Generation of optimal schedules for metro lines using model predictive control

This paper presents a new methodology for computation of optimal train schedules in metro lines using a linear-programming-based model predictive control formulation. The train traffic model is comprised of dynamic equations describing the evolution of train headways and train passenger loads along the metro line, considering the time variation of the passenger demand and all relevant safety and operational constraints for practical use of the generated schedule. The performance index is a weighted sum of convex piecewise-linear functions for directly or indirectly modelling the waiting time of passengers at stations, onboard passenger comfort, train trip duration and number of trains in service. The proposed methodology is computationally very efficient and can generate optimal schedules for a whole day operation as well as schedules for transition between two separate time periods with known schedules. The use and performance of the proposed methodology is illustrated by an application to a metro line similar to the North-South line of São Paulo Underground.     

Model predictive control: Recent developments and future promise

This paper recalls a few past achievements in Model Predictive Control, gives an overview of some current developments and suggests a few avenues for future research.     

Selecting operating points for discrete-time gain scheduling

Gain scheduling is a popular approach for nonlinear control system design. A controller is obtained by designing a set of controllers at operating points and then linearly interpolating controller values between them. However, little guidance has been provided in the literature for the selection of operating points. We use interval mathematics and a classical synthesis design approach to determine a near minimal set of design points and assess the quality of a gain scheduled controller. A sufficient condition for the assignment of the system closed loop poles is developed, and an algorithm for selecting the operating points is provided. An example is given to demonstrate the approach.     

Surge tank control in a cane raw sugar factory

The performance of the juice circuit in a cane raw sugar factory is critical to the production of high quality sugar, and hence its saleability on the international market. In this paper, we present a control project that deals with this aspect of the raw sugar production process. The problem that is addressed is to control surge tanks within the juice circuit in order to steady the flow (minimisation of the rate of change) into a settling vessel known as the clarifier. This is a particularly important problem since the clarifier’s efficiency is reduced by rapid flow rate variations with the ultimate result being a reduction in raw sugar quality due to increased extraneous matter in the sugar. The new solution involves using gain-scheduled feedforward techniques to control the existing surge tanks so that the available capacity is used in an efficient way. The new control scheme was implemented on existing hardware and achieved the desired level of performance.     

Feedforward model predictive control

This paper examines the role played by feedforward in model predictive control (MPC). We contrast feedforward with preview action. The latter is standard in model predictive control, whereas feedforward has been rarely, if ever, used in contemporary formulations of MPC. We argue that feedforward can significantly improve performance in the presence of measurement noise and certain types of model uncertainty.     

On optimality of nonlinear model predictive control

In this note the optimality property of nonlinear model predictive control (MPC) is analyzed. It is well known that the MPC approximates arbitrarily well the infinite horizon (IH) controller as the optimization horizon increases. Hence, it makes sense to suppose that the performance of the MPC is a not decreasing function of the optimization horizon. This work, by means of a counterexample, shows that the previous conjecture is fallacious, even for simple linear systems.     

Application of position and inertial-rate control to a 2-DOF gyroscopic platform

This paper presents a control application for the inertial stabilization of a gyroscopic platform with two degrees of freedom (2-DOF). The purposes of this application are, first, to control the angular positions of the platform in the absence of inertial disturbances and second, to control velocities measured in an inertial frame, while rejecting the disturbances associated with moving components. With regard to the first objective, a switching-control strategy is proposed in order to reduce the effects of friction as the main source of undesirable non-linear behaviors. Regarding the inertial-rate control, a master–slave control structure is suggested to achieve the desired specifications. Simulation and experimental results are presented, showing the performance attained on a real platform.     

Distributed model predictive control of dynamically decoupled systems with coupled cost

This paper considers the distributed model predictive control (DMPC) of systems with interacting subsystems having decoupled dynamics and constraints but coupled costs. An easily-verifiable constraint is introduced to ensure asymptotic stability of the overall system in the absence of disturbance. The constraint introduced has a parameter which allows for the performance of the DMPC system to approach that controlled by a centralized model predictive controller. When the subsystems are linear and additive disturbance is present, the added constraint ensures the state of each subsystem converges to its respective minimal disturbance invariant set. The approach is demonstrated via several numerical examples.     

Incorporating state estimation into model predictive control and its application to network traffic control

Model predictive control (MPC) is of interest because it is one of the few control design methods which preserves standard design variables and yet handles constraints. MPC is normally posed as a full-state feedback control and is implemented in a certainty-equivalence fashion with best estimates of the states being used in place of the exact state. This paper focuses on exploring the inclusion of state estimates and their interaction with constraints. It does this by applying constrained MPC to a system with stochastic disturbances. The stochastic nature of the problem requires re-posing the constraints in a probabilistic form. Using a gaussian assumption, the original problem is approximated by a standard deterministically-constrained MPC problem for the conditional mean process of the state. The state estimates’ conditional covariances appear in tightening the constraints. ‘Closed-loop covariance’ is introduced to reduce the infeasibility and the conservativeness caused by using long-horizon, open-loop prediction covariances. The resulting control law is applied to a telecommunications network traffic control problem as an example.