Example applications of the linear adaptive design technique

Adaptive controllers can be designed by a variety of different methodologies that have been developed over the past 35 years. However, all these methodologies have one thing in common; they lead to adaptive controllers that are intriniscatly non-linear in structure. Recently a new, unorthodox approach to the adaptive control problem has been developed. This new methodology leads to a new class of adaptive controllers that, in many cases, are entirely linear and have all-constant parameters (constant gains). In the present paper this new approach to adaptive control is used to design‘linear adaptive controllers’for two example applications, and the closed-loop adaptive performance obtained in each case is illustrated by digital simulation tests. These results demonstrate that the new linear adaptive controllers are able to produce a surprisingly high-degree of adaptation over significant ranges of plant parameter variations and disturbances.     

Adaptive non-linear control with incomplete state information

Motivated by several recent adaptive non-linear control results which use either full-state or single-output feedback, we present two new adaptive design tools and show how they can be used to construct systematic design procedures for non-linear systems with incomplete state information. The main features of these procedures are illustrated on a simple third-order system. We also provide the geometric conditions which give a co-ordinate-free characterization of one of the partial-state-feedback forms to which these procedures are applicable.     

An indirect model reference adaptive controller based on the multirate sampling of the plant output

The use of sampled-data multirate-output controllers for model reference adaptive control of possibly non-stably invertible linear systems with unknown parameters is investigated. Multirate-output controllers contain a multirate sampling mechanism with different sampling period at each system output. Such a control allows us to assign an arbitrary discrete-time transfer function matrix for the sampled closed-loop system and does not make assumptions on the plant other than controllability, observability and the knowledge of two sets of structural indices, namely the controllability and the observability indices. An indirect adaptive control scheme based on these sampled-data controllers is proposed which estimates the unknown plant parameters (and consequently the controller parameters) on-line from sequential data of the inputs and the outputs of the plant, which are recursively updated within the time limit imposed by a fundamental sampling period T₀. Using the proposed adaptive algorithm, the model reference adaptive control problem is reduced to the determination of a fictitious static state feedback controller owing to the merits of multirate-output controllers. Known indirect model reference adaptive control techniques usually resort to the direct computation of dynamic controllers. The controller determination reduces to the simple problem of solving a linear algebraic system of equations, whereas in known indirect model reference adaptive control techniques, matrix polynomial Diophantine equations usually need to be solved. Moreover, persistent excitation of the continuous-time plant is provided without making any special richness assumption on the reference signals.     

Adaptively controlling non-linear systems,using trajectory approximations

The structure underlying most adaptive algorithms is a linear parametrized set. This set either represents the universe of controllers the adaptive algorithm can choose from in order to achieve the control task or it may represent a class of models the adaptive algorithm may exploit to approximate the open-loop plant behaviour. In the latter approach the controller used to close the loop is selected via some non-linear map of the identified model parameters. The emphasis is on approximating the vector field that generates the trajectories of the system. Alternatively we propose to predict the trajectories over a short period of time directly, not indirectly involving a representation of the underlying vector fields. The feasibility of such an approach using a one-step-ahead-type algorithm for both prediction and control is analysed. The scheme is hybrid in that the plant is continuous-time, whilst the control action is implemented in discrete time. The control action is of the model reference type. The algorithm is applied to a class of (non)-linear time-varying systems of a given structure (known relative degree) and possessing a stable inverse. Given input/output measurements only, the algorithm can enforce a desired response within guaranteed error bounds. Robustness properties with respect to partial state measurement (e.g. neglecting parasitic dynamics) and violation of the stable inverse assumption are investigated.     

Parallel feedforward and simplified adaptive control

Simple adaptive control systems were recently shown to be globally stable and to maintain robustness in the presence of disturbances if the controlled plant is ‘almost strictly positive real’, namely, if there exists a positive definite static output feedback (unknown and not needed for implementation) such that the resulting closed-loop transfer function is strictly positive real. This paper is an attempt to show in an intuitive way how to use parallel feedforward and the stabilizability properties of systems in order to satisfy the ‘almost positivity’ condition. The feedforward configuration may be stationary, if some prior knowledge is given, or adaptive, in general. This way, simple adaptive controllers can be implemented in a large number of complex control systems, without requiring the order of the plant or the pole excess as prior knowledge     

