On approximate linearization of nonlinear control systems

A method for the approximate linearization of nonlinear control systems based on the ‘state-space exact linearization’ method is presented. An explicit procedure, both for the single-input and for the multiple-input case, is given, which is straightforward to implement.     

Soft variable-structure controls: a survey

Variable-structure controls are normally understood to be controls that have sliding modes and robustness as their main objective. In addition to sliding-mode controls, there are also variable-structure controls, which were developed for the purpose of intentionally precluding sliding modes and achieving high regulation rates and short settling times. Two types of such controls may be distinguished, variable-structure controls that switch between different parameters and a systematic further development of them called “soft variable-structure controls” that continuously vary controllers' parameters or structures and achieve nearly time-optimal control performance. This paper surveys soft variable-structure controls, compares them to other controls, taking a submarine dive-control as an example, and presents an outlook on their auspicious further development.     

Automatic differentiation and nonlinear controller design by exact linearization

Various modern algorithms for controller design are based on differential-geometric concepts. A method of particular importance is called exact linearization via feedback. In this case, the implementation of the controller requires the computation of Lie derivatives, which have been computed symbolically. This can be very time consuming. We present a new computation method relying on automatic differentiation.     

Remarks on universal nonsingular controls for discrete-time systems

For analytic discrete-time systems, it is shown that uniform forward accessibility implies the generic existence of universal nonsingular control sequences. A particular application is given by considering forward accessible systems on compact manifolds. For general systems, it is proved that the complement of the set of universal sequences of infinite length is of the first category. For classes of systems satisfying a descending chain condition, and in particular, for systems defined by polynomial dynamics, forward accessibility implies uniform forward accessibility.     

Global stabilization of multiple integrators with bounded controls

This paper deals with the global stabilization of a chain of integrators by means of bounded feedback. Two nonlinear control laws made of summation of saturation of the state are proposed. The first one extends that of Sussmann, Sontag and Yang [(1994). IEEE Transactions on Automatic Control, 39(12), 2411–2425] and the second proposes variable saturation level to improve the performance. Both remain very simple and significantly improve the efficiency of the approach, which is very competitive with respect to the other existing methods, especially for its performance/complexity ratio. The robustness with respect to measurement delay and model uncertainty is numerically tested.     

磁悬浮系统的两种线性化控制方法

本文首先利用动力学和电磁学方法建立了磁悬浮系统的模型 ,然后给出了直接反馈线性化方法的控制器设计 ,接着给出了基于平衡点展开的控制器设计 ,最后将两种控制方法的性能做了仿真比较 ,得出了两种方法的优劣结论。     

Input-output pseudolinearization on controlled invariant submanifolds

The original notion of input-output pseudolinearization on equilibrium submanifolds is extended to general controlled invariant submanifolds for nonlinear systems. Input-output pseudolinearizing feedback laws render the input-output behavior of linearizations about nominal trajectories in the submanifold trajectory-independent and equal to that of a fixed linear time-invariant system, thereby facilitating the subsequent construction of control laws for stabilization and tracking. Sufficient existence conditions are derived that are weaker than the familiar relative degree conditions for nonlinear input-output decoupling that have come to be associated with exact input-output linearization.     

Modeling and control of a single-phase marine cooling system

This paper presents two model-based control design approaches for a single-phase marine cooling system. Models are derived from first principles and aim at describing significant system dynamics including nonlinearities and transport delays, while keeping the model complexity low. The two approaches investigated are: a baseline design for performance comparison and a nonlinear robust control design. Performance and robustness of performance for the two control designs are evaluated through a simulation example. Both designs show good robustness towards parameter variations, while the nonlinear robust design performs better in terms of disturbance rejection.     

Microprocessor-based controls for drilling — retrofitting aspects

This paper considers the updating of NC (numerical control) machine tools with control systems demonstrating modern features. To illustrate such machine tool retrofitting, the paper describes the structure of microprocessor-based hardware and software which was developed to achieve improved control of a first generation NC drilling machine.     

Feedback linearization control for a distributed solar collector field

This article describes the application of a feedback linearization technique for control of a distributed solar collector field using the energy from solar radiation to heat a fluid. The control target is to track an outlet temperature reference by manipulating the fluid flow rate through the solar field, while attenuating the effect of disturbances (mainly radiation and inlet temperature). The proposed control scheme is very easy to implement, as it uses a numerical approximation of the transport delay and a modification of the classical control scheme to improve startup in such a way that results compared with other control structures under similar conditions are improved while preserving short commissioning times. Experiments in the real plant are also described, demonstrating how operation can be started up efficiently.     

Nonlinear control for global stabilization of multiple-integrator system by bounded controls

The global stabilization problem of the multiple-integrator system by bounded controls is considered. A nonlinear feedback law consisting of nested saturation functions is proposed. This type of nonlinear feedback law that is a modification and generalization of the result given in [1] needs only [（n ＋ 1）/2] （n is the dimensions of the system） saturation elements, which is fewer than that which the other nonlinear laws need. Furthermore, the poles of the closedloop system can be placed on any location on the left real axis when none of the saturation elements in the control laws is saturated. This type of nonlinear control law exhibits a simpler structure and can significantly improve the transient performances of the closed-loop system, and is very superior to the other existing methods. Simulation on a fourth-order system is used to validate the proposed method.     

