Yaprak Yalçin

A Direct Discrete-time IDA-PBC Design Method for a Class of Underactuated Hamiltonian Systems

Abstract In this paper, a direct discrete time design method in the sense of passivity-based control (PBC) is investigated. This method, which is known as interconnection and damping (IDA), deals with the stabilization of under-actuated mechanical systems and, it is based on the modification of both the potential and kinetic energies. In order to give a direct discrete time IDA-PBC design method, the discrete time counterpart of matching conditions is derived using an appropriate discrete gradient. The discrete-time matching conditions are obtained as a set of linear partial differential equations which can be solved off-line parametrically and a set of linear equations. The unknown parameters of linear partial differential equations and the linear equations have to be solved at each sampling time, to calculate control rule. Moreover, a design procedure is given to solve these matching conditions for a class of Hamiltonian systems. To illustrate the effectiveness and the appropriateness of the proposed method, the example of pendulum on a cart is considered.

Discrete time immersion and invariance adaptive control for systems in strict feedback form

This paper presents a new design procedure for the adaptive stabilization (regulation) via state feedback for discrete-time nonlinear systems in parametric strict-feedback form. The algorithm utilizes discrete-time adaptive backstepping in the controller construction together with a new method for the parameter estimator design. This approach provides a recursive construction which guarantees boundness of the closed-loop trajectories and global convergence to the origin of the state of the closed-loop system. The performance of the proposed method are illustrated by simulations.

Disturbance Attenuation in Hamiltonian Systems via Direct Discrete-Time Design

Abstract The discrete-time disturbance attenuation problem for a class of Hamiltonian systems is considered. In order to give a sufficient condition for the solution of the considered problem, firstly an appropriate discrete gradient is proposed, which enables the derivation of the discrete time version of the given Hamiltonian systems. The disturbance attenuation problem characterised by means of L 2 gain is redefined in the discrete-time setting. The proposed direct discrete-time design method is used to solve the disturbance attenuation problem for the double pendulum system in simulations.

Discrete time immersion and invariance adaptive control via partial state feedback for systems in block strict feedback form

Abstract This paper presents a new method for the adaptive (tracking) regulation via partial state feedback for a class of discrete-time nonlinear systems in parametric strict-feedback form. A procedure is proposed based on immersion and invariance control approach where the parameter estimator and state observer designs are accomplished simultaneously. The algorithm utilizes discrete-time adaptive backstepping in the controller construction while providing a design without over parametrization. The proposed controller construction guarantees boundedness of the closed-loop trajectories and global (tracking) convergence to the origin of the state of the closed-loop system. The performance of the proposed method is illustrated by simulations.

A new approach on angular position control of fan and plate system

In this paper, a linear control technique based on a PID controller, which is the most used controller type in the industrial applications, is proposed for the angular position control of fan and plate system that has a nonlinear characteristic. Although the system is nonlinear, in the experimental studies, it is observed that for any small region in which the system can be considered as linear, the system (the linear model obtained around an operating point) has the same characteristic in the all operating regions. A new control approach is proposed by using this property of the system to guarantee the stability and operation without any overshoot.

Discrete-Time Immersion and Invariance Adaptive Control of a Slider-crank Mechanism

Abstract A discrete-time adaptive nonlinear control procedure is developed based on immersion and invariance control, and using back-stepping for the regulation of slider-crank system. A convenient parametric formulation of the system dynamics is established. A novel parameter estimator design is presented, and the back-stepping controller is constructed considering the certainty equivalence principle.

A new approach for the design of relay control circuits

Nowadays, the use of electronic control units are limited in applications that require high safety integrity. Therefore, to satisfy the conditions for applications requiring high reliability, control circuits are used instead of digital electronic control units like PLCs. Due to the lack of efficient, simple and applicable methods in the literature, design of control circuits are mainly based on heuristic methods. In this study, existing problems related to the application of the known formal methods will be examined and an effective solution will be proposed.

Implementation of a PID-neural network with PLC

Abstract PID (Proportional-Integral-Derivative) controllers are widely used in industry, since they are robust and easy to design. To make a system behave, as it is desired, it is enough to determine the appropriate PID coefficients. But, sometimes it would be really difficult to obtain mathematical model of system. Recently, as an alternative, PID like neural networks for abovementioned situations, are used for control purposes. In this study, a neural network of which input-output functions are chosen by the help of classical PID structure has been realized with the programmable logic controller (PLC). The applied training method in realization deals with major disadvantages of neural networks long learning and convergence times.