Parameter estimation of unstable, limit cycling systems using adaptive feedback linearization: example of delta wing roll dynamics

Adaptive control methods are widely used for the control of both linear and nonlinear dynamical systems. Among the adaptive control approaches, Model Reference Adaptive Control (MRAC) method has a systematic design feature in which response of a stable reference model is targeted to be followed by the dynamical system. In general, Linear Time Invariant (LTI) Reference Models are considered in the MRAC design and the adaptation rule is formulated accordingly. In this paper, the linear reference model is altered with a stable nonlinear one and the adaptation rule is re-formulated to cope with the nonlinearity. The stable nonlinear reference model is generated by using the State Dependent Riccati Equation (SDRE) approach and the adaptation rule is also updated by using the same SDRE idea. The effects of altering the linear reference model to the nonlinear counterpart are shown in the MRAC formulations. In addition to the new MRAC formulations, the proposed MRAC algorithm is applied to a 3 DoF helicopter test bed to reveal the advantages of the nonlinear reference model.

Robust Model Reference Adaptive Control in the Presence of Parasitics

In this paper, a novel adaptive interval type-2 fuzzy sliding mode control (AIT2FSMC) methodology is proposed based on the integration of sliding mode control and adaptive interval type-2 fuzzy control for chaotic system. The AIT2FSMC system is comprised of a fuzzy control design and a hitting control design. In the fuzzy control design, an interval type-2 fuzzy controller is designed to mimic a feedback linearization (FL) control law. In the hitting control design, a hitting controller is designed to compensate the approximation error between the FL control law and the interval type-2 fuzzy controller. The parameters of the interval type-2 fuzzy controller, as well as the uncertainty bound of the approximation error, are tuned adaptively. The adaptive laws are derived in the sense of Lyapunov stability theorem, thus the stability of the system can be guaranteed. The proposed control system compared to adaptive fuzzy sliding mode control (AFSMC). Simulation results show that the proposed control systems can achieve favorable performance and robust with respect to system uncertainties and external disturbances.

The purpose of this work was to develop and evaluate the accuracy of several predictive models of variation in tumor volume throughout the course of radiation therapy. Nineteen patients with oropharyngeal cancers were imaged daily with CT-on-rails for image-guided alignment per an institutional protocol. The daily volumes of 35 tumors in these 19 patients were determined and used to generate (1) a linear model in which tumor volume changed at a constant rate, (2) a general linear model that utilized the power fit relationship between the daily and initial tumor volumes, and (3) a functional general linear model that identified and exploited the primary modes of variation between time series describing the changing tumor volumes. Primary and nodal tumor volumes were examined separately. The accuracy of these models in predicting daily tumor volumes were compared with those of static and linear reference models using leave-one-out cross-validation. In predicting the daily volume of primary tumors, the general linear model and the functional general linear model were more accurate than the static reference model by 9.9% (range: -11.6%-23.8%) and 14.6% (range: -7.3%-27.5%), respectively, and were more accurate than the linear reference model by 14.2% (range: -6.8%-40.3%) and 13.1% (range: -1.5%-52.5%), respectively. In predicting the daily volume of nodal tumors, only the 14.4% (range: -11.1%-20.5%) improvement in accuracy of the functional general linear model compared to the static reference model was statistically significant. A general linear model and a functional general linear model trained on data from a small population of patients can predict the primary tumor volume throughout the course of radiation therapy with greater accuracy than standard reference models. These more accurate models may increase the prognostic value of information about the tumor garnered from pretreatment computed tomography images and facilitate improved treatment management.

In this study, the design of Sliding Mode Control (SMC) has been carried out based on a second order reference model with a specified transfer function. The primary objective of this study is to determine the SMC controller parameters according to the desired time response in the output signal. The aim is to determine the optimal control gains that minimize the difference between the reference and plant outputs in a systematic way. By minimizing the error between the reference model and the SMC controlled system model, the optimal SMC parameters, specifically the sliding surface slope ( λ ) and the switching function coefficient ( K ), are obtained. Integral performance criteria were used to minimize the error. Both the reference system and the system controlled by the SMC have second-order transfer functions. While the natural frequency ( ω n ) in the reference model system remains constant, the damping ratio ( ζ ) was varied between 0.5 and 1. For each ζ value in the reference system, the optimal SMC parameters ( λ and K ) were obtained by using the Fmincon optimization algorithm to minimize the error between the two systems based on the selected integral performance criteria. By applying the obtained SMC parameters to the controlled system, unit step responses were obtained in the output of the controlled system. T optimization process was performed based on the transfer functions of two different known systems, and the variation of the optimal SMC parameters according to the damping ratio of the reference model was presented in tables and graphs. The simulation results confirm that the proposed method significantly improves the accuracy and robustness of tracking compared to conventional SMC tuning approaches. These results demonstrate the effectiveness of the proposed method for designing reliable and efficient controllers for second-order dynamic systems. The success of the reference model-based second-order system controlled by the SMC method is clearly demonstrated by the generated graphs and tables. This study introduces a new optimization-based SMC design approach by establishing an explicit analytical relationship between the damping ratio and the controller parameters. In the proposed method uses regression, which avoids the need for iterative tuning and repeated calibration.