Feedback linearization based control of a rotational hydraulic drive

The technique of feedback linearization is used to design controllers for displacement, velocity and differential pressure control of a rotational hydraulic drive. The controllers, which take into account the square-root nonlinearity in the system's dynamics, are implemented on an experimental test bench and results of performance evaluation tests are presented. The objective of this research is twofold: firstly, to present a unified method for tracking control of displacement, velocity and differential pressure; and secondly, to experimentally address the issue of whether the system can be modeled with sufficient accuracy to effectively cancel out the nonlinearities in a real-world system.     

基于LabVIEW的非线性励磁控制器

本文介绍了以LabVIEW为开发平台设计的非线性励磁控制器。文中首先介绍了直接反馈线性化理论 ,然后介绍了软件和硬件的设计 ,并给出了仿真结果。仿真结果表明该控制器能显著改善系统的暂态稳定性。LabVIEW的使用为设计带来许多便利和强大的功能。     

非线性大系统的分散线性化与分散控制

将非线性控制系统的精确线性化方法应用于非线性大系统,提出了非线性大系统 的分散线性化方法,并得到了非线性系统可分散线性化的充要条件.按照这个方法,可将难度 较大的一类非线性大系统分散控制器的设计转化为易于处理的线性大系统分散控制器的设 计.在得到该线性大系统的分散控制器后,可通过分散坐标变换的逆变换将线性大系统的控 制器变换为原非线性大系统的控制器.同时,控制器的分散性保持不变.该方法明显地降低了 该类非线性大系统分散控制器的设计难度.     

Optimal compensation of nonlinearities in the presence of noise

The problem of feedback linearization for control systems containing sign-type (jump) nonlinearities is considered. Sometimes it is theoretically possible to cancel such nonlinearities by feedback. But, even in that case, such cancellation involves the use of discontinuous feedback laws, which can behave poorly in the presence of noise. We formulate and solve a problem that allows us to obtain optimal feedback compensation of nonlinearities, assuming additive noise in the measurements. Some simple examples are included to illustrate the advantages of our approach.     

非线性控制系统的全局输出调节

讨论了非线性控制系统的全局输出调节.首先推广精确线性化方法,通过状态反馈 和微分同胚将非线性系统的全局输出调节问题,转化为线性系统对非线性系统的跟踪问题. 通过提出可解性的概念,得到线性系统对非线性系统全局跟踪的条件,该结果是线性系统结 果的推广.在反馈同胚变换全局成立条件下,得到非线性控制系统全局输出调节问题的充分 条件,该条件对外部系统只做较弱的可解性假设,在反馈同胚变换局部成立的条件下,可得局 部结果.     

Nonlinear control of coal-fired steam power plants

This work proposes a nonlinear control strategy for steam power plants that efficiently controls the superheated steam temperature while accommodating large and frequent variations in power demand. The variables to be controlled are the pressure in the boiler, power generation, and superheater/reheater temperatures. The proposed strategy decomposes the overall plant into three separate subsystems and applies decoupling with deadtime compensation for each one of them. The derived strategy is implemented within a MATLAB/Simulink environment for different setpoint tracking and disturbance rejection cases, showing excellent performance and robustness.     

On nonlinear control of Euler-Lagrange systems: Disturbance attenuation properties

In this brief note we analyse the (local) disturbance attenuation properties of some asymptotically stabilizing nonlinear controllers for Euler-Lagrange systems reported in the literature. Our objective in this study is twofold: first, to compare the performance of these schemes from a perspective different from stabilizability; second, to quantify the basic tradeoff between robust stability and robust performance for these designs. We consider passivity-based and feedback linearization schemes developed for the control of DC-to-DC converters and rigid robots. For the DC-to-DC problem we show that for both controllers there exists a lower bound to the achievable attenuation level, i.e. a lower bound to the ₂-gain of the closed loop operator from disturbance to regulated output, which is independent of the design parameters. Also, for the passivity based scheme we obtain an upper bound for the disturbance attenuation, which is insured provided we sacrifice the convergence rate. For rigid robots we show that both approaches yield arbitrarily good disturbance attenuation without compromising the convergence rate.     

Quotient submanifolds for static feedback linearization

A procedure for finding locally the linearizing output of a single input nonlinear affine system is proposed. It relies on successive integrations of one-dimensional distributions and projections along these submanifolds. The algorithm proceeds recursively reducing the dimension one by one of both the number of coordinates and the number of vector fields, until the solution is obtained. A variant of the algorithm is also proposed, which does not require the computation of the full initial distribution. The proof of convergence of this second algorithm shows the importance of a new anti-symmetrical product. Besides providing a new insight into the involutivity condition, the algorithm can lead to a simple way of integrating the system of partial differential equations defining the linearizing output.     

On the largest feedback linearizable subsystem

A feedback invariant set of integers is associated with any nonlinear multivariable system which is linear with respect to the inputs: it is shown to be the set of controllability indices of the largest feedback linearizable subsystem, i.e. the largest subsystem which can be made locally linear and controllable by means of nonsingular feedback transformations.