On the Performance of a Nonlinear Position-Velocity Controller to Stabilize Rotor-Active Magnetic-Bearings System

The performance of a nonlinear position-velocity controller in stabilising the lateral vibrations of a rotor-active magnetic-bearings system (RAMBS) is investigated. Cubic nonlinear position-velocity and linear position-velocity controllers are introduced to stabilise RAMBS lateral oscillations. According to the proposed control law, the nonlinear system model is established and then investigated with perturbation analysis. Nonlinear algebraic equations that govern the steady-state oscillation amplitudes and the corresponding phases are derived. Depending on the obtained algebraic equations, the different frequency response curves and bifurcation diagrams are plotted for the studied model. Sensitivity analysis for the linear and nonlinear controllers’ gains is explored. Obtained analytical results demonstrated that the studied model had symmetric bifurcation behaviours in both the horizontal and vertical directions. In addition, the integration of the cubic position controller made the control algorithm more flexible to reshape system dynamical behaviours from the hardening spring characteristic to the softening spring characteristic (or vice versa) to avoid resonance conditions. Moreover, the optimal design of the cubic position gain and/or cubic velocity gain could stabilise the unstable motion and eliminate the nonlinear effects of the system even at large disc eccentricities. Lastly, numerical validations for all acquired results are performed, where the presented simulations show accurate correspondence between numerical and analytical investigations.

Nonlinear Control of a Pneumatic Actuator Based on a Dynamic Friction Model

This paper presents a new controller for the position of a pneumatic actuator. The controller is designed based on the multiple-surface sliding control method in combination with a frictional compensator. The multiple-surface sliding control method is applied to deal with the nonlinear characteristics of the pneumatic system, and the frictional compensator is applied to compensate for the friction force in the pneumatic actuator. The friction force is estimated based on a dynamic friction model (the LuGre model). Both simulation and experimental studies are done to evaluate the new controller. The evaluation results indicate significant improvement in the tracking position error of the new controller comparing to the multiple-surface sliding controller without friction compensation and other nonlinear controllers.

Stabilization of port-Hamiltonian systems by nonlinear boundary control in the presence of disturbances

In this paper, we are concerned with the stabilization of linear port-Hamiltonian systems of arbitrary order $N \in \N$ on a bounded $1$-dimensional spatial domain $(a,b)$. In order to achieve stabilization, we couple the system to a dynamic boundary controller, that is, a controller that acts on the system only via the boundary points $a,b$ of the spatial domain. We use a nonlinear controller in order to capture the nonlinear behavior that realistic actuators often exhibit and, moreover, we allow the output of the controller to be corrupted by actuator disturbances before it is fed back into the system. What we show here is that the resulting nonlinear closed-loop system is input-to-state stable w.r.t.~square-integrable disturbance inputs. In particular, we obtain uniform input-to-state stability for systems of order $N=1$ and a special class of nonlinear controllers, and weak input-to-state stability for systems of arbitrary order $N \in \N$ and a more general class of nonlinear controllers. Also, in both cases, we obtain convergence to $0$ of all solutions as $t \to \infty$. Applications are given to vibrating strings and beams.

LMI-Based Analysis and Stabilization of Nonlinear Descriptors with Multiple Delays via Delayed Nonlinear Controller Schemes

This paper presents a convex approach for nonlinear descriptor systems with multiple delays; it allows designing delayed nonlinear controllers such that the closed-loop system holds exponential estimates for convergence. The proposal takes advantage of an equivalent convex representation of the given descriptor model together with Lyapunov-Krasovskii functionals; thus, the conditions are in the form of linear matrix inequalities, which can be efficiently solved by commercially available software. To avoid possible saturation in the actuators, conditions for bounding the control input are also given. Numerical and academic examples illustrate the performance of the proposal.

Modeling and nonlinear energy-based anti-swing control of underactuated dual ship-mounted cranes systems

As the volume and the mass of the payload increases, it is often necessary to use two ship-mounted cranes to jointly transport huge payloads under marine environment. Compared with a single ship-mounted crane, dual ship-mounted cranes contain more state variables, geometric constraints and coupling dynamics, which bring more challenges in kinematic analysis and controller design for such complicated underactuated systems. In order to solve these problems, the dynamic model of the dual ship-mounted cranes systems are established based on Lagrange's method. Considering different practical requirements, two energy-based nonlinear controllers for dual ship-mounted cranes are developed, including a full state feedback control method and an output feedback control method. More preciously, during the control design process, the saturation constraints of the controllers have been fully considered. Meanwhile, the proposed controllers can achieve accurate positioning of the double-constrained derricks as well as effective elimination of payload swing. The stability of the equilibrium point of the closed-loop system is analyzed by using Lyapunov techniques and Lasalle's invariance principle. As far as we know, the modeling and the output feedback controller design of dual ship-mounted cranes are proposed for the first time in this paper. At the same time, the design and analysis process does not need to linearize the complex nonlinear dynamics equations, while the proposed output feedback control method is robust against the situations when the velocity signals are unknown/unavailable. Finally, a series of experiments are carried out to verify the effectiveness of the proposed nonlinear controllers.