Singularity-free multivariable model reference adaptive control

Application of Multivariable Model Reference Adaptive Control to a Binary Distillation Column

A multivariable model reference adaptive control algorithm is presented for the case when the high-frequency gain matrix is unknown. Only an upper bound on the norm of the matrix needs to be known a priori. A transformation of the parameters, with a sort of hysteresis, is used to guarantee that a controller matrix, which is normally the inverse of the estimate of the high-frequency gain matrix, remains nonsingular. It is shown that all the signals in the adaptive system are bounded and that the tracking error and the regressor error converge to zero for all bounded reference inputs. Furthermore, exponential convergence is achieved when the regressor vector is persistently exciting.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stability is improved for a multivariable model reference adaptive control algorithm when the high-frequency gain matrix is unknown. Only an upper bound on the norm of the matrix is required. A transformation of the parameters, with a sort of 'hysteresis', is used to guarantee that a controller matrix, which is nominally the inverse of the high-frequency gain matrix, remains nonsingular. It is shown that all the signals in the adaptive system are bounded and that the tracking error and the regressor error converge to zero for all bounded reference inputs. Furthermore, exponential convergence is achieved when the regressor vector is persistently exciting. >

The landing of a civil transport aircraft is one of the most critical phases due to parametric uncertainties and strong crosswind conditions. In this paper, separate controllers are designed for longitudinal and lateral-directional channels for the landing phase, which is divided into the final approach, flare, and decrab. A multivariable model reference adaptive control scheme is implemented with state feedback for output tracking. The safety and flight performance of the autolanding control system are demonstrated through Monte Carlo simulations of a nonlinear civil transport aircraft model.

Aircraft damage causes large uncertain system parametric and structural changes which lead to unknown deviations of the aircraft equilibrium points and unknown coupling of the aircraft dynamics. To deal with such unknown changes, we use a sequential linear model with a dynamics offset to represent a linearized aircraft system before and after damage. A state feedback multivariable model reference adaptive control (MRAC) scheme is developed for such a linear model, with adaptive compensation of the uncertain dynamics offset as well as system parametric uncertainties. Desired closed-loop signal boundedness and asymptotic output tracking are established. Numerical values of linearized models from the NASA GTM were used in the simulation study and its results verified the desired system performance despite uncertain damage.

SummaryA novel multivariable composite model reference adaptive control scheme is developed for multivariable fractional‐order systems with arbitrary relative degree. Firstly, by introducing right gain matrix to substitute left gain matrix, the stringent symmetry assumption is no longer required. The design procedures of controller with certain and uncertain high‐frequency gain matrix are then provided, respectively. The (robust) stability of the resulting closed‐loop control system is investigated by indirect Lyapunov method. It is shown that the composite model reference adaptive control can achieve better performance on output tracking than that of model reference adaptive control. Finally, the effectiveness and applicability of the proposed control scheme are demonstrated in 3 numerical examples.

Multivariable adaptive control based consensus flight control system for UAVs formation

In this paper, it will be proposed a design of indirect multivariable model reference adaptive control systems, which includes the on-line structural estimation of the interactor matrix. A newly developed derivation of the interactor will be used for the calculation. Simulation results which confirm the validity of the proposed method will be also presented.

A method is presented for the design of multivariable model reference adaptive control systems by Lyapunov's second method. The method can be applied to a class of systems in which the misaligned elements of the plant matrices cannot be compensated independently.

Petri Nets for Real Time Control Algorithms Decomposition

Summary Using multiple interacting drugs to control both the mean arterial pressure (MAP) and cardiac output (CO) of patients with different sensitivity to drugs is a challenging task which this paper attempts to address. A multivariable model reference adaptive control (MRAC) algorithm is developed using a two-input, two-output patient model. The control objective is to maintain the homodynamic variables MAP and CO at the normal values by simultaneously administering two drugs; sodium nitroprusside (SNP) and dopamine (DPM). Computer simulations were carried out to investigate the performance of this controller. The results show that the proposed adaptive scheme is robust with respect to disturbances and variations in model parameters.

Adaptive Fault Detection and Fault-Tolerant Control of NASA Generic Transport Aircraft Model

This paper derives a stable multivariable model reference adaptive control (MRAC) scheme for systems with abrupt parameter variations (which may cause uncertain sign changes in the system’s high frequency gain matrix), motivated by the application to in-flight aircraft systems with damages. Such sign changes are illustrated by an aircraft model with asymmetric abrupt damages, and their uncertainty is handled by a Nussbaum gain based adaptive control design to control the aircraft for both healthy and post-damage situations, by adapting controller parameters autonomously after the damages occur, for which the knowledge of time instants, structures and values of the damages is not required. A piecewise continuous Lyapunov function is utilized to prove the desired system stability and tracking properties in the presence of damages.

This paper investigates the use of neural networks (NNs) in conventional model reference adaptive control (MRAC) to control a nonlinear magnetic levitation system. In the conventional MRAC scheme, the controller is designed to realize plant output convergence to a reference model output based on a plant which is linear. This scheme is effectively for controlling linear plants with unknown parameters. However, using MRAC to control the nonlinear magnetic levitation system in real time is a difficult control problem. In this paper, we incorporate a NN in MRAC to overcome the problem. The control input is given by the sum of the output of the adaptive controller and the output of the NN. The NN is used to compensate the nonlinearity of the plant that is not taken into consideration in the conventional MRAC. From experiment results, it has been shown that the plant output can converge to the reference model output after using NN in MRAC.

Partial-state feedback multivariable MRAC and reduced-order designs