Sliding modes in constrained systems control

Abstract—In this paper, a sliding-mode-based design framework for fully actuated mechanical multibody system is discussed. The framework is based on the possibility to represent complex motion as a collection of tasks and to find effective mapping of the system coordinates that allows decoupling task and constraint control so one is able to enforce concurrently, or in certain time succession, the task and the constraints. The approach seems naturally encompassing the control of motion systems in interaction, and it allows application to bilateral control, multilateral control, etc. Such an approach leads to a more natural interpretation of the system tasks, simpler controller design, and easier establishment of the systems hierarchy. It allows a unified mathematical treatment of task control in the presence of constraints required to be satisfied by the system coordinates. In order to show the applicability of the proposed techniques, simulation and experimental results for high-precision systems in microsystem assembly tasks and bilateral control systems are presented

Sliding modes in electrical drives and motion control

In this paper application of Sliding Mode Control (SMC) to electrical drives and motion control systems is discussed. It is shown that in these applications simplicity in implementation makes concepts of SMC a very attractive design alternative. Application in electrical drives control is discussed for supply via different topologies of the supply converters. Motion control is discussed for single degree of freedom motion control systems as an extension of the control of mechanical coordinates in electrical drives. Extension to multi-body systems is discussed very briefly

Sliding modes in power electronics and motion control

In the paper the general approach to motion control systems in the sliding mode framework is discussed in details. It has been shown that, due to the fact that a motion control system with n d.o.f may be mathematically formulated in a unique way as a system composed on n 2 d.o.f systems, design of such a system may be formulated in a unique way as a requirement that the generalized coordinates must satisfy certain algebraic constrain. Such a formulation leads naturally to sliding mode methods to be applied where sliding mode manifolds are selected to coincide with desired constraints on the generalized coordinates. In addition to the above problem the design of full observer for IM based drive is discussed

On deterministic and stochastic sliding modes via small diffusion approximation

We study solutions of a system of ordinary differential equations with discontinuity of its vector field on a smooth surface via small additive diffusion perturbations. When a diffusion term tends to zero, one obtains limiting sliding modes on the surface with explicit representation for its motion law. Stochastic sliding modes are also established

Automobile Road Vibration Reproduction using Sliding Modes

Sliding mode controllers have a reputation for their robustness against parameter variations, modeling errors and disturbances. They have been successfully applied in several practical situations which demonstrated the potential of sliding mode control for other control problems. However research has mainly been focused on continuous-time sliding mode controllers. In practical applications, where the continuous-time system is sampled by the computer, it is often assumed that the sampling time is sufficiently fast to consider the sampled system as a continuous-time system. This paper aims at providing an overview of the design procedure for discrete-time, output-based, sliding mode controllers, based on discrete-time models. The applicability of these controllers were suggested by the SCOOP project where extra robustness has to be gained by extending the controller setup by the sliding mode feed-back controller

Sliding modes for a phase-field system

In the present contribution the sliding mode control (SMC) problem for a phase-field model of Caginalp type is considered. First we prove the well-posedness and some regularity results for the phase-field type state systems modified by the state- feedback control laws. Then, we show that the chosen SMC laws force the system to reach within finite time the sliding manifold (that we chose in order that one of the physical variables or a combination of them remains constant in time). We study three different types of feedback control laws: the first one appears in the internal energy balance and forces a linear combination of the temperature and the phase to reach a given (space dependent) value, while the second and third ones are added in the phase relation and lead the phase onto a prescribed target ~$\phi^*$. While the control law is non-local in space for the first two problems, it is local in the third one, i.e., its value at any point and any time just depends on the value of the state