Presence Of Saturation Constraints Research Articles

Saturated approximation-free prescribed performance trajectory tracking control for autonomous marine surface vehicle

This paper devotes to tackling the saturated approximation-free tracking control problem for unmanned marine surface vehicles with prescribed performance metrics. Firstly, a smooth dead zone-based model is introduced herein to address the saturation nonlinearity. Then, the tracking error dynamics in presence of saturation constraints and uncertainties are formulated accordingly. After that, the capability to preset the evolution range of tracking errors is guaranteed by means of the prescribed performance technology. It follows that a saturated approximation-free control scheme is developed based on the sliding mode control. Notably, the lumped uncertainties and the saturation nonlinearity are well handled totally free of the online estimations such that the control scheme is simple and intuitiveness for implementation. It is theoretically verified that the controller can achieve the stabilization of the system. Finally, simulation results are presented to illustrate the controller's efficacy.

Distributed Nonlinear AIMD Algorithms for Electric Bus Charging Plants

Recently, the introduction of electric vehicles has given rise to a new paradigm in the transportation field, spurring the public transport service in the direction of using completely electric bus fleets. In this context, one of the main challenges is that of guaranteeing an optimal scheduling of the charging process, while reducing the power supply requested from the main grid, and improving the efficiency of the resource allocation. Therefore, in this paper, a power allocation strategy is proposed in order to optimize the charging of electric bus fleets, while fulfilling the limitation imposed on the maximum available power, as well as ensuring limited charging times. Specifically, relying on real bus charging scenarios, a charging optimization algorithm based on a Nonlinear Additive Increase Multiplicative Decrease (NAIMD) strategy is proposed and discussed. This approach is designed on the basis of real charging power curves related to the batteries of the considered vehicles. Moreover, the adopted NAIMD algorithm allows us to minimize the sum of charging times in the presence of saturation constraints in a distributed way and with a small amount of aggregated data sent over the communication network. Finally, an extensive simulation campaign is illustrated, showing the effectiveness of the proposed approach both in allocating the power resources and in sizing the maximum power capacity of charging plants in progress.

Discrete-time sliding mode control of a class of linear uncertain saturated systems

This paper proposes a new design approach of discrete-time sliding mode control of a class of linear uncertain systems in presence of saturation constraint. The saturation constraint is reported on inputs vector and it is subject to constant limitations in amplitude. The uncertainty is being norm bounded reported on both dynamic and control matrices. In general, sliding mode control strategy consists on two essential phases. The design of the quasi-sliding surface is the first phase which is formulated as a pole assignment of linear uncertain and saturated system in a specific region through convex optimisation. The solution to this problem is therefore numerically tractable via linear matrix inequalities optimisation. The controller design is the second phase of the sliding mode control design, which leads to the development of a continuous and nonlinear control law. An approximation on the trajectory deviation of the uncertain saturated system compared to the ideal behaviour is proposed to provide robustness of the nonlinear control. Finally, the validity and the applicability of this approach are illustrated by a multivariable numerical example of a robot pick and place.

Discrete-time sliding mode control of a class of linear uncertain saturated systems

This paper proposes a new design approach of discrete-time sliding mode control of a class of linear uncertain systems in presence of saturation constraint. The saturation constraint is reported on inputs vector and it is subject to constant limitations in amplitude. The uncertainty is being norm bounded reported on both dynamic and control matrices. In general, sliding mode control strategy consists on two essential phases. The design of the quasi-sliding surface is the first phase which is formulated as a pole assignment of linear uncertain and saturated system in a specific region through convex optimisation. The solution to this problem is therefore numerically tractable via linear matrix inequalities optimisation. The controller design is the second phase of the sliding mode control design, which leads to the development of a continuous and nonlinear control law. An approximation on the trajectory deviation of the uncertain saturated system compared to the ideal behaviour is proposed to provide robustness of the nonlinear control. Finally, the validity and the applicability of this approach are illustrated by a multivariable numerical example of a robot pick and place.

Robust Attitude Tracking Control of Spacecraft in the Presence of Disturbances

I T IS well known that spacecraft usually operate in the presence of various disturbances and that their control input usually is limited because of actuator saturation. Therefore, two problems, disturbance rejection and saturation constraint accommodation, should be addressed in attitude control. Both problems have attracted considerable research interest in the existing literature. However, only limited results explicitly dealt with them simultaneously [1–5]. Di Gennaro [1] designed a dynamic controller that can globally asymptotically stabilize the spacecraft in the presence of saturation constraint and gravity gradient torque. However, the rejection of other disturbances is not guaranteed. Boskovic et al. [2,3] designed sliding-mode controllers, which are discontinuous and can cause chattering [6]. To avoid chattering, the boundary layer method was used in [2,3]. However, this method can only guarantee bounded attitude and angular velocity errors. To achieve global asymptotic stability with a smooth controller, Boskovic et al. [4] designed a continuous adaptive tracking controller with a condition necessary for guaranteeing the convergence of the attitude error to zero. However, it is difficult to know in what cases that condition can be satisfied. Moreover, according to [7], there do exist some disturbances in the presence of which that condition cannot be satisfied. Wallsgrove and Akella [5] designed a smooth controller using a hyperbolic tangent function. Although the angular velocity error converges to zero, the convergence of the attitude error to zero is not proved in [5]. Moreover, this controller gives rise to numerical problems in simulations of long duration. This paper proposes a controller without the aforementioned drawbacks. II. Spacecraft Attitude Dynamics

Stabilization of Satellite Motion Relative to a Coulomb Spacecraft Formation

Coulomb spacecraft are satellites that can actively control their electrostatic charge and thus exploit intervehicle electrostatic forces to control tight relative motion. The stabilization problem of a cluster of unequal Coulomb spacecraft is studied. Previous research has developed a nonlinear control law to stabilize the relative motion of one satellite relative to another. With only two spacecraft present, with equal mass and charging limits, Newton’s second law greatly simplified the control development. This control strategy is generalized here to stabilize the relative motion of a satellite relative to a larger cluster of Coulomb spacecraft with unequal satellite masses and individual charge saturation limits. The chief cluster motion can be either circular or elliptic. The nonlinear control methodology exploits an orbit element difference description of the satellite relative motion. Although the control is shown to stabilize the relative motion of a Coulomb satellite about any set of desired orbit element differences, convergence is shown thus far only when controlling exclusively the semimajor axis differences. Thus, this control is able to achieve bounded relative motion of the Coulomb satellite, even in the presence of saturation constraints. A simple structured control approach is numerically investigated to control the entire cluster. Numerical simulations illustrate the relative motion control behavior with the cluster chief or center of mass being on an elliptic high Earth orbit.

An adaptive predictive regulator with input saturations

Two approaches for the adaptive predictive control of SISO linear time-invariant plants subject to saturations on both the control variable and its increment are investigated. In the desaturating approach, the saturations are disregarded in the design phase, and their impact on performance is reduced by resorting to an anti-windup implementation of the controller. In the optimisation approach, at each time step an optimisation problem is solved that explicitly takes into account the presence of saturation constraints. Using a predictive control scheme with terminal input and output constraints, BIBO stability is proven for both approaches in the non-adaptive case. These results are exploited to prove BIBO stability also in the adaptive case for the desaturating approach as well as for a mixed desaturation/optimisation scheme.