Robust Adaptive Control

The problem of developing a control law which can force the output of a linear time-varying plant to track the output of a stable linear time-invariant reference model is discussed. It is shown that the standard model reference controller, used for linear time-invariant plants, cannot guarantee zero tracking error in general when the plant is time-varying. A new model reference controller is proposed which guarantees stability and zero tracking error for a general class of linear time-varying plants with known parameters. When the time-varying plant parameters are unknown but vary slowly with time, it is shown that the new controller can be combined with a suitable adaptive law so that all the signals in the closed loop remain bounded for any bounded initial conditions and the tracking error is small in the mean. The assumption of slow parameter variations in the adaptive case can be relaxed if some information about the frequency or the form of the fast varying parameters is available a priori. Such information can be incorporated in an appropriately designed adaptive law so that stability and improved tracking performance is guaranteed for a class of plants with fast varying parameters. >

This paper presents an adaptive control system for the trajectory control and stabilization of an aeroelastic system with unstructured model uncertainties using output feedback. The equations of motion of the chosen aeroelastic system describe the plunge and pitch motion of a structurally nonlinear wing section. A single trailing edge flap is used for the purpose of control. For feedback only the pitch angle or the plunge displacement is measured. Unlike the linearly parameterized adaptive systems, in this study the structure of model uncertainties is unknown. Adaptive control laws for the trajectory control of the pitch angle and the plunge displacement are derived. The controller has the structure of an inverse (a feedback linearizing) control system. But the unknown function in the inverse control law arising from the uncertainties in the model is compensated using its estimate constructed by a high gain observer. Simulation results are presented which show that in the closed-loop system, trajectory control of the selected output (pitch angle or plunge displacement) is accomplished and the state vector converges to zero. Furthermore, it is observed that stability and trajectory tracking are preserved in the presence of measurement noise. ca h, hr Ia m U xa

SummaryThe rejection of unknown periodic disturbances in the plant output through adaptive feedback has been an active area of research. In most successful efforts, it is assumed that the plant model is a known LTI stable system. In this paper, we relax the assumption of stable known plant and consider the case where the plant model can be unstable with unknown parameters. We do assume, however, that the plant model is minimum phase and use the model reference adaptive control structure to meet the objectives of reference tracking and unknown periodic disturbance rejection without amplifying the effect of broadband noises. The cost of achieving these objectives is the use of overparameterization that adds to the number of computations. The main contribution of this paper is that it shows that the problem of rejecting unknown periodic disturbances can be solved for unstable plants with unknown parameters as long as they are minimum phase. Numerical examples illustrate the effectiveness of the proposed control methodology.

This paper explores the model reference adaptive control problem for a class of switched linear systems under arbitrary switching with no need for the measurability of the system state. Based on the state of reference model and the measurable output error, adaptive laws and controllers are designed for switched systems. Each subsystem may have its individual reference model and controller, which increases the design flexibility. The introduction of the closed-loop reference model is to get a better transient performance of the whole switched systems. A numerical example is provided to verify the effectiveness of the main results.

This paper proposes a novel approach to design a centralized model matching integer/fractional-order (FO) controller for multivariable processes. As a first step, for a linear time-delay process, a desired closed-loop reference model is formulated with the inclusion of a linear quadratic regulator with integral controller. The reference model is formulated with the objective of embodying the desired closed-loop specifications. The second step involves equating the closed-loop system with the reference model, leading to a synthesis equation that yields a higher-order controller. In the third step, the lower-order approximant of the controller is obtained by matching a set of approximate generalized time moments/approximate generalized Markov parameters of the higher-order controller to that of its lower-order approximate at a few expansion points in the s-plane. The selection of an optimal set of expansion points is formulated in an optimization problem frame with the aim of minimizing the area between responses of the desired and designed closed-loop systems, keeping the stability of the designed closed-loop system as a constraint. The efficacy of the proposed approach is illustrated by the design of different controllers for time-delay-dominated nonsquare process and FO square process. Comparative analysis is carried out using time-domain performance indices by introducing parameter uncertainty and disturbance signals. To demonstrate the applicability of the proposed method, a real-time investigation is carried out with the design and implementation of a controller for interacting hybrid (conical and spherical) tank process setup.

An algorithm for multiple model adaptive control of a time-variant plant in the presence of measurement noise is proposed. This algorithm controls the plant using a bank of PID controllers designed on the base of time invariant input/output models. The control signal is formed as weighting sum of the control signals of local PID controllers. The main contribution of the paper is the objective function minimized to determine the weighting coefficients. The proposed algorithm minimizes the sum of the square general error between the model bank output and the plant output. An equation for on-line determination of the weighting coefficients is obtained. They are determined by the current value of the general error covariance matrix. The main advantage of the algorithm is that the derived general error covariance matrix equation is the same as this in the recursive least square algorithm. Thus, most of the well known RLS modifications for the tracking timevariant parameters can be directly implemented. The algorithm performance is tested by simulation. Results with both SISO and MIMO time variant plants are obtained.

MODEL REFERENCE ADAPTIVE ESTIMATION AND CONTROL APPLIED TO A CONTINUOUS FLOW FERMENTATION PROCESS

On the use of bifurcation analysis for robust controller tuning for nonlinear systems

Adaptive Control of Linear Time-Varying Plants