Constrained dynamical systems, robust model reference adaptive control, and unreliable reference signals

In this paper, we present robust model reference adaptive control laws that guarantee uniform ultimate boundedness of the trajectory tracking error for nonlinear dynamical systems subject to constraints on the state space and the measured output, and affected by matched, unmatched, and parametric uncertainties, as well as uncertainties in the initial conditions. A common assumption in the design of control laws for trajectory tracking is that the reference model or the reference signal verify the constraints imposed on the closed-loop system's trajectory. The control laws presented in this paper do not rely on this assumption and guarantee satisfactory results also in case the reference trajectory or the reference output signal do not verify the given constraints and hence, may draw the plant's trajectory or measured output outside their constraint sets. A numerical example illustrates the feasibility of the theoretical results presented.

A recently introduced class of the well-posed error systems and the corresponding robust model reference adaptive control (MRAC) laws for systems represented by parabolic or hyperbolic partial differential equations (PDEs) with spatially varying parameters is extended to encompass the disturbance rejection capability. The disturbance is modeled as a space-time-varying signal generated by a parabolic PDE with known parameters or as a spatially-varying time-invariant signal.

This paper analyzes the dynamics of tilt-rotor quadcopters with H-configuration and synthesizes a control system for these vehicles. Our analysis is the first to show a nonlinear effect in the vehicle's rotational dynamics due to the fact that not all propellers of a tilt-rotor are aligned to one of the vehicle's principal axes. The proposed control system relies on an original robust model reference adaptive control law to guarantee user-defined constraints on both the trajectory tracking error and the adaptive gains at all despite parametric, matched, and unmatched uncertainties due to unknown external disturbances and dangling payloads.

This article presents an innovative control architecture for tilt-rotor quadcopters with H-configuration transporting unknown, sling payloads. This control architecture leverages on a thorough analysis of the aircraft's equation of motion, which reveals gyroscopic effects that were not fully characterized and were disregarded while synthesizing control algorithms in prior publications. Furthermore, the proposed control architecture employs barrier Lyapunov functions and a novel robust model reference adaptive control law to guarantee a priori user-defined constraints on both the trajectory tracking error and the control input, despite poor information on the aircraft's inertial properties and the presence of unknown, unsteady payloads. Flight tests involving a quadcopter pulling an unmodeled cart by means of a thin rope of unknown length, which is slack at the beginning of the mission, verify the effectiveness of the theoretical results.

Comments on a robust model reference adaptive control for non-minimum phase systems with unknown or time-varying delay

This paper presents the development of an equilibrated three-phase power source, which is able to generate sinusoidal waveforms with adjustable amplitudes and frequencies, as well as several arbitrary waveforms. The setup is based on a computer-controlled three-phase PWM inverter system, whose model is rewritten using /spl alpha//spl beta/0 transformation. A robust model reference adaptive controller (RMRAC) is used to assure system robustness and performance. Simulation and experimental results are used to show the closed-loop system performance, when different waveforms are generated under several operation conditions.

In this paper, a robust model reference adaptive controller is presented for robots based on neural network parametrization. The controller is based on applying direct adaptive techniques to a basic fixed controller for better control performance, while a sliding mode control is introduced to guarantee robust closed-loop stability. It is shown that if bounded basis function networks are used for the parallel NN, uniformly stable adaptation is assured and asymptotic tracking of the reference signal is achieved.

This work proposes a vector speed control scheme for Permanent Magnet Synchronous Motors (PMSM) which is robust against parameter uncertainties. It is based on a control law called VS-RMRAC (Variable Structure Robust Model Reference Adaptive Control). Such control law consists on a discrete time modification of the continuous control law presented in [1]. This paper main contribution is the proposal of a vector speed control scheme based on this controller for PMSM. Simulation and experimental results shows that the proposed scheme is robust against parameter uncertainties, which allows implementing this system without accurate plant knowledge. Obtained results show also system capability to compensate load disturbance applied to the motor axis.

This paper proposes the application of a combined adaptive controller for the current control loop of a Shunt Active Power Filter (Shunt APF). The proposed approach uses a Variable Structure Controller (VS) together with a Robust Model Reference Adaptive Controller (RMRAC), leading to a VS-RMRAC algorithm. The control law u = ¿ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sup> ¿ is comprised by two set of parameters. One set is related with the RMRAC while the other part is related with the VS controller. The VS parameters are used to improve the transient response, and its effect increases when the estimation error increases. The VS-RMRAC is experimentally tested and compared with a Dead Beat current controller in a three-phase four-wire Shunt APF.

This paper investigates a robust model reference adaptive control (MRAC) method for a three-phase constant-voltage constant-frequency (CVCF) inverter with an output LC filter. The proposed MRAC method is designed to stabilize the error dynamics of the system by a feedback control term in the steady state and attenuate the parameter uncertainties of the system by an updated MRAC term. Unlike the conventional proportional-derivative control (PDC) scheme, the proposed MRAC scheme ensures the fast convergence of the output errors to the exponential trajectories predefined by the reference models. Furthermore, the adaptive state-feedback mechanism can guarantee the fast dynamic response in the transient state without using load current sensors or observers. The asymptotic stability is mathematically proven by a Lyapunov theory. The feasibility of the proposed controller is confirmed through extensive experimental studies on a prototype three-phase CVCF inverter with a TI TMS320LF28335 DSP. Finally, comparative experimental results of three control methods (i.e., conventional PDC, feedback linearization control, and proposed MRAC) are provided to validate the superior performance of the proposed method such as fast transient response, low total harmonic distortion, and robustness to parameter uncertainties under critical load conditions (i.e., abrupt load changes, unbalanced loads, and distorted nonlinear loads).

Decentralized robust model reference adaptive control for interconnected time-delay systems

A novel model-reference robust adaptive controller that does not require a priori knowledge of the high-frequency-gain sign is proposed. The scheme is applicable to minimum-phase plants of arbitrary relative degree and ensures that in the absence of unmodeled dynamics the tracking error converges to zero and all the signals remain bounded. The control law uses a particular projected parameter vector instead of the current estimates to avoid division by zero. >

The three-link robotic manipulator plays an important role in industrial automation, where productivity and efficiency are directly related to precise motion control. However, its dynamics are highly nonlinear and strongly coupled, making the control problem challenging. In this work, a novel decoupling technique is introduced, where each joint acceleration is modeled as being primarily influenced by its own torque and velocity, while the remaining coupling dynamics are considered as uncertainties. Following this approach, simplified decoupled state-space equations are derived for all three links. A conventional Model Reference Adaptive Controller (MRAC) is then designed to track the desired reference model. While effective under ideal conditions, the conventional MRAC suffers from parametric divergence in the presence of external disturbances. To overcome this issue, a robust MRAC is proposed, which explicitly accounts for parametric uncertainties and disturbance effects. Simulation results demonstrate that the robust MRAC achieves superior performance compared to the conventional MRAC, maintaining stability and accurate trajectory tracking even under uncertainty and external disturbances.

Adaptive robust motion control of linear motors for precision manufacturing

A Design of Decentralized Robust Model Reference Adaptive Control System