SPEECH ENHANCEMENT

All adaptive control strategies are free of any controller reconfiguration/redesign and have retrofit functionality. 37 2.3 Device response and control inputs under the considered failure scenario (2.79) using . a) Comparison of the output tracking errors of the proposed controller (red) with ASMC (blue) [4] and ABSC (green) [5]; (b) pitch angle tracking θ using the proposed ARFTC; (c) slope rate q according to the proposed ARFTC; (d) control input u1 and u2 corresponding to the proposed ARFTC; (e) control inputsu1andu2 using ASMC [4]; (f) Control inputs u1 and u2 using ABSC procedure [5].

Introduction

Fault Tolerant Control

Approaches to FTC Design

The illustration in Figure 1.7 shows the operation procedure of an active FTC scheme from an event-driven perspective, starting from the occurrence of a fault/failure until it is recovered. The timing diagram in Figure 1.7 (right) shows the temporal relationship between the events that occurred within this active FTC architecture.

Figure 1.2: Illustration of the types of actuator faults and failures in dynamical systems.

Literature Review

This motivated the design of fault-tolerant active controllers for nonlinear systems subject to complete actuator failures. Actuator failures in nonlinear systems with model uncertainty have also been compensated using adaptive sliding mode control (ASMC) [4,30,74].

Research Motivation

In contrast to the finite number of actuator failures, an adaptive compensation of a possibly infinite number of unknown actuator failures using direct adaptive control methodologies fails to provide the overall dynamics limit of the closed-loop system. The method proposed in [6] ensures the convergence of the tracking error in the mean square sense.

Contributions of the Thesis

Experimental research on the attitude control of a 2DOF helicopter system (dual rotor MIMO system) justifies the effectiveness and practicality of the proposed control algorithm. iii) Finite Time Adaptation (FTAC) based compensation of actuator errors in nonlinear uncertain systems. The attributes of the proposed guidance methodology are the boundedness of all closed-loop trajectories; finite-time transient output and steady-state performance recovery in the event of failures; asymptotically accurate output tracking; final time-accurate estimation of the system and the uncertainties caused by failures; and the potential to compensate for infinite actuator failures.

Thesis Organization

Then, the objective of the proposed FTC actuator with the inherent assumptions is formulated in Section 2.2.2. The proposed design procedure and stability analysis of the proposed controller are explained in Sections.

Adaptive Robust Fault Tolerant Controller (ARFTC)

System Dynamics with Actuator Failures

First, the dynamics of the considered nonlinear systems with actuator failure are described in section 2.2.1. The reference path to be tracked by the system is the output of the reference state variable model with relative degree ℘ as given below in (2.6).

Problem Statement

Furthermore, the improvement of transient and steady state performance of the tracking error e(t) = y(t)−yr(t), at the onset of faults and failures in terms of maximum overshoot, convergence time and steady state error must be established. The failure compensation design assumes no a priori knowledge of the active actuators in action on the system (2.1) under the total loss of atmost (m−1) thereof.

Proposed Actuator Failure Compensator Design

Therefore, the second order sliding mode control of (2.14) with respect to sliding variables reduces to the finite time stabilization of the perturbed double integrator dynamics given by, . Finally, the synthesis of the overall control law v is based on Gao's reaching law approach [108] and subsequent analysis of the equations of motion.

Stability Analysis

Therefore, it can be said that the finite time stability of z℘ provides asymptotic stability of the order error dynamics (℘−1). 2ϑ, |s1|= 0 is reached in finite time, which in turn guarantees the asymptotic stability of the tracking error dynamics of order (℘−1).

Figure 2.1: Schematic representation the proposed fault tolerant control scheme

Simulation Results and Discussion

The tracking performance of the proposed controller is compared with that of ASMC [4] and ABSC [5]. The output tracking of the pitch angle θ using the proposed control strategy is shown in Figure 2.3(b) and the equivalent pitch rate q is shown in Figure 2.3(c).

Table 2.1: Aircraft model parameters Terminologies for the aircraft model α The angle of attack (AoA)

Summary

Further, the control input using ASMC in [4] is not smooth and experiences noise which is undesirable.

Adaptive Multiple Model Fault Tolerant Control (AMMFTC) for Infinite Actuator Failures 51

Adaptive Fault Tolerant Control Design

Backstepping Control Design

The N adaptive identifiers/estimators are described by differential equations with non-zero initial values for the unknown parameter vector as follows. N denotes each of the adaptive identification models, xˆ(µ) and θˆ(µ) are the estimates of the state vector and the unknown parameter vector θ∗ from that µ, respectively. identification model. Referring to equations, the identification error dynamics for each of the N adaptive estimators are derived as, .

Now use the plant dynamics in (3.1), and take the first time derivative of the error variables yield, .

Main Results

Stability Analysis of the Proposed Control System
Transient Performance Analysis for the Proposed AMMFTC

Secondly, to prove the asymptotic stability of the tracking error z(t), it would be shown that it belongs to the class of L2[Th, Th+1) integrable signals. Therefore, it is not easy to prove the stability of the closed-loop adaptive system affected by infinitely occurring actuator disturbances. Let us consider the adaptive closed-loop system consisting of the nonlinear system (3.1), the adaptive parameter estimation law (3.12) and the control law in (3.37).

Let us consider the adaptive closed-loop system consisting of the nonlinear system (3.1), the estimation of the adaptive parameters θˆs under the second adaptation layer given by θˆs.