Enhancing optimal controllers via techniques from robust and adaptive control

Optimal control strategies for both non-linear and linear plants and indices are notoriously sensitive to modelling errors and external noise disturbances. In this paper a general framework to enhance robustness of an optimal control law is presented, with emphasis on the non-linear case. The framework allows a blending of off-line non-linear optimal control, on-line linear robust feedback control for regulation about the optimal trajectory and on-line adaptive techniques to enhance performance/robustness. The adaptive-Q techniques are those developed in previous work based on the Youla-Kucera parametrization for the class of all stabilizing two-degree-of-freedom controllers. Some general fundamental stability properties are developed which are new, at least for the non-linear plant and linear robust controller case. Also, performance enhancement results in the presence of unmodelled linear dynamics based on an averaging analysis are reviewed. A convergence analysis based on averaging theory appears possible in principle for any specific non-linear system but is beyond the scope of the present paper. Certain model reference adaptive control algorithms come out as special cases. A non-linear optimal control problem is studied to illustrate the efficacy of the techniques, and the possibility of further performance enhancement based on functional learning is noted.     

An adaptive control scheme using multiple reference models

This paper develops an extended model reference adaptive control scheme to expand the capacity of state feedback state tracking adaptive control to handle the plant‐model matching uncertainties for single‐input LTI systems. The extended scheme is developed, using multiple reference model systems (only one of which is required to be able to match the controlled plant), and multiple controllers (which are updated from adaptive laws generated from multiple reference model systems based estimation errors), as two key features of such design to relax a plant‐model matching condition. A switching mechanism is constructed using those multiple estimation errors, capable of selecting the suitable control input from the multiple control signals, to achieve the desired system performance. An aircraft flight control example is presented to show the capacity of such design in relaxing a practical design condition. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive control of time-varying plants: Simple examples

The design and properties of an adaptive model reference scheme and an adaptive pole placement control scheme for linear time-varying plants are demonstrated via two simple examples. The two new schemes combine new control laws that are appropriate for time-varying plants with estimators that can utilize any available a prior; information on the structure of the parameter variations and are applicable to plants which are not necessarily slowly time-varying. As illustrated by simulations, the new adaptive controllers exhibit good performance even in cases of fast plant parameter variations.     

Design of PI and PID controllers with transient performance specification

Proportional-integral-derivative (PID) controllers are widely used in industrial control systems because of the reduced number of parameters to be tuned. The most popular design technique is the Ziegler-Nichols method, which relies solely on parameters obtained from the plant step response. However, besides being suitable only for systems with monotonic step response, the compensated systems whose controllers are tuned in accordance with the Ziegler-Nichols method have generally a step response with a high-percent overshoot. In this paper, tuning methods for proportional-integral (PI) and PID controllers are proposed that, like the Ziegler-Nichols method, need only parameters obtained from the plant step response. The methodology also encompasses the design of PID controllers for plants with underdamped step response and provides the means for a systematic adjustment of the controller gain in order to meet transient performance specifications. In addition, since all the development of the methodology relies solely on concepts introduced in a frequency-domain-based control course, the paper has also a didactic contribution.     

Adaptive control of a stochastic non-linear system: An example

In this paper a simple non-linear stochastic system is analysed. Various problem formulations are discussed and the performances of the resulting non-linear adaptive controllers are investigated. The adaptive controllers are based on predictions of the output of the process.     

A comparative study of normalized and unnormalized tuning errors in parameter adaptive control

In the past year several advances in the development of adaptive control for non-linear systems have made it clear that algorithms not using error normalization have several significant advantages over algorithms which do, in spite of their much greater complexity. In this paper simple examples are used to give a detailed account of the essential differences in structure between adaptive algorithms of the normalized and unnormalized types. It is explained why only the latter readily generalize to non-linear process models with non-global Lipschitz non-linearities. It is shown that one of these algorithms is capable of stabilizing linear process models with different relative degrees.     

Linear adaptive control of a single-tether system

A control law for a single-tether orbiting satellite system based on a reduced order linear adaptive control technique is presented. The main advantages of this technique are its design simplicity and the facts that specific system parameters and model linearization are not required when disigning the conroller. Two controllers are developed: one which uses only tension in the tether as control actuation and one which uses both tension and in-plane thrusters as control actaution. Both a sixth-order non-linear and an 11th-order bead model of a tethered satellite system are used for simulation purposes, demonstrating the ability of the controller to manage an uncertain system. Retrieval and stationkeeping results using these non-linear models and the linear adaptive controller demonstrate the feasibility of the method. The robustness of the controller with respect to parameter uncertainties is also demonstrated by changing the non-linear model and parameters whithin the model without redesigning the controller.     

