Adaptive Discrete Second Order Sliding Mode Control with Application to Nonlinear Automotive Systems

Sliding mode control (SMC) is a robust and computationally efficient model-based controller design technique for highly nonlinear systems, in the presence of model and external uncertainties. However, the implementation of the conventional continuous-time SMC on digital computers is limited, due to the imprecisions caused by data sampling and quantization, and the chattering phenomena, which results in high frequency oscillations. One effective solution to minimize the effects of data sampling and quantization imprecisions is the use of higher order sliding modes. To this end, in this paper, a new formulation of an adaptive second order discrete sliding mode control (DSMC) is presented for a general class of multi-input multi-output (MIMO) uncertain nonlinear systems. Based on a Lyapunov stability argument and by invoking the new Invariance Principle, not only the asymptotic stability of the controller is guaranteed, but also the adaptation law is derived to remove the uncertainties within the nonlinear plant dynamics. The proposed adaptive tracking controller is designed and tested in real-time for a highly nonlinear control problem in spark ignition combustion engine during transient operating conditions. The simulation and real-time processor-in-the-loop (PIL) test results show that the second order single-input single-output (SISO) DSMC can improve the tracking performances up to 90%, compared to a first order SISO DSMC under sampling and quantization imprecisions, in the presence of modeling uncertainties. Moreover, it is observed that by converting the engine SISO controllers to a MIMO structure, the overall controller performance can be enhanced by 25%, compared to the SISO second order DSMC, because of the dynamics coupling consideration within the MIMO DSMC formulation.Comment: 12 pages, 7 figures, 1 tabl

Robust predictive feedback control for constrained systems

A new method for the design of predictive controllers for SISO systems is presented. The proposed technique allows uncertainties and constraints to be concluded in the design of the control law. The goal is to design, at each sample instant, a predictive feedback control law that minimizes a performance measure and guarantees of constraints are satisfied for a set of models that describes the system to be controlled. The predictive controller consists of a finite horizon parametric-optimization problem with an additional constraint over the manipulated variable behavior. This is an end-constraint based approach that ensures the exponential stability of the closed-loop system. The inclusion of this additional constraint, in the on-line optimization algorithm, enables robust stability properties to be demonstrated for the closed-loop system. This is the case even though constraints and disturbances are present. Finally, simulation results are presented using a nonlinear continuous stirred tank reactor model

A robust MPC/ISM hierarchical multi-loop control scheme for robot manipulators

In this paper, we propose a robust hierarchical multi-loop control scheme aimed at solving motion control problems for robot manipulators. The kernel of the proposed control scheme is the inverse dynamics-based feedback linearized robotic MIMO system. A first loop is closed relying on an Integral Sliding Mode (ISM) controller, so that matched disturbances and uncertain terms due to unmodelled dynamics, which are not rejected by the inverse dynamics approach, are suitably compensated. An external loop based on Model Predictive Control (MPC) optimizes the evolution of the controlled system in the respect of state and input constraints. The motivation for using ISM, apart from its property of providing robustness to the scheme in front of a significant class of uncertainties, is also given by its capability of enforcing sliding modes of the controlled system since the initial time instant, which is a clear advantage in the considered case, allowing one to solve the model predictive control optimization problem relying on a set of linearized decoupled SISO systems which are not affected by uncertain terms. As a consequence, a standard MPC can be used and the resulting control scheme is characterized by a low computational load with respect to conventional nonlinear robust solutions. The verification and the validation of our proposal have been carried out with satisfactory results in simulation, relying on a model of an industrial robot manipulator with injected noise, to better emulate a realistic set up. Both the model and the noise have been identified on the basis of real data. ©2013 IEEE

On relationship between time-domain and frequency-domain disturbance observers and its applications

This paper provides a generic analysis of the relationship between time/frequency-domain DOB design methodology. It is discovered that the traditional frequency-domain DOBs using a low pass filter with unity gain can only handle disturbances satisfying matching condition, while the traditional time-domain DOBs always generate an observer with a high order. A Functional Disturbance OBserver (FDOB) is proposed to improve the existing results together with its design guideline, frequency analysis and existence condition. Compared with the existing frequency-domain DOBs, the proposed FDOB can handle more classes of disturbances, while compared with the existing time-domain DOBs the proposed FDOB can generate an observer with a lower order. Numerical examples are presented to illustrate the main findings of this paper including a rotary mechanical system of nonminimum phase