition, it can be five orders of magnitude more robust than the standard LQR-observer controller based on their real stability radii. The new decentralized controller design method is applied to a large flexible space structure system with 5 inputs and 5 outputs and of order 24.     

A novel adaptive backstepping design of turbine main steam valve control

The problem of transient stability for a single machine infinite bus system with turbine main steam valve control is addressed by means of a novel adaptive backstepping method in this paper. The recursive design procedure of the proposed controller is much simpler than that of the existing controller based on conventional adaptive backstepping method. In the system, the damping coefficient is measured inaccurately, and the reactance of transmission line also contains a few uncertainties. A nonlinear robust controller and parameter updating laws are obtained simultaneously. The system does not need to be linearized, and the closed-loop error system is guaranteed to be asymptotically stable. The design procedure and simulation results demonstrate the effectiveness of the proposed design.     

Nonfragile guaranteed cost control for Delta operator-formulated uncertain time-delay systems

With consideration that the controller parameters may vary from the designed value when the controller is realized, based on Lyapunov stability theory, a design method of nonfragile guaranteed cost control for a class of Delta operator-formulated uncertain time-delay systems is studied. A sufficient condition for the existence of the nonfragile guaranteed cost controller is given. A numeric example is then given to illustrate the effectiveness and the feasibility of the designed method. The results show that even if the parameters of the designed controller are of variations, the closed-loop system is still asymptotically stable and the super value of the cost function can also be obtained, while the closed-loop system will be unstable if the variations of the controller parameters are not considered when the controller is designed. The nonfragile guaranteed cost controller derived from the traditional shift operator method may cause the closed-loop system to be unstable, while the nonfragile guaranteed cost controller based on Delta operator method can avoid the unstable problem of the closed-loop system.     

Height and attitude active disturbance rejection controller design of a small-scale helicopter

Small-scale helicopters are very attractive because of their unique features.However,autonomous flight control for small-scale helicopters is still a challenging work because they are naturally unstable,strongly nonlinear,and sensitive to disturbances.In this paper,we focus on the design of a height and attitude active disturbance rejection controller(ADRC)for a small-scale helicopter constructed in our lab.Firstly,a comprehensive nonlinear model for the platform is presented,which is obtained through first principles modeling and system identification.The controller is designed using backstepping technique incorporated with extended state observer(ESO),which is used to estimate the unknown disturbances.Then,the estimate is introduced into the control law to compensate for the disturbances.The design specifications of military rotorcraft are introduced to guide the controller design to achieve specified control performance.Considering the physical limitations,reference models are designed to shape the desired control responses.At last,several flight simulations are carried out to validate the effectiveness and robustness of the proposed controller.The results show that the proposed controller works well and Level 1 performance can be achieved.     

Adaptive fuzzy decentralized control for nonlinear large-scale systems based on high-gain observer

An adaptive fuzzy decentralized backstepping output-feedback control approach is proposed for a class of nonlinear large-scale systems with completely unknown functions,the interconnections mismatched in control inputs,and without the measurements of the states.Fuzzy logic systems are employed to approximate the unknown nonlinear functions,and an adaptive high-gain observer is developed to estimate the unmeasured states.Using the designed high-gain observer,and combining the fuzzy adaptive control theory with backstepping approach,an adaptive fuzzy decentralized backstepping output-feedback control scheme is developed.It is proved that the proposed control approach can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded(SUUB),and that the observer errors and the tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters.Finally,a simulation example is provided to show the eectiveness of the proposed approach.     

Improved backstepping control for large angle maneuvers of spacecraft

For the control of large angle maneuvers of a spacecraft, variable gain backstepping control is proposed. The controller can make the states of the system converge to the commanded position along the input vector field orientation. The controller stabilizes the system with the amplitude of the commanded torques decreased. Considering the uncertainty of the disturbance torques and the estimation error of the inertia matrix, the control design is improved to provide strong self-adaptability and robustness of the system. Simulation is conducted, and the results show that the design has good tracking performance and convergence, consistent with the theoretical analysis.     

Globally asymptotic stabilization for nonlinear time-delay systems with ISS inverse dynamics

The output feedback stabilization is considered for a class of nonlinear time-delay systems with inverse dynamics in this paper.An appropriate state observer is constructed for the unmeasurable system states in order to realize the control objective.By adopting the backstepping and Lyapunov-Krasovskii functional methods,a systematic design procedure for a memoryless output feedback control law is presented.It is shown that the designed controller can make the closed-loop system globally asymptotically stable while keeping all signals bounded.An illustrative example is discussed to show the effectiveness of the proposed control strategy.     

