Analyzing the Noise Behaviour of a Model Reference Adaptive Controller which uses Simultaneous Probing, Estimation and Control

In classical model reference adaptive control, the goal is to design a controller to make the closed-loop system act like a prespecified stable reference model. A recent approach yields a linear periodic controller which simultaneously performs probing, estimation, and control. This linear controller is not only able to handle time-varying systems, but also provides exponential stability. In addition, from simulations, it is found that the controller has excellent noise rejection in certain cases. In this thesis, we used the induced noise gain as the measurement of noise rejection. For plants that are minimum phase with relative degree one, we started with the case where the plant is first order and linear time-invariant. Then we moved to the case where the plant is first order and linear time-varying. Finally, we extended to the general case where the plant is linear time-varying with relative degree one. For the above cases, we quantitatively investigated how certain control parameters affect the induced noise gain

Robust adaptive flight control systems in the presence of time delay

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2013.This electronic version was submitted and approved by the author's academic department as part of an electronic thesis pilot project. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from department-submitted PDF version of thesis.Includes bibliographical references (p. 161-165).Adaptive control technology is a promising candidate to deliver high performance in aircraft systems in the presence of uncertainties. Currently, there is a lack of robustness guarantees against time delay with the difficulty arising from the fact that the underlying problem is nonlinear and time varying. Existing results for this problem have been quite limited, with most results either being local or at best, semi-global. In this thesis, robust adaptive control for a class of plants with global boundedness in the presence of time-delay is established. This class of plants pertains to linear systems whose states are accessible. The global boundedness is accomplished using a standard adaptive control law with a projection algorithm for a range of non-zero delays. The upper bound of such delays, i.e. the delay margin, is explicitly computed. The results of this thesis provide a highly desirable fundamental property of adaptive control, robustness to time-delays, a necessary step towards developing theoretically verifiable flight control systems.by Megumi Matsutani.Ph.D

Azadi Controller Influentially Succeeds in the Eminent Plant Automations

667-670This paper is devoted to present Azadi controller, which is based on a positive feedback surrounded with two negative feedbacks. This controller performs influential over the classical optimum PID controllers. Classical PID controllers have been extensively applied to the linear or nonlinear systems for many years. There are many approaches to tune these PID controllers. Among those, are Zigler-Nicols (ZN), Chien-Hrones-Reswick (CHR), Cohen–Coon (CC), and some optimum controllers such as Modulus Optimum (MO), Symmetrical Optimum (SO). However, when the plant has larger delays, Smith predictor (SP) becomes a good candidate to overcome the plant oscillations. Azadi controller actually is an adaptive controller which performs much better than those optimum classical controllers from many control features such as rise time, overshoots, settling time, or steady state errors. The simulation results confirm the ability of Azadi controller to suppress the plant oscillations. Besides, the simplicity of Azadi controller with just three parameters with its good performances suggests Azadi controller to be a good candidate for any linear, nonlinear, or time varying plants

Development of U-model enhansed nonlinear systems

Nonlinear control system design has been widely recognised as a challenging issue where the key objective is to develop a general model prototype with conciseness, flexibility and manipulability, so that the designed control system can best match the required performance or specifications. As a generic systematic approach, U-model concept appeared in Prof. Quanmin Zhu’s Doctoral thesis, and U-model approach was firstly published in the journal paper titled with ‘U-model based pole placement for nonlinear plants’ in 2002.The U-model polynomial prototype precisely describes a wide range of smooth nonlinear polynomial models, defined as a controller output u(t-1) based time-varying polynomial models converted from the original nonlinear model. Within this equivalent U-model expression, the first study of U-model based pole placement controller design for nonlinear plants is a simple mapping exercise from ordinary linear and nonlinear difference equations to time-varying polynomials in terms of the plant input u(t-1). The U-model framework realised the concise and applicable design for nonlinear control system by using such linear polynomial control system design approaches.Since the first publication, the U-model methodology has progressed and evolved over the course of a decade. By using the U-model technique, researchers have proposed many different linear algorithms for the design of control systems for the nonlinear polynomial model including; adaptive control, internal control, sliding mode control, predictive control and neural network control. However, limited research has been concerned with the design and analysis of robust stability and performance of U-model based control systems.This project firstly proposes a suitable method to analyse the robust stability of the developed U-model based pole placement control systems against uncertainty. The parameter variation is bounded, thus the robust stability margin of the closed loop system can be determined by using LMI (Linear Matrix Inequality) based robust stability analysis procedure. U-block model is defined as an input output linear closed loop model with pole assignor converted from the U-model based control system. With the bridge of U-model approach, it connects the linear state space design approach with the nonlinear polynomial model. Therefore, LMI based linear robust controller design approaches are able to design enhanced robust control system within the U-block model structure.With such development, the first stage U-model methodology provides concise and flexible solutions for complex problems, where linear controller design methodologies are directly applied to nonlinear polynomial plant-based control system design. The next milestone work expands the U-model technique into state space control systems to establish the new framework, defined as the U-state space model, providing a generic prototype for the simplification of nonlinear state space design approaches.The U-state space model is first described as a controller output u(t-1) based time-varying state equations, which is equivalent to the original linear/nonlinear state space models after conversion. Then, a basic idea of corresponding U-state feedback control system design method is proposed based on the U-model principle. The linear state space feedback control design approach is employed to nonlinear plants described in state space realisation under U-state space structure. The desired state vectors defined as xd(t), are determined by closed loop performance (such as pole placement) or designer specifications (such as LQR). Then the desired state vectors substitute the desired state vectors into original state space equations (regarded as next time state variable xd(t) = x(t) ). Therefore, the controller output u(t-1) can be obtained from one of the roots of a root-solving iterative algorithm.A quad-rotor rotorcraft dynamic model and inverted pendulum system are introduced to verify the U-state space control system design approach for MIMO/SIMO system. The linear design approach is used to determine the closed loop state equation, then the controller output can be obtained from root solver. Numerical examples and case studies are employed in this study to demonstrate the effectiveness of the proposed methods

