Farshad Khorrami

Decentralized adaptive control of a class of large-scale interconnected nonlinear systems

Decentralized adaptive control design for a class of large-scale interconnected nonlinear systems with unknown interconnections is considered. The motivation behind this work is to develop decentralized control for a class of large-scale systems which do not satisfy the matching condition requirement. To this end, large-scale nonlinear systems transformable to the decentralized strict feedback form are considered. Coordinate-free geometric conditions under which any general interconnected nonlinear system can be transformed to this form are obtained. The interconnections are assumed to be bounded by polynomial-type nonlinearities. Global stability and asymptotic regulation are established using classical Lyapunov techniques. The controller is shown to maintain robustness for a wide class of systems obtained by perturbation in the dynamics of the original system. Furthermore, appending additional subsystems does not require controller redesign for the original subsystems. Finally, the scheme is extended to the model reference tracking problem when global uniform boundedness of the tracking error to a compact set is established.

Modeling and adaptive nonlinear control of electric motors

1 Introduction.- 2 Dual-Axis Linear Stepper (Sawyer) Motors.- 3 Modeling of Stepper Motors.- 4 Stepping.- 5 Feedback Linearization and Application to Electric Motors.- 6 Robust Adaptive Control of a Class of Nonlinear Systems.- 7 Robust Adaptive Control of Stepper Motors.- 8 Current Control of Stepper Motors Using Position Measurements Only.- 9 Voltage Control of Stepper Motors Using Position and VelocityMeasurements.- 10 Voltage Control of PM Stepper Motors Using Position Measurement Only.- 11 Brushless DC Motors.- 12 Induction Motor: Modeling and Control.- 13 Adaptive Control of Induction Motors.- 14 Passivity-Based Control of Electric Motors.- 15 Torque Ripple Reduction for Step Motors.- 16 Friction Compensation in Servo-Drives.- A Fundamentals of AC Machines.- B.1 Case of Position-Only Dependent Transformations.- C Torque Maximization with Current and Voltage Constraints (Field Weakening).- C.1 Low-Speed Range.- C.2 High-Speed Range.- C.3 Intermediate-Speed Range.- C.4 Transition Speeds.- D Stable System Inversion.- E Lyapunov Stability Theorems.- F Backstepping.- G Input-to-State Stability and Nonlinear Small Gain.

Decentralized adaptive output feedback design for large-scale nonlinear systems

In this paper, we present a global, decentralized adaptive design procedure for a class of large-scale nonlinear systems, which utilizes only local output feedback. The advocated scheme guarantees robustness to parametric and dynamic uncertainties in the interconnections and also rejects any bounded disturbances entering the system. The systems belonging to this class are those which can be transformed using a global diffeomorphism to the output feedback canonical form, where the interconnections are a function of subsystem outputs only. The uncertainties are assumed to be bounded by an unknown pth-order polynomial in the outputs. The resulting controller maintains global robustness and disturbance rejection properties. The output tracking error is shown to be bounded within a compact set, the size of which can be made arbitrarily small by appropriate choice of the control gains. For the case where the objective is regulation, global asymptotic regulation of all the states of the closed-loop system is achieved.

Dynamic high-gain scaling: State and output feedback with application to systems with ISS appended dynamics driven by all States

We propose a dynamic high-gain scaling technique and solutions to coupled Lyapunov equations leading to results on state-feedback, output-feedback, and input-to-state stable (ISS) appended dynamics with nonzero gains from all states and input. The observer and controller designs have a dual architecture and utilize a single dynamic scaling. A novel procedure for designing the dynamics of the high-gain parameter is introduced based on choosing a Lyapunov function whose derivative is negative if either the high-gain parameter or its derivative is large enough (compared to functions of the states). The system is allowed to contain uncertain terms dependent on all states and uncertain appended ISS dynamics with nonlinear gains from all system states and input. In contrast, previous results require uncertainties to be bounded by a function of the output and require the appended dynamics to be ISS with respect to the output, i.e., require the gains from other states and the input to be zero. The generated control laws have an algebraically simple structure and the associated Lyapunov functions have a simple quadratic form with a scaling. The design is based on the solution of two pairs of coupled Lyapunov equations for which a constructive procedure is provided. The proposed observer/controller structure provides a globally asymptotically stabilizing output-feedback solution for the benchmark open problem proposed in our earlier work with the provision that a magnitude bound on the unknown parameter be given.

Global high-gain-based observer and backstepping controller for generalized output-feedback canonical form

We provide results and extensions for global output feedback design for systems in the generalized output-feedback canonical form. Our investigations reveal several conceptual and structural connections between high-gain design and two recent results on the generalized output-feedback canonical form. The recognition of these links provides new insight into the stabilization mechanisms of these designs, particularly in the observer design. Furthermore, we have extended the results to include output dependent upper diagonal terms and also shown that the additional scaling proposed in a recent paper can be removed through a simultaneous stabilization result (i.e., solving a special pair of coupled matrix Lyapunov equations). We provide necessary and sufficient conditions for solvability of these coupled Lyapunov equations. The removal of the additional scaling makes the connection between the obtained results and proofs and our earlier results assuming cascading upper diagonal dominance (CUDD) more transparent. Moreover, removing the additional scaling (and possibly introducing a negative scaling) provides a better guaranteed convergence of the observer errors and allows smaller controller gains. It is shown that the high gain scaling induces the CUDD structure on the observer error dynamics. Finally, the design utilizes a reduced-order observer.