四旋翼无人机鲁棒自适应姿态控制

 四旋翼无人机的姿态控制是自主飞行控制的核心,针对四旋翼姿态易受外界环境干扰和内部参数摄动等不确定性影响的问题,设计了一种鲁棒自适应反步控制器,以提高四旋翼的鲁棒性。建立了四旋翼完整的姿态运动模型,并将其转化为含有广义不确定性的多输入多输出非线性系统。根据该系统满足严格反馈的结构特点,设计了反步控制器; 针对系统中存在的外部干扰和内部参数摄动等不确定性,引入了一类鲁棒自适应函数来抵消该不确定性对系统的影响; 采用非线性跟踪微分器估计虚拟控制量的微分信号,减小了反步控制器设计中普遍存在的“计算膨胀”问题; 通过构造Lyapunov 函数证明闭环系统是稳定且指数收敛的。仿真结果表明,所设计控制器具有良好的控制效果和鲁棒性。     

Robust‐decentralized tracking control for a class of uncertain MIMO nonlinear systems with time‐varying delays

A new control design method based on signal compensation is proposed for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems in block‐triangular form with nonlinear uncertainties, unknown virtual control coefficients, strongly coupled interconnections, time‐varying delays, and external disturbances. By this method, the controller design is performed in a backstepping manner. At each step of backstepping procedure, a nominal virtual controller is first designed to get desired output tracking for the nominal disturbance‐free subsystem, and then a robust virtual compensator is designed to restrain the effect of the uncertainties, delays involved in the subsystem, and the couplings among the subsystems. The designed controller is linear and time‐invariant, so the explosion of complexity in the control law is avoid. It is proved that robust stability and robust practical tracking property of the closed‐loop system can be ensured, and the tracking errors can be made as small as desired. Copyright © 2013 John Wiley & Sons, Ltd.     

车载惯性稳定平台的神经网络滑模控制

三轴车载惯性稳定平台为复杂的MIMO非线性系统,针对其在不确定扰动下的伺服控制问题,本文设计了一种神经网络反演滑模控制器(NNBSMC).首先,选用反演法对其解耦,同时引入滑模控制律增加系统的抗干扰性;其次针对框架间的非线性摩擦力与系统耦合选用RBF神经网络作为扰动估计器,以便实时估计与补偿;然后采用前向增稳通道应对建...     

The Mimo Predictive Pid Controller Design

This paper is concerned with the design of Multi‐Inputs and Multi‐Outputs (MIMO) predictive PID controllers, which have similar performance to that obtainable from model‐based predictive controllers. A new PID control structure is defined which incorporates the prediction of future outputs and uses future set point. A method is proposed to calculate the optimal values of the PID gains from generalised predictive control results. A decentralized version of the predictive PID controllers is presented and the stability of the closed loop system is studied. Simulation studies demonstrate the superior performance of the proposed controller compared with a conventional PID controller. The results are also compared with generalised predictive control solutions.     

水上无人机自主着水控制系统设计

针对水上无人机在高海况下的着水问题,本文在分析了不同着水阶段特性的基础上,提出了一种自主着水控制系统设计方案.该方案将整个系统分为速度控制子系统和姿态控制子系统.速度控制子系统包含速度动态逆控制器和油门切换模块,姿态控制子系统包含海浪滤波器俯仰角反步控制器、高度PID控制器、俯仰角切换模块和T-S模糊推理模块.其中,海浪滤波器能有效滤除受扰姿态角中的海浪高频扰动,避免了着水之后舵面的频繁抖动;俯仰角反步控制器采用指令滤波的反步法设计,有效缓解了高海况下的舵面饱和问题.最后,在不同海况条件下进行了仿真.仿真结果表明所设计的控制系统具有良好的控制性能.     

Decentralised controller design based on structured singular values

In this study, structured singular values are used in a different way from those commonly used in the robust control literature. It is shown that subject to conditions based on structured singular values, each local area controller can be designed independently. A MATLAB? program is developed to plot inverse structured singular values of multi input multi output (MIMO) system relative error matrix. This plot can be used to predict the stability of the global system with decentralised controller. Therefore decentralised controller design problem can be translated into an equivalent problem of decentralized controller design for a MIMO control system.     

Direct decentralized neural control for nonlinear MIMO magnetic levitation system

A direct modified Elman neural networks (MENNs)-based decentralized controller is proposed to control the magnets of a nonlinear and unstable multi-input multi-output (MIMO) levitation system for the tracking of reference trajectories. First, the operating principles of a magnetic levitation system with two moving magnets are introduced. Then, due to the exact dynamic model of the MIMO magnetic levitation system is not clear, two MENNs are combined to be a direct MENN-based decentralized controller to deal with the highly nonlinear and unstable MIMO magnetic levitation system. Moreover, the connective weights of the MENNs are trained online by back-propagation (BP) methodology and the convergence analysis of the tracking error using discrete-type Lyapunov function is provided. Based on the direct and decentralized concepts, the computational burden is reduced and the controller design is simplified. Furthermore, the experimental results show that the proposed control scheme can control the magnets to track various periodic reference trajectories simultaneously in different operating conditions effectively.     

Decentralized adaptive backstepping stabilization of interconnected systems with dynamic input and output interactions

So far there is still no result available for backstepping based decentralized adaptive stabilization of unknown systems with interactions directly depending on subsystem inputs, even though such interactions commonly exist in practice. In this paper, we provide a solution to this problem by considering both input and output dynamic interactions. To clearly illustrate our approaches, we will start with linear systems and then extend the results to nonlinear systems. Each local controller, designed simply based on the model of each subsystem by using the standard adaptive backstepping technique without any modification, only employs local information to generate control signals. It is shown that the designed decentralized adaptive backstepping controllers can globally stabilize the overall interconnected system asymptotically. The L₂ and L_∞ norms of the system outputs are also established as functions of design parameters. This implies that the transient system performance can be adjusted by choosing suitable design parameters.