Robust control of uncertain feedback linearizable systems based on adaptive disturbance estimation

In this paper, an adaptive disturbance estimation-based control of a class of uncertain feedback linearizable systems with the presence of, both, external perturbations as well as non-modeled dynamics is considered. The aim of the control design was to solve the tracking trajectory problem for a class of output-based linearizable uncertain systems. An adaptive scheme is proposed for developing a state estimator of the uncertain dynamics. The estimation of both, the states and the uncertain dynamics is attained despite the limited knowledge of the plant and the information contained in the output signal. The uncertain section in the linearized system was approximated by a class of time-dependent combination of the system states. The observer implemented a parametric identifier to obtain the time varying parameters associated to the estimation of the uncertain section. This method ensured the adequate estimation process of the uncertainties/perturbations, measured in terms of the mean square error. Simultaneously, an adaptive gain associated to the observer adjusts its trajectories to provide the ultimate boundedness of the estimation error. Once the states of the uncertain system are obtained, a feedback controller rejects actively the perturbations that affect the system by a compensation scheme. Two numerical examples were developed to show the observer-based control performance.     

Vibrational control of underactuated mechanical systems control design through averaging analysis

An open loop vibrational control for an underactuated mechanical system with amplitude and frequency modulation is investigated. Since there is no direct external input to an unactuated joint, the dynamic coupling between the actuated and unactuated joint is utilized for controlling the unactuated joint. Feedback linearization has been performed to fully incorporate the known nonlinearities of the underactuated system considered. The actuated joints are firstly positioned to their desired locations, and then periodic oscillatory inputs are applied to the actuated joints to move the remaining unactuated joints to their target positions. The amplitudes and frequencies of the vibrations introduced are determined through averaging analysis. A systematic way of obtaining an averaged system for the underactuated system via a coordinate transformation is developed. A manipulator in the zero gravity space can be vibrationally controlled in the event of actuator failure. A control design example of the 2R planar manipulator with a free joint with no brake is provided.     

Robust control design for a wheel loader using and feedback linearization based methods

The heavy equipment industry is building more and more equipment with electro-hydraulic control systems. The existing industry practices for the design of control systems in construction machines primarily rely on classical designs coupled with ad-hoc synthesis procedures. Such practices produce desirable results, but lack a systematic procedure to account for invariably present plant uncertainties in the design process as well as coupled dynamics of the multi-input multi-output (MIMO) configuration. In this paper, two H_∞ based robust control designs are presented for an automatic bucket leveling mechanism of a wheel loader. In one case, the controller is designed for the base plant model. In another case, the controller is designed for the plant with a feedback linearization control law applied yielding improved stability robustness. A MIMO nonlinear model for an electro-hydraulically actuated wheel loader linkage is considered. The robustness of the controller designs are validated by using analysis and by simulation using a complete nonlinear model of the wheel loader linkage and hydraulic system.     

Robust feedback linearization for nonlinear processes control

In this research, a robust feedback linearization technique is studied for nonlinear processes control. The main contributions are described as follows: 1) Theory says that if a linearized controlled process is stable, then nonlinear process states are asymptotically stable, it is not satisfied in applications because some states converge to small values; therefore, a theorem based on Lyapunov theory is proposed to prove that if a linearized controlled process is stable, then nonlinear process states are uniformly stable. 2) Theory says that all the main and crossed states feedbacks should be considered for the nonlinear processes regulation, it makes more difficult to find the controller gains; consequently, only the main states feedbacks are utilized to obtain a satisfactory result in applications. This introduced strategy is applied in a fuel cell and a manipulator.     

Robust decentralized hybrid adaptive output feedback fuzzy control for a class of large-scale MIMO nonlinear systems and its application to AHS

This paper presents a novel observer-based decentralized hybrid adaptive fuzzy control scheme for a class of large-scale continuous-time multiple-input multiple-output (MIMO) uncertain nonlinear systems whose state variables are unmeasurable. The scheme integrates fuzzy logic systems, state observers, and strictly positive real conditions to deal with three issues in the control of a large-scale MIMO uncertain nonlinear system: algorithm design, controller singularity, and transient response. Then, the design of the hybrid adaptive fuzzy controller is extended to address a general large-scale uncertain nonlinear system. It is shown that the resultant closed-loop large-scale system keeps asymptotically stable and the tracking error converges to zero. The better characteristics of our scheme are demonstrated by simulations.     