Experimental results on adaptive nonlinear control and input preshaping for multi-link flexible manipulators

Abstract Adaptive input precompensators in conjunction with nonlinear controllers for multi-link flexible manipulators are considered in this paper. In an earlier paper, we had shown that application of a nonlinear inner-loop control reduces the variations in frequencies due to the geometrical configuration for multi-link flexible manipulators. This results in a better performance when input preshaping or any other controller based on a linear model is designed. To improve the performance of the system to parameter variations (e.g. changes in payload), an adaptive version of the advocated controller is utilized. This is achieved by estimating the time of application of the impulses for on-line preshaping and in the case of payload uncertainty, estimation of the payload and real-time adjustment of the nonlinear inner-loop based controller. Frequency domain Time-Varying Transfer Function Estimate (TTFE) and Empirical Transfer Function Estimate (ETFE) system identification algorithms are proposed for estimation of vibrational modes and unknown payload. Experimental results on a two-link flexible manipulator with adaptive nonlinear control and preshaping are provided to show the effectiveness of the advocated controllers. Overall, the present paper completely generalizes the adaptive input preshaping technique for multi-link flexible manipulators.

Adaptive nonlinear excitation control of power systems with unknown interconnections

Adaptive nonlinear excitation control of large-scale power systems is considered in this paper. The approach used is an adaptive feedback linearizing control to enhance the robustness to unknown or varying interconnection parameters like equivalent reactances of the transmission lines. Control design based on external feedback linearization may not be robust to handle varying power-system configurations. Inexact cancellation of terms due to uncertainties may result in performance deterioration like inter-system oscillations. Adaptation in estimated parameters is utilized to achieve an asymptotically exact cancellation of terms. It is shown that the adaptive control results in bounded states and maintains the desired performance. The control scheme developed is applied to a power system with two generators and an infinite bus connected through a network of transformers and transmission lines. Simulation studies for unknown interconnections arising due to faults and subsequent line switchings in the transmission network are carried out. The performance using the nonadaptive feedback linearizing control is shown to degrade for network configuration variations arising due to transmission line faults. The response obtained using the proposed scheme is compared with that using a conventional IEEE Type I excitation control. The studies validate the fact that connective stability and robust performance is maintained for unknown interconnection topology using the adaptive feedback linearizing scheme. >

Experiments on rigid body-based controllers with input preshaping for a two-link flexible manipulator

Input precompensators in conjunction with linear and nonlinear rigid body based controllers for flexible-link manipulators are considered in this paper. The objective is to preshape the reference input signals. This is accomplished by convolving the reference signal with a sequence of impulses so that a vibration free output is achieved. The time of the application of the impulses is dependent upon the modal frequencies and the amplitudes are functions of the damping of the modal frequencies. Experimental and simulation results on a two-link flexible manipulator show the effectiveness of the advocated controllers.

Adaptive control of systems with backlash hysteresis at the input

A new compact dynamical model for backlash inverse is presented. This model may be utilized for both backlash at the input or at the output. Two cases are considered: the case where the backlash spacing is known as well as the case of unknown backlash spacing. For the latter case, an adaptive update law is developed to compensate for the unknown spacing. The adaptive backlash inverse controller is a break-away from existing backlash compensators which are mostly implemented in discrete-time and utilize complex control algorithms. The advocated results are applied to a one degree-of-freedom system affected by backlash. The stability of the closed-loop system is shown using Lyapunov arguments. Simulation results show that the control methodology greatly improves tracking performance over a PD type controller.

A high-gain scaling technique for adaptive output feedback control of feedforward systems

In this note, we propose an adaptive output feedback control design technique for feedforward systems based on our recent results on dynamic high-gain scaling techniques for controller design for strict-feedback systems. The system is allowed to contain uncertain functions of all the states and the input as long as the uncertainties satisfy certain bounds. Unknown parameters are allowed in the bounds assumed on the uncertain functions. If the uncertain functions involve the input, then the output-dependent functions in the bounds on the uncertain functions need to be polynomially bounded. It is also shown that if the uncertain functions can be bounded by a function independent of the input, then the polynomial boundedness requirement can be relaxed. The designed controllers have a very simple structure being essentially a linear feedback with state-dependent dynamic gains and do not involve any saturations or recursive computations. The observer utilized to estimate the unmeasured states is similar to a Luenberger observer with dynamic observer gains. The Lyapunov functions are quadratic in the state estimates, the observer errors, and the parameter estimation error. The stability analysis is based on our recent results on uniform solvability of coupled state-dependent Lyapunov equations. The controller design provides strong robustness properties both with respect to uncertain parameters in the system model and additive disturbances. This robustness is the key to the output feedback controller design. Global asymptotic results are obtained.