Decentralized adaptive linear control of complex systems using relative deadzones

This paper aims to analyse the system stability when decentralized adaptive controllers are applied to multi-input/multi-output non-linear interconnected systems. The local adaptive controllers are designed based on linear models by employing relative deadzones. Using a small-gain-type argument, we can derive an M-matrix test condition for local stability. If the system to be controlled can be described by global Lipschitz functions, a global stable closed-loop system is obtained. © 1997 by John Wiley & Sons, Ltd.     

Application of Neural Networks to Disturbances Encountered Landing Control

Neural network applications to aircraft automatic landing control are presented. Conventional automatic landing systems (ALSs) can provide a smooth landing, which is essential to the comfort of passengers. However, these systems work only within a specified operational safety envelope. When the conditions are beyond the envelope, such as turbulence or wind shear, they often cannot be used. The objective of this paper is to investigate the use of neural networks in ALSs and to make these systems more intelligent. Current flight control law is adopted in the intelligent controller design. Tracking performance and robustness are demonstrated through software simulations. This paper presents five different neural network controllers to improve the performance of conventional ALSs based on a modified learning-through-time process. Simulation results show that the neural network controllers can successfully expand the safety envelope to include more hostile environments such as severe turbulence     

规则自适应模糊控制在同步发电机励磁系统中的应用

对于像电力系统这样的典型非线性系统,采用常规PID控制器很难保证系统在不同工作状态下均取得良好的控制效果.采用模糊参数自适应PID励磁控制器对解决小干扰下的励磁控制问题具有较好的控制效果.当系统工作状态变化较大以及遇到较强的干扰时,系统控制性能将趋于恶化.为解决此问题,提出了同步发电机励磁系统的规则自适应模糊控制方案.主要讨论在模糊集Ai、Bi 的比例因子K1、K2、K3给定的条件下,通过调整 di 的取值来实现控制规则的自适应问题, 该规则自适应机构由两组关于控制规则自生成与自校正的元规则组成.仿真结果表明,所提出的方案正确可行并具有良好的性能.     

Passive adaptive control of non-linear systems

We develop a new recursive procedure for the design of adaptive controllers for non-linear systems with unknown parameters and unmeasured states. The use of novel nonlinear damping terms endows the closed-loop systems with the remarkable property of boundedness for arbitrary parametric uncertainty even when the adaptation is switched off. The combination of these nonlinear terms with interlacing functions produces ‘damped interlacing’, which results in new passivity and transient performance properties. Damped interlacing allows us to construct a full Lyapunov function that encompasses all the variables of the adaptive system.     

Linear and non-linear adaptive control of alcoholic fermentation process: Experimental results

This paper deals with the experimental implementation of several control algorithms on a continuous flow fermentation process. The regulation and tracking problems of the substrate concentration are considered. Our objective is to show the advantages and drawbacks of these algorithms in tracking and regulation behaviour, overshoot, knowledge contribution, number of tuning parameters, etc. The different controllers described in this paper are the PI controller, the non-linear adaptive L/A algorithm, the linear adaptive controller (predictive control with partial state reference model) and the adaptive controller based on the non-linear structure of the process model (pole placement control). These controllers are applied to a pilot-scale fermentation system with satisfactory results.     

Co-ordinate transformation in back-stepping design for a class of non-linear systems

In this paper the problem of existence and construction of a co-ordinate transformation is investigated for non-linear systems appearing in feedback linearization and back-stepping adaptive control problems. Conditions are derived to completely characterize the classes of non-linear systems that are transformable to the simple triangular and parametric simple triangular forms via linear transformations. the conditions are shown to be invariant under linear co-ordinate transformations and non-linear feedback. For systems satisfying these conditions, the development of the co-ordinate transformation is shown to be equivalent to that of their first-order approximations and is straightforward.     

高压直流换流站分散鲁棒自适应控制器的设计

针对高压直流输电系统（HVDC），提出了一种换流站的分散鲁棒自适应控制器的设计方法，设计中引入自适应非线性阻尼项来抑制系统非线性不确定参数和未知有界干扰的影响，同时采用反演设计方法来克服控制器设计的复杂性，最后获得高压直流输电系统换流站的分散鲁棒自适应控制策略的一般表达式，并提供了整个系统的稳定性证明，所得控制器仅利用本地测量量实现，控制策略具有分散性和适应性，通过NETOMAC数字仿真，仿真结果证明该控制器比常规的PI控制器具有更好的控制效果。