Fast adaptation for an uncertain nonlinear system using adaptive feedback linearization with optimal control modification

Robust Adaptive Control

Optimal control modification has been developed to improve robustness to model-reference adaptive control. For systems with linear matched uncertainty, optimal control modification adaptive law can be shown by a singular perturbation argument to possess an outer solution that exhibits a linear asymptotic property. Analytical expressions of phase and time delay margins for the outer solution can be obtained that allows a free design parameter of the adaptive law to be selected to satisfy stability margins. Various modifications were developed to increase robustness of MRAC by adding damping to the adaptive law. Two well-known modifications in adaptive control are the s -modification 15 and e- modification. 17 These modifications have been used extensively in adaptive control. This paper introduces a new adaptive law based on an optimal control formulation to minimize the L2 norm of the tracking error. The optimality condition results in a damping term proportional to the persistent excitation. The analysis shows that the optimal control modification can allow fast adaptation with a large adaptive gain without causing high-frequency oscillations and can provide improved stability robustness while preserving the tracking performance. One of the features of this adaptive law is its asymptotic linear property for systems with linear matched uncertainty as exhbited by a singular perturbation argument. Due to the asymptotic linear property, the optimal control modification exhibits a linear mapping between the input and output. As a result, it is possible to compute analytically stability margins for this adaptive control scheme. With the use of the gradient projection operator, a free design parameter of the optimal control modification can be designed to satisfy stability margins for its asymptotic solution. Simulation results demonstrate the effectiveness of the method.

This paper presents a Single Network Adaptive Critic (SNAC) aided Nonlinear Dynamic Inversion (NDI) optimization controller with a Proportional-Derivative (PD) based Optimal Control Modification (OCM) design for fast pitch rate adaptation in an MRAC flight control system. The advantages of adding SNAC to the NDI MRAC controller with OCM adaptation are presented. It is seen from simulation results that the SNAC aided NDI controller with the OCM adaptation has fewer high frequency oscillations and increased robustness to the different network architectures of the OCM. Three variations of OCM uncertainty estimation basis functions, namely the OCM – Linear (OCM-L), OCM – Bias (OCM-B) and OCM Linear and Bias (OCM-LB) are included in this paper. The responses of the SNAC aided NDI and traditional NDI controllers, using the same OCM adaptation technique are compared. Simulation results run on a nonlinear model of a small single piston engine are included for demonstration.

This paper presents the optimal control modification for linear uncertain plants. The Lyapunov analysis shows that the modification parameter has a limiting value depending on the nature of the uncertainty. The optimal control modification exhibits a linear asymptotic property that enables it to be analyzed in a linear time invariant framework for linear uncertain plants. The linear asymptotic property shows that the closed-loop plants in the limit possess a scaled input-output mapping. Using this property, we can derive an analytical closed-loop transfer function in the limit as the adaptive gain tends to infinity. The paper revisits the Rohrs counterexample problem that illustrates the nature of non-robustness of model-reference adaptive control in the presence of unmodeled dynamics. An analytical approach is developed to compute exactly the modification parameter for the optimal control modification that stabilizes the plant in the Rohrs counterexample. The linear asymptotic property is also used to address output feedback adaptive control for non-minimum phase plants with a relative degree 1.

In this paper, we introduce a direct fractional order adaptive control design based on model reference adaptive control (MRAC) structure for a class of commensurate fractional order linear systems with an arbitrary relative degree, and whose parameters are unknown. By generalising the application of standard direct MRAC strategy to plants described by fractional order models, we develop a fractional adaptive control scheme (FOMRAC) based on the output feedback. We also define an adaptation control law ensuring the stability of the closed-loop system and the good tracking of the reference trajectory. The asymptotic stability of the fractional order control system is proven using an extension of the Lyapunov theorem. Simulation results show the effectiveness of the proposed control method even for plants with model parametric variations and additive noises.

A new form of nonlinear control scheme is presented in this brief where the concepts of feedback linearization and adaptive control schemes are combined together to design an adaptive partial feedback linearizing controller. The newly proposed scheme is exercised on a single machine infinite bus (SMIB) power system in order to design its excitation controller in order to eliminate the parameter sensitivity problems of the feedback linearization scheme. The SMIB system is first linearized using the partial feedback linearization technique and the parameters appearing in the feedback linearized model are estimated using the adaptive control scheme. The proposed adaptive partial feedback linearizing excitation controller of the SMIB system uses the estimated values of parameters. The stability of the SMIB system is also analyzed using the Lyapunov stability theory while using the proposed scheme. Simulation studies are carried out to demonstrate the effectiveness of the proposed control scheme over an existing partial feedback linearizing scheme.

The purpose of this chapter is to redesign the standard adaptive control schemes by using hybrid structure composed by Model Reference Adaptive Control (MRAC) or Adaptive Pole Placement Control (APPC) strategies, associated to Variable Structure (VS) schemes for achieving non-standard robust adaptive control strategies. The both control strategies is now on named VS-MRAC and VS-APPC. We start with the theoretical base of standard control strategies APPC and MRAC, discussing their structures, as how their parameters are identified by adaptive observers and their robustness properties for guaranteeing their stability. After that, we introduce the sliding mode control (variable structure) in each control scheme for simplifying their design procedure. These design procedure are based on stability analysis of each hybrid robust control scheme. With the definition of both hybrid control strategies, it is analyzed their behavior when controlling system plants with unmodeled disturbances and parameter variation. It is established how the adaptive laws compensates these unmodeled dynamics. Furthermore, by using simple systems examples it is realized a comparison study between the hybrid structures VS-APPC and VSMRAC and the standard schemes APPC and MRAC. As the hybrid structures use switching laws due to the sliding mode scheme, the effect of chattering is analyzed on the implementation and consequently effects on the digital control hardware where sampling times are limiting factor. For reducing these drawbacks it is also discussed possibilities which kind of modifications can employ. Finally, some practical considerations are discussed on an implementation on motor drive systems.

