Halil I. Basturk

State derivative feedback for adaptive cancellation of unmatched disturbances in unknown strict-feedback LTI systems

Solutions exist for the problem of canceling sinusoidal disturbances by the measurement of the state or by the measurement of an output for linear and nonlinear systems. In this paper, an adaptive backstepping controller is designed to cancel sinusoidal disturbances forcing an unknown linear time-invariant system in controllable canonical form which is augmented by a linear input subsystem with unknown system parameters. The state-derivatives of the original subsystem and the state of the input subsystem are the only measurements that are used in the design of the controller. The design is based on four steps, (1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters, (2) design of an adaptive disturbance observer for both disturbance and its derivative, (3) design of an adaptive controller for the virtual control input, and (4) design of the final adaptive controller by using the backstepping procedure. It is proven that the equilibrium of the closed-loop adaptive system is stable and the state of the considered original subsystem converges to zero as t � ∞ with perfect disturbance estimation. The effectiveness of the controller is illustrated with a simulation example of a third order system.

Adaptive wave cancelation by acceleration feedback for ramp-connected air cushion-actuated surface effect ships

We solve the problem of cargo transfer in high sea states over a ramp from a large, medium-speed, roll-on/roll-off (LMSR) vessel to a smaller connector vessel of a surface effect ship (SES) type. Our aim is to reduce ramp motion between the LMSR and SES in order to provide a safer environment for cargo transfer. We design an air cushion actuated controller to estimate and cancel the wave disturbance and stabilize the heave of the SES via heave acceleration feedback with actuation of the louver area for the case where the hydrodynamic and other parameters of the SES are not known a priori and the pressure dynamics of the air cushion contains nonlinearly parameterized unknown terms. We demonstrate the effect of our control design in simulations in a time-domain seakeeping code, named AEGIR.

Adaptive Cancellation of Matched Unknown Sinusoidal Disturbances for LTI Systems by State Derivative Feedback

Solutions already exist for the problem of canceling sinusoidal disturbances by measurement of state or an output for linear and nonlinear systems. In this paper, we design an adaptive controller to cancel matched sinusoidal disturbances forcing a linear time-invariant system by using only measurement of state-derivatives. Our design is based on three steps; (1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector, (2) design of an adaptive disturbance observer and, (3) design of an adaptive controller. We prove that the equilibrium of the closed-loop adaptive system is globally uniformly asymptotically stable and locally exponentially stable. The effectiveness of the controller is illustrated with a simulation example of a second-order system.

Adaptive cancelation of matched unknown sinusoidal disturbances for unknown LTI systems by state derivative feedback

Solutions already exist for the problem of canceling sinusoidal disturbances by measurement of the state or by measurement of an output for unknown linear and nonlinear systems. In this paper, we design an adaptive controller to cancel matched sinusoidal disturbances forcing a linear time-invariant system with unknown system parameters in controllable canonical form by using only measurement of state-derivatives. Our design is based on three steps, 1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on both unknown disturbance parameters and unknown plant parameters, 2) design of an adaptive disturbance observer and, 3) design of an adaptive controller. We prove that the equilibrium of the closed loop adaptive system is stable and state of the considered system goes to zero as t → ∞ with perfect disturbance estimation. The effectiveness of the controller is illustrated with a simulation example of a second order system.

Cancellation of unmatched biased sinusoidal disturbances for unknown LTI systems in the presence of state delay

Abstract In this paper, the problem of unmatched unknown sinusoidal disturbance cancellation in the presence of delay in the virtual control input of unknown LTI systems, is solved. Firstly, the disturbance is parameterized. Secondly, the delay is represented as a transport PDE. These two steps allow us to approach the problem as an adaptive control design problem for an uncertain coupled ODE–PDE system. An infinite-dimensional backstepping procedure is employed to compensate the state delay and a finite-dimensional backstepping procedure is used to overcome unmatched disturbance condition. Finally, an adaptive controller is designed and it is proven that the equilibrium of the closed-loop system is stable, and that the state of the closed-loop system converges to zero as t → ∞ while perfect disturbance estimation is achieved. The effectiveness of the controller is illustrated with a simulation example of a third-order system.