Figure 3.4: Illustration explaining the interdependence between kzk ∞ , controller gain parameters and actuator failure transit time T ∗

Simulation Studies

Numerical Example
Application to an Aircraft System

Adaptive Multiple Model Fault Tolerant Control (AMMFTC) for Uncertain Multi-

Problem Formulation

The actuator failure value u¯F j , the actuation effectiveness index Kj , the failure time instant F j , and the actuator index are all unknown. The non-singularity of the actuation matrix for an actuator failure pattern is the decisive factor that determines whether an actuator failure pattern is compensable or not. In other words, this classification criterion, if met, guarantees the existence of a fault-tolerant adaptive controller, which can ensure the stability of the closed-loop system in case of actuator failures.

Furthermore, under the grouping scheme G, since the actuators are grouped based on their similarity in structural properties, at least one actuator in each of the groups Gk should be operational corresponding to an actuator failure pattern.

Adaptive Multiple Model Fault Tolerant Control (AMMFTC) Design

Controller Synthesis
Design of Parameter Estimator using Multiple Identification Models . 99

This fact would be evident during the performance of the stability analysis of the closed-loop dynamics that would follow. The time derivative of the unknown parameter vector θ∗(t), which represents the parametric uncertainty caused by system and actuator failure, satisfies θ˙∗(t)∈ L1[0,∞), i.e. At the beginning, we prove the input to the stability state of the closed-loop tracking error dynamics with θ˜s and θ˙ˆs as input.

The analysis procedure in step ℘ for each of the results is not straightforward.

Simulation Study

Therefore, the suitability of the mass-spring-damper system as a benchmark to illustrate the fruitful features of the proposed adaptive FTC methodology is justified. It is found that the relative level of the system with respect to each of the outputs. To illustrate the robustness of the proposed AMMFTC scheme to actuator failures, the system is deliberately subjected to sudden and unknown actuator failures according to Eqs.

In fact, as expected, the comparison reflects the fruitful features of the proposed adaptive FTC methodology.

Figure 3.13: Schematic diagram of a coupled mass-spring-damper system

Experimental Study on a Twin Rotor MIMO System

The terms Lm and Lt define the torque of the main rotor and the tail rotor, respectively. The TRMS outputs are elevation and roll angles and are denoted by y1 and y2. For the experimental implementation of the proposed adaptive controller using multiple models, all the states of the system must be available.

The CE and TV of the control inputs uv and uh corresponding to the proposed controller indicate reasonably good input performance without excessive chatter.

Figure 3.17: Schematic of cross-coupled twin rotor MIMO system or a 2-DOF helicopter for control development

Summary

Consistent with the purpose of FTC, the performance of the proposed AMMFTC scheme for control of MIMO nonlinear uncertain systems affected by abrupt actuator faults has been demonstrated through extensive simulations in Section 3.3.4. Furthermore, the proposed control methodology was experimentally implemented to control the attitude of a dual-rotor MIMO system (TRMS). Given the fact that a sudden decrease in thrust forces generated by the rotors mimics the occurrence of actuator failures, it is certainly not possible to practically realize actuator failures in such an experimental setup.

Therefore, under this scenario, it is reasonable to assume that the proposed adaptive controller will exhibit similar characteristics in post failure scenarios if a satisfactory transient and steady state is achieved at start-up.

Finite Time Adaptation based Compensation (FTAC) of Infinite Actuator Failures

Some Preliminary Definitions

Problem Formulation

Design Assumptions

Fault Tolerant Control Design with Finite Time Adaptation

Design of Finite Time Parameter Estimator
Controller Design

Stability Analysis

Simulation Studies

Finite Time Adaptation based Compensation (FTAC) of Actuator Failures in Multi-

Problem Formulation

For the above condition to be true for the clustering scheme G, a maximum of (mi−1) actuator failures are allowed in each of the clusters Gi. This condition ensures the controllability of the nonlinear MIMO system in the presence of actuator faults and total failures; guaranteeing the existence of an adaptive control solution to the FTC problem. To design the control inputs vk for each of the actuator groups Gk with k = 1, q to ensure the limitability of all closed-loop signals.

Asymptotic exponential convergence of the output tracking error (y−yr) to the origin under nominal (fault-free) conditions and in the case of actuator faults and faults unknown at the time of their occurrence, fault patterns and magnitudes, i.e. glue.

Proposed Finite Time Adaptation based Controller (FTAC)

Controller Synthesis
Design of Parameter Estimator with Finite Time Convergence

First, the design of the parameter estimator requires that the nonlinear system dynamics in be represented as a parametric ξ model as given below. The following proposition, the stability properties of the proposed finite time parameter estimator and other auxiliary signals are summarized. The proof of finite time stability of θ˜ = 0 and the derivation of the settling time function Ts follow the same procedure as in the proof of Proposition 4.1 (i).

Nevertheless, the important milestones of the proof are given in the following text for ease of understanding.

Stability Analysis of the Proposed Control System

In the following, the theorem states the stability characteristics of the closed-loop signals when the system is affected by a limited number of actuator faults. Let us consider the nonlinear MIMO system dynamics with unknown parameters, affected by a finite number of actuator errors. Subsequent exactly similar steps as in the proof of Theorem 3.8(i) with the substitution θ˜s= ˜θ gives the following.

Needless to say, the procedure for arriving at the L1-integrability of the tracking error vector enz(t), although not trivial, is the same as that which has been followed in the proof of Theorem 4.2 (ii) with small modifications.

Simulation Study

Experimental Study on a Twin Rotor MIMO System

Summary