The sliding mode control algorithm and Lyapunov-based methods, have received much attention recently due to their ability to directly handle nonlinear systems while guaranteeing closed-loop tracking stability. In this work, a unique model-free sliding mode control technique has developed solely based on previous control inputs. The new method requires only knowledge of the system order and state measurements and does not require a theoretical model of the dynamic system. Lyapunov’s stability theorem is used in the controller formulation process to ensure closed-loop asymptotic stability. High frequency chattering of the control effort is reduced by using a smoothing boundary layer into the control law. Parameters variation during control operating and noise effect cannot be handled by the model-free controller if the controller tuning parameters are chosen arbitrarily since tracking performance becomes unacceptable. In addition, in previous work, the bounds of the input influence gain parameters were assumed to be known to derive the model-free controller. Therefore, in this work, a new approach is proposed for estimating the increment to the switching gain in real-time to ensure the sliding condition (which guarantees closed-loop tracking stability) is satisfied using a control law form that assumes a strictly unitary input influence gain. In formulation of estimation law, an exponential forgetting factor is combined with the least-squares estimator to ensure the updated data are used and past data are excluded. An automatic bounded forgetting tuning technique is developed to maintain the benefits of data forgetting while avoiding the possibility of gain unboundedness in absence of persistent excitation. The tuning estimator is assured that the resulting gain matrix is upper bounded regardless of the persistent excitation by suspending the data forgetting if the gain matrix reaches the specified upper bound. Simulations are performed on a series of linear and nonlinear SISO and MIMO systems with and without including actuator time-delay effects. Finally, a model is developed to simulate a quadcopter as a real-world application case. In all cases, the controller achieved perfect or near-perfect tracking performance using updated controller and on-line estimator tuning process.

Library of Congress Subject Headings

Sliding mode control; Lyapunov stability; Quatrotor helicopters--Automatic control--Computer simulation

Publication Date


Document Type


Student Type


Degree Name

Mechanical Engineering (MS)

Department, Program, or Center

Mechanical Engineering (KGCOE)


Agamemnon Crassidis

Advisor/Committee Member

Sergey Lyshevski

Advisor/Committee Member

Jason Kolodziej


RIT – Main Campus

Plan Codes