Adaptive model based control for wastewater treatment plants

In biological wastewater treatment, nitrogen and phosphorous are removed by activated sludge. The process requires oxygen input via aeration of the activated sludge tank. Aeration is responsible for about 60% of the energy consumption of a treatment plant. Hence optimization of aeration can contribute considerably to the increase of energy-efficiency in wastewater treatment. To this end, we introduce an adaptive model based control strategy for aeration called adaptive WOMBAT. The strategy is an improvement of the original WOMBAT, which has been successfully implemented at wastewater treatment plant Westpoort in Amsterdam. In this paper we propose to improve the physics-based model by introducing automatic parameter adaptation. In an experimental model setup the adaptive model based control algorithm proves to result in better effluent quality with less energy consumption. Moreover, it is able to react to the varying circumstances of a real treatment plant and can, therefore, operate without human supervision

A New Approach to Multi-Model Adaptive Control

Adaptive control is an approach used to deal with systems with uncertain or time-varying parameters. A classical adaptive controller typically consists of a linear time-invariant (LTI) control law together with a tuning mechanism which adjusts its parameters. Usually, though not exclusively, discrete-time adaptive controllers provide only asymptotic stability and possibly bounded-noise bounded-state stability; neither exponential stability nor a bounded noise gain is typically proven. Recently it has been shown that if we employ a parameter estimator based on the original Projection Algorithm together with projecting the parameter estimates onto a given compact and convex set, then the adaptive controller guarantees linear-like closed-loop behavior: exponential stability, a bounded noise gain and a convolution bound on the exogenous inputs. In this thesis, the overarching objective is to show that we can prove these same desirable linear-like properties in a wide range of adaptive control problems without the convexity assumption: the main idea is to use multiple estimators and a switching algorithm. Indeed, we show that those properties arise in a surprisingly natural way. We first prove a general result that exponential stability and a convolution bound on the closed-loop behavior can be leveraged to show tolerance to a degree of time-variations and unmodelled dynamics, i.e. such closed-loop properties guarantee robustness. After reviewing the original Projection Algorithm and introducing the reader to our slightly revised version, we turn our attention to controller design, with a focus on a non-convex set of plant uncertainty. As a starting point, we first consider first-order plants incorporating a simple switching algorithm. We then extend the approach to a class of nonlinear plants (which have stable zero dynamics); we consider both cases of convex and non-convex sets of parameter uncertainty. Afterwards, we turn to possibly non-minimum phase LTI plants; first we consider the stabilization problem for which we have two convex sets of uncertainty; then, we turn to the problem of tracking the sum of a finite number of sinusoids of known frequencies subject to an unknown plant order and a general compact set of uncertainty

Nonlinear and adaptive control

The primary thrust of the research was to conduct fundamental research in the theories and methodologies for designing complex high-performance multivariable feedback control systems; and to conduct feasibiltiy studies in application areas of interest to NASA sponsors that point out advantages and shortcomings of available control system design methodologies

Gain Bounds for Multiple Model Switched Adaptive Control of General MIMO LTI Systems

For the class of MIMO minimal LTI systems controlled by an estimation based multiple model switched adaptive controller (EMMSAC), bounds are obtained for the closed loop lp gain, 1 ? p ? ?, from the input and output disturbances to the internal signals