Sliding mode control of I/O linearizable systems with uncertainty

In this paper we explore the application of sliding mode control to process control problems. Sliding mode control is presented as a natural tool for robust design of state feedback controllers for minimum phase input–output linearizable systems with uncertainty. An example is presented to illustrate some of the issues involved in the design of sliding mode robust controllers.     

Signal-to-noise ratio constrained feedback control: Robust stability analysis

The explicit consideration of a communication channel model in a feedback control loop is known to be constrained by a fundamental limitation for stabilizability on the channel signal-to-noise ratio (SNR) when the linear time invariant (LTI) plant model is unstable. The LTI modelling approach for real, usually nonlinear, processes compromises accuracy versus complexity of the resulting model. This in turn introduces a gap between the proposed model and the real process, which is known as the model uncertainty. In this paper we then study SNR limitations by considering the continuous-time scenario and the case of an additive coloured Gaussian noise (ACGN) channel with bandwidth limitation, for which we then quantify the infimal SNR subject to the simultaneous presence of plant, channel and noise model uncertainties. We observe, for the special case of memoryless additive white Gaussian noise (AWGN) channels, that the obtained SNR limitation subject to plant model uncertainty can be redefined as a channel capacity limitation for stabilization.     

龙门移动式数控机床横梁磁悬浮控制系统研究

针对龙门移动式数控机床中的移动横梁,提出了采用磁悬浮技术,实现无摩擦驱动的新型控制方案。首先,建立了横梁磁悬浮系统的数学模型,利用反馈线性化方法,将非线性模型转化为线性模型,再采用PI状态反馈设计的方法,设计一个悬浮控制器。该反馈线性化是一种全局线性化的方法,优于传统的局部近似线性化的方法。仿真结果表明,该悬浮控制器可以保证全局稳定,使系统具有良好的鲁棒性。     

Robustness of discrete-time state feedback control systems

This paper presents stability robustness results for linear multivariable discrete-time systems with uncertainties. Robust stability of the full-state feedback linear quadratic regulator in the presence of perturbations of the system parameters is investigated. These results are based on recently developed bounds on structured perturbations of a stable linear discrete-time system. The paper applies these results to a paper-machine head box system example.     

Robust output feedback distributed model predictive control of networked systems with communication delays in the presence of disturbance

In this work, an output feedback cooperative distributed model predictive control is developed for a class of networked systems composed of interacting subsystems interconnected through their states, in which it handles bounded disturbances and time varying communication delays. A distributed buffer based prediction strategy is used to compensate bounded delays and predict those states, which are coupled between subsystems that their actual values may not available due to delays. In the design of robust distributed model predictive control, distributed moving horizon estimation is employed so that convergence and boundedness of the estimation error are ensured. Furthermore, robust exponential stability of the closed loop system is established. The effectiveness of the proposed method is illustrated using two interconnected continuous stirred tank reactors.     

Predictive feedback control

In this work a new method for designing predictive controllers for linear single-input/single-output systems is presented. It uses only one prediction of the process output J time intervals ahead to compute the correspondent future error. Then, the predictive feedback controller is defined by introducing a filter which weights the last w predicted errors. In this way, the resulting control action is computed by observing the system future behavior and also by weighting present and past errors. This last feature improves the closed-loop performance to disturbance rejection as shown through simulations of two linear systems and a nonlinear continuous stirred tank reactor.     

Robust model predictive control for switched linear systems

Developed is a robust model predictive control scheme for a class of discrete-time switched linear systems. The system is described in linear fractional transformation form in the presence of model uncertainty and induced norm bounded disturbances. The objective is to minimize the upper bound of an infinite horizon cost function subject to a terminal inequality. A Lyapunov function analysis for the switched system shows guaranteed closed-loop stability. Taking into account the switching structure of the system, the predictive control design problem along with sufficient conditions for the existence of a solution is expressed in terms of Riccati–Metzler inequalities. Then, these inequalities are turned into a linear matrix inequality feasibility problem. Three cases are analyzed to demonstrate the performance and effectiveness of the proposed robust model predictive controller for switched discrete-time linear systems.     

