Robust Model Predictive Control With Integral Sliding Mode in Continuous-Time Sampled-Data Nonlinear Systems

n/

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

Model-based event-triggered robust MPC/ISM

A model-based event-triggered control scheme based on the combined use of Model Predictive Control (MPC) and Integral Sliding Mode (ISM) control is proposed in this paper. The aim is to reduce to a minimum the number of transmissions of the plant state over the network, in order to alleviate delays and packet loss induced by the network overload, while guaranteeing robust stability and constraints fulfillment. The presented control scheme includes a model-based controller and a smart sensor, both containing a copy of the nominal model of the plant. The sensor intelligence is provided by a triggering condition, which enables to determine when it is necessary to transmit the measured state and to update the nominal model. The controller includes an ISM component, which has the role of compensating the uncertainties, and a MPC term which optimizes the system evolution. The control system performance are assessed in simulation relying on an illustrative mechanical example

Model free control based on GIMC structure

Abstract: Many control researches for complicated and uncertain system are model-dependent and therefore require some prior knowledge for the complex systems. To avoid this problem, a number of model-free controllers are proposed. However, it is difficult to determine the control performance as the controller is not designed according certain system model especially when there are uncertainties and/or nonlinear dynamics in the system. To get over this problem, the model free controller (MFC) based on generalized internal model control (GIMC) structure is proposed in this paper. The MFC is used to attenuate the disturbance or uncertainty, and the system performance is determined by the nominal model and the nominal model controller. The parameters of nominal-model controller can be easily changed for meeting the change of the desired requirements. Moreover, the robust controller in the original GIMC is disassembled and rearranged to make the proposed methods easier to use, and the proposed method makes the controller be more flexible and greatly improves the system performance. Finally, the experiment results show that the MFC can be used to control the nonlinear systems and get the expected performance. The statistical analysis of performance for servo and regulatory behaviors also shows that the proposed method can achieve a better control performance than just using model free controller

Dynamic Landing of an Autonomous Quadrotor on a Moving Platform in Turbulent Wind Conditions

Autonomous landing on a moving platform presents unique challenges for multirotor vehicles, including the need to accurately localize the platform, fast trajectory planning, and precise/robust control. Previous works studied this problem but most lack explicit consideration of the wind disturbance, which typically leads to slow descents onto the platform. This work presents a fully autonomous vision-based system that addresses these limitations by tightly coupling the localization, planning, and control, thereby enabling fast and accurate landing on a moving platform. The platform's position, orientation, and velocity are estimated by an extended Kalman filter using simulated GPS measurements when the quadrotor-platform distance is large, and by a visual fiducial system when the platform is nearby. The landing trajectory is computed online using receding horizon control and is followed by a boundary layer sliding controller that provides tracking performance guarantees in the presence of unknown, but bounded, disturbances. To improve the performance, the characteristics of the turbulent conditions are accounted for in the controller. The landing trajectory is fast, direct, and does not require hovering over the platform, as is typical of most state-of-the-art approaches. Simulations and hardware experiments are presented to validate the robustness of the approach.Comment: 7 pages, 8 figures, ICRA2020 accepted pape

Dynamic Tube MPC for Nonlinear Systems

Modeling error or external disturbances can severely degrade the performance of Model Predictive Control (MPC) in real-world scenarios. Robust MPC (RMPC) addresses this limitation by optimizing over feedback policies but at the expense of increased computational complexity. Tube MPC is an approximate solution strategy in which a robust controller, designed offline, keeps the system in an invariant tube around a desired nominal trajectory, generated online. Naturally, this decomposition is suboptimal, especially for systems with changing objectives or operating conditions. In addition, many tube MPC approaches are unable to capture state-dependent uncertainty due to the complexity of calculating invariant tubes, resulting in overly-conservative approximations. This work presents the Dynamic Tube MPC (DTMPC) framework for nonlinear systems where both the tube geometry and open-loop trajectory are optimized simultaneously. By using boundary layer sliding control, the tube geometry can be expressed as a simple relation between control parameters and uncertainty bound; enabling the tube geometry dynamics to be added to the nominal MPC optimization with minimal increase in computational complexity. In addition, DTMPC is able to leverage state-dependent uncertainty to reduce conservativeness and improve optimization feasibility. DTMPC is demonstrated to robustly perform obstacle avoidance and modify the tube geometry in response to obstacle proximity

Hierarchical Model Predictive/Sliding Mode control of nonlinear constrained uncertain systems

This paper presents an overview of some hierarchical control schemes composed by a high level Model Predictive Control (MPC) and a low level Sliding Mode Control (SMC). The latter is realized by using the so-called Integral Sliding Mode (ISM) control approach and is meant to reject the matched disturbances affecting the plant, thus providing a system with reduced uncertainty for the MPC design. Both continuous and discrete-time solutions are discussed in the paper. Moreover, assuming the presence of a network in the control loop, a networked version of the control scheme is presented. It is a model-based event-triggered MPC/ISM control scheme aimed at minimizing the packets transmission. The input-to-state (practical) stability properties of the proposed approaches are also addressed in the paper

Sliding mode control of constrained nonlinear systems

This technical note introduces the design of sliding mode control algorithms for nonlinear systems in the presence of hard inequality constraints on both control and state variables. Relying on general results on minimum-time higher-order sliding mode for unconstrained systems, a general order control law is formulated to robustly steer the state to the origin, while satisfying all the imposed constraints. Results on minimum-time convergence to the sliding manifold, as well as on the maximization of the domain of attraction, are analytically proved for the first-order and second-order sliding mode cases. A general result is presented regarding the domain of attraction in the general order case, while numerical results on the estimation of the domain of attraction and on minimum-time convergence are discussed for the third-order case, following a procedure applicable to a sliding mode of any order

A Discrete-Time Optimization-Based Sliding Mode Control Law for Linear Systems with Input and State Constraints

This paper proposes a discrete-time sliding mode control (DSMC) strategy for linear (possibly multi-input) systems with additive bounded disturbances, which guarantees the satisfaction of input and state constraints. The control law is generated by solving a finite-horizon optimal control problem at each sampling instant, aimed at obtaining a control variable that is as close as possible to a reference DSMC law, but at the same time enforces constraint satisfaction for all admissible disturbance values. Contrary to previously-proposed control approaches merging DSMC and model predictive control, our proposal guarantees the satisfaction of all standard properties of DSMC, and in particular the finite-time convergence of the state into a boundary layer of the sliding manifold

MPC for Robot Manipulators with Integral Sliding Modes Generation

This paper deals with the design of a robust hierarchical multiloop control scheme to solve motion control problems for robot manipulators. The key elements of the proposed control approach are the inverse dynamics-based feedback linearized robotic multi-input-multi-output (MIMO) system and the combination of a model predictive control (MPC) module with an integral sliding mode (ISM) controller. The ISM internal control loop has the role to compensate the matched uncertainties due to unmodeled dynamics, which are not rejected by the inverse dynamics approach. The external loop is closed relying on the MPC, which guarantees an optimal evolution of the controlled system while fulfiling state and input constraints. The motivation for using ISM, apart from its property of providing robustness to the scheme with respect to a wide class of uncertainties, is also given by its capability of enforcing sliding modes of the controlled system since the initial time instant, allowing one to solve the MPC optimization problem relying on a set of linearized decoupled single-input-single-output (SISO) systems that are not affected by uncertain terms. The proposal has been verified and validated in simulation, relying on a model of a COMAU Smart3-S2 industrial robot manipulator, identified on the basis of real data