In recent years we have witnessed the publication in various control and applications journals of some papers where it is suggested to add to the standard model reference adaptive controller an input filter and to use high adaptation gains. It has been claimed that these modifications improve the performance of the system. The purpose of this brief note is to discuss these claims. A key contribution of the paper is the proof that parameter adaptation “freezes” as the adaptation gain goes to infinity-effectively stopping the stabilization (or performance improvement) mechanism due to adaptation.

Active control systems are used on aircraft to reduce loads due to gusts and manoeuvres, reduce the effect of noise, and could also increase the speed at which flutter occurs. Unfortunately most aeroservoelastic systems include some form of nonlinearity, and this increases the complexity of the feedback system and also facilitates the likelihood of Limit Cycle Oscillations occurring. Previous work on the application of Adaptive Feedback Linearisation to aeroelastic systems has demonstrated the promising potential of this method when applying control in the presence of substantial nonlinearity. In this work, Adaptive Feedback Linearisation is applied to an aeroelastic model of a cantilevered flexible wing with a cubic hardening structural nonlinearity in an engine pylon. Using assumed vibration modes, a suitable model of the wing is developed, into which structural nonlinearity is incorporated. Closed-loop control is implemented on the aeroservoelastic system via linearising feedback computed through the Adaptive Feedback Linearisation algorithm. The advantage of the latter is the guaranteed stability of the closed-loop aeroelastic system, despite lack of knowledge of the exact description of the nonlinearity. It is shown how such an approach can be used to delay the onset of flutter or limit cycle oscillations.

Fast adaptive pose tracking control for satellites via dual quaternion upon non-certainty equivalence principle

Torque ripple reduction of Brushless DC Motors (BLDCs) with concentrated winding is an attractive subject in variable speed AC drives. In ideal BLDC with trapezoidal back-EMF torque ripple elimination can be achieved using rectangular stator current, while in motors with non-ideal back-EMF, feeding the rectangular current leads to more torque ripple. In this paper at first, a mathematical expression for torque ripple harmonics is done. Then for a non-ideal BLDC motor with known harmonic contents of back-EMF, calculation of desired reference current amplitudes, which are required to eliminate some selected harmonics of torque ripple, is reviewed. In order to inject the reference currents to the motor windings, an adaptive input-output feedback linearization control is proposed, which generates the reference voltages for three phases Voltage Source Inverter (VSI). Also, this method is robust against the motor parameter variations like as stator's resistance and leakage inductance. The effectiveness of the proposed method is evaluated with simulation in the two harmonic selection methods.

Design of an Adaptive Pole Placement Control System Using Adaptive Observer

This article proposes an adaptive input-output Feedback Linearization Control ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FLC</i> ) techniques for Synchronous Reluctance Motor ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SynRM</i> ) drives, taking into consideration the iron losses. As a main original content, this work proposes a control law based on a new dynamic model of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SynRM</i> including iron losses as well as the on-line estimation of the static inductances. The on-line estimation of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SynRM</i> static inductances permits to inherently take into consideration the magnetic saturation phenomena occuring on both axes. As a major result, it permits a null stator current steady state tracking error even with a proportional derivative controller. The estimation law is obtained thanks to a Lyapunov-based analysis and thus the stability of the entire control system, including the estimation algorithm, is intrinsically guaranteed. The proposed adaptive <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FLC</i> technique, has been tested experimentally on a suitably developed test set-up, and compared experimentally with its non-adaptive versions in both tuned and detuned working conditions. Moreover, a sensitivity analysis of the performance of the adaptive <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FLC</i> to the variations of the stator resistance at low speed has been made. Finally, an analysis of the effects of the iron losses on the control performance and stability at high speed in the field weakening region at medium/high loads has been made.

Realizations and performances of nonlinear control algorithms by digital signal processors (DSP) are discussed in this paper. The author explains some of the important DSP features that make it possible to calculate certain mathematical operations at high speed. Basic principles of a few nonlinear control approaches are summarized, with the objective of pointing out key calculations in adaptive control, feedback linearization and variable structure control. Several references and example implementations are used to illustrate the feasibility of implementing complex nonlinear control algorithms with modern DSPs. The examples presented are: feedback linearizing control of a magnetic bearing, variable structure control of a magnetic bearing, and variable structure control of a resonant link DC-DC converter. Experimental studies are also used to point out some possible shortcomings and pitfalls of using present-day DSPs for nonlinear control. One conclusion is that modern digital signal processing devices are well suited for certain types of control algorithms, but further advances in the technology can be explored.

This paper discusses the design of a control system for robotic-assisted Minimal Invasive Surgery. Adaptive control, feedback linearization and operational space techniques are used to develop a tele-manipulation system with haptic force feedback. The operational space control has a position-position tele-operation architecture with a haptic device in the loop. The medical instrument end point position is controlled by the surgeon while the robot posture is automatically adjusted to fulfill both instrument end point and trocar positions. Force feedback is felt by the surgeon through a virtual coupling. Explicit posture control techniques are used to deal with trocar constraints. Simulation results were carried out using the WAM™ robot simulator and the Phantom Desktop haptic device.