Adaptive backstepping cancelation of unmatched unknown sinusoidal disturbances for unknown LTI systems by state derivative feedback

Solutions already exist for the problem of canceling sinusoidal disturbances by measurement of the state or by measurement of an output for unknown linear and nonlinear systems. In this paper, we design an adaptive backstepping controller to cancel sinusoidal disturbances forcing an unknown linear time-invariant system in controllable canonical form which is augmented by a linear input subsystem with unknown system parameters by using only measurement of state-derivatives of the original subsystem and state of the input subsystem. Our design is based on four steps, (1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on both unknown disturbance parameters and unknown plant parameters, (2) design of an adaptive disturbance observer for both disturbance and its derivative, (3) design of an adaptive controller for virtual control input, and (4) design final adaptive controller by using backstepping procedure. We prove that the equilibrium of the closed-loop adaptive system is stable and state of the considered original subsystem goes to zero as t → ∞ with perfect disturbance estimation. The effectiveness of the controller is illustrated with a simulation example of a third order system.

Pitch Control Design for Tandem Lifting Body Catamaran by Aft Lifting Body Actuation

We design an adaptive controller to stabilize the pitch of the tandem lifting body catamaran with actuation of the aft lifting body for the case where the hydrodynamic and other parameters are not known a priori. We consider two scenarios: 1) we assume the pitch and the pitch rate to be available for feedback and 2) we use only the pitch rate and the pitch acceleration in the adaptive control design. Our designs are based on three steps: 1) parametrization of the unknown sinusoidal wave disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters; 2) design of an adaptive disturbance observer for the wave disturbance; and 3) design of an adaptive controller. We demonstrate the effect of our control designs in simulations, using a time-domain seakeeping code, named AEGIR.

A backstepping approach for an active suspension system

In this paper, the control design problem for an active suspension system to maintain the comfort and safety of the vehicle body is considered. The road disturbance is modelled as a finite sum of sinusoidal functions with unknown frequencies, amplitudes and phases. The disturbance is parameterized and an adaptive controller is designed by using the backstepping technique. It is proven that the equilibrium of the closed loop system is stable and the vertical acceleration of the vehicle body tends to zero despite road disturbances. The effectiveness of the controller is illustrated with a simulation of a road test.

Adaptive Backstepping Cancelation of Unmatched Unknown Sinusoidal Disturbances for LTI Systems by State Derivative Feedback

Solutions already exist for the problem of canceling sinusoidal disturbances by measurement of the state or by measurement of an output for linear and nonlinear systems. In this paper, we design an adaptive backstepping controller to cancel unmatched sinusoidal disturbances forcing a linear time-invariant system which is augmented by a linear input subsystem by using only measurement of state-derivatives of the original subsystem and state of the input subsystem. Our design is based on four steps, 1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters, 2) design of an adaptive disturbance observer for both disturbance and its derivative, 3) design of an adaptive controller for virtual control input, and 4) design final controller by defining error system and using backstepping procedure. We prove that the equilibrium of the closed-loop adaptive system is stable and state of the considered error system goes to zero as t → ∞ with perfect disturbance estimation. The effectiveness of the controller is illustrated with a simulation example of a third order system.Copyright

Rejection of sinusoidal disturbances for known LTI systems in the presence of output delay

Abstract This paper focuses on estimation and cancellation of unknown sinusoidal disturbances in a known LTI system with the presence of a known output delay. Parametrizing the disturbance and representing the delay as a transport PDE, the problem is converted to an adaptive control problem for ODE–PDE cascade. An existing state observer is used to estimate the ODE system states. The exponential stability of the equilibrium of the closed-loop and error system is proved. The perfect estimation of the disturbance and state is shown. Moreover, the convergence of the state to zero as t → ∞ is achieved in the closed loop system. The effectiveness of the controller is demonstrated in a numerical simulation.