Robust nonlinear control of a 6 DOF parallel manipulator : Task space approach

This paper presents a robust nonlinear controller for a 6 degree of freedom (DOF) parallel manipulator in the task space coordinates. The proposed control strategy requires information on orientations and translations in the task space unlike the joint space or link space control scheme. Although a 6 DOF sensor may provide such information in a straightforward manner, its cost calls for a more economical alternative. A novel indirect method based on the readily available length information engages as a potential candidate to replace a 6 DOF sensor. The indirect approach generates the necessary information by solving the forward kinematics and subsequently applying alpha-beta-gamma tracker. With the 6 DOF signals available, a robust nonlinear task space control (RNTC) scheme is proposed based on the Lyapunov redesign method, whose stability is rigorously proved. The performance of the proposed RNTC with the new estimation scheme is evaluated via experiments. First, the results of the estimator are compared with the rate-gyro signals, which indicates excellent agreement. Then, the RNTC with on-line estimated 6 DOF data is shown to achieve excellent control performance to sinusoidal inputs, which is superior to those of a commonly used proportional-plus-integral-plus-derivative controller with a feedforward friction compensation under joint space coordinates and the nonlinear controller under task space coordinates.     

Robust control for rotational inverted pendulums using output feedback sliding mode controller and disturbance observer

This paper presents a system modeling, controller design and implementation for a rotational inverted pendulum system (RIPS), which is an under-actuated system and has the problem of unattainable velocity state. Two control strategies are applied to theRIPS. One is a sliding mode control method using the parameterization of both the hyperplane and the compensator for output feedback. The other is the disturbance observer which estimates disturbance and some modeling errors of RIPS with less computational effort. Some simulations and various kinds of experiments are performed in order to verify that the proposed controller has the ability to control RIPS whose velocity is assumed to be unavailable. The results of the simulations and experiments show that the proposed control system has superior performance for disturbance rejection and regulation at certain initial conditions as well as the robustness to model uncertainties.     

加工过程QFT控制及与自适应控制的结合

阐述了定量反馈理论（QFT）的基本原理和设计步骤。并给出了设计实例。为了进一步改善系统性能。在QFT的基础上提出了QFT与自适应控制相结合的方案。QFT能克服对象的不确定性。保障系统的鲁棒性。自适应控制可以提高系统的控制精度。仿真结果表明。这种方法适合高精度系统的鲁棒控制。     

Robust LQG controller design for lightly damped uncertain linear systems

In this note, we consider lightly damped uncertain linear systems with natural frequency variations. This type of uncertainty has multiple uncertain parameters with multiple rank structure. It is well known that the conventional LQG or LQG/LTR methods can not be applied to such system bccause of the instability and the design conservatism. To overcome such shortcomings, we propose a systematic method to design robust LQG controllers. The proposed method requires only the LQG tuning parameters and the structure information of uncertainty. It will be shown that our approach can be effectively applied to flexible structure control design problems. Center for Noise and Vibration Control (NoViC), Dept. of Mech Eng., Korea Advanced Institute of Science and Technology (KAIST)     

加工中心龙门磁悬浮高度的滑模控制

针对龙门加工中心中的移动横梁,提出了采用磁悬浮技术,实现无摩擦驱动的新型控制方案。根据所建立的横梁磁悬浮系统的数学模型,应用基于微分几何的反馈线性化方法将非线性的电磁悬浮系统转化为线性系统,然后利用积分滑模控制器来对整个系统进行鲁棒控制。仿真研究结果表明,与传统控制方法相比,系统具有很强的抗扰性和较高的刚度,横梁能够实现无摩擦稳定悬浮。     

Robust control of saturating systems with Markovian packet dropouts under distributed MPC

In this work, a robust control methodology is presented for saturating systems with packet dropouts under distributed model predictive control framework. The sequence of time instants when data dropout happens is modeled by a Markov chain. A packet dropout compensation strategy and an augmented Markov jump linear model are considered simultaneously. To design distributed model predictive controllers, the entire system is decomposed into coupled subsystems. Considering the influences of neighbor subsystems, a distributed predictive control synthesis involving packet dropouts and Markovian probabilities is developed by minimizing the worst-case performance index at each time instant. The input saturation constraints are also incorporated into the robust controller design under distributed model predictive control framework. Furthermore, both the recursive feasibility of the proposed robust control under distributed model predictive control and the closed-loop mean-square stability are proved. To show the effectiveness, the proposed methodology is validated by simulations on a continuous stirred tank reactor process and a DC control system.