Dominik Pisarski

Optimal balancing of road traffic density distributions for the Cell Transmission Model

In this paper, we study the problem of optimal balancing of traffic density distributions. The optimization is carried out over the sets of equilibrium points for the Cell Transmission Traffic Model. The goal is to find the optimal balanced density distribution that maximizes the Total Travel Distance. The optimization is executed in two steps. At the first step, we consider a nonlinear problem to find a uniform density distribution that maximizes the Total Travel Distance. The second step is to solve the constrained quadratic problem to find the near balanced optimal equilibrium point. At both steps, we use decomposition methods. The quadratic optimization problem is solved by using the Dual Problem. The computational algorithms associated to such a problem are given.

Smart Suspension System for Linear Guideways

This paper presents a new method for the semi-active control of the span system of linear guideways subjected to a travelling load. Two elastic beams are coupled by a set of controlled dampers. The relative velocity of the spans provides an opportunity for efficient control via semi-active suspension. The magnitude of the moving force is assumed to be constant by neglecting inertial forces. The response of the system is solved in modal space. The full analytical solution is based on the power series method and can be given over an arbitrary time interval. The control strategy is formulated by using bilinear optimal control theory. As a result, bang-bang controls are taken into account. The final solution is obtained as a numerical mean value. Several examples demonstrate the efficiency of the proposed method. The controlled system outperforms passive solutions over a wide range. Due to the simplicity of its design, the presented solution should be interesting to engineers.

Nash Game-Based Distributed Control Design for Balancing Traffic Density Over Freeway Networks

In this paper, we study the problem of optimal balancing of vehicle density in freeway traffic. The optimization is performed in a distributed manner by utilizing the controllability properties of the freeway network represented by the Cell Transmission Model. By using these properties, we identify the subsystems to be controlled by local ramp meters. The optimization problem is then formulated as a noncooperative Nash game that is solved by decomposing it into a set of two-players hierarchical and competitive games. The process of optimization employs the communication channels matching the switching structure of system interconnectivity. By defining the internal model for the boundary flows, local optimal control problems are efficiently solved by utilizing the method of linear quadratic regulator. The developed control strategy is tested via numerical simulations in two scenarios for uniformly congested and transient traffic.

Distributed Control Design for Structures Subjected to Traveling Loads

This paper presents a novel distributed control method that adapts the structures subjected to traveling loads. The adaptation is realized by changes of the damping of the structure’s supports. The control objective is to provide smooth passage of vehicles and to extend the safe life-time of the carrying structures. The results presented in the previous works of the author exhibited high performance of supports with an open-loop switching damping policy. In this paper, the goal is to develop a state feedback strategy that is significantly less sensitive to the system parameters and much simpler for practical implementation. Further efforts are put into designing a distributed controller architecture, where only the local and the relevant neighboring states are used to compute the control decisions. The proposed controller is validated experimentally. It exhibits high performance in a wide range of travel speeds. The practicality of the proposed solution should attract the attention of practicing engineers.

Analysis and design of equilibrium points for the Cell-Transmission Traffic Model

The problem of equilibrium points for the Cell Transmission Model is studied. The structure of equilibrium sets is analyzed in terms of model parameters and boundary conditions. The goal is to determine constant input flows, so that the resultant steady state of vehicle density is uniformly distributed along a freeway. The necessary and sufficient conditions for the existence of one-to-one relation between input flow and density are derived. The equilibrium sets are described by formulas that allow to design a desired balanced density. A numerical example for the case of a two-cell system is presented.

Optimal control of structures subjected to traveling load

The problem of the optimal semi-active control of a structure subjected to a moving load is studied. The control is realized by a change of damping of the structure’s supports. The objective is to provide a smooth passage for vehicles and extend the time needed for the safety service of the carrying structures. In contrast to the previous works of the author, in this paper, the model used takes into account time-varying passage speeds, which allows a broader application, in particular, to robotics. The study of the optimal control problem produces a practical condition that justifies whether, for a given set of parameters, the controlled system can outperform its passively damped equivalent. For the optimization, an efficient method of parametrized switching times is developed and tested via a numerical example. The designed optimal control is examined on a real test stand. The experiments are carried out for three different passage scenarios. In terms of the assumed metrics the proposed method outperforms the passive case by over 40%.

Vibration Control of Double-Beam System with Multiple Smart Damping Members

A control method to stabilize vibration of a double cantilever system with a set of smart damping blocks is designed and numerically evaluated. The externally controlled magnetorheological sheared elastomer damping block is considered, but other smart materials can be used as well. The robust bang-bang control law for stabilization the bilinear system is elaborated. The key feature of the closed loop controller is the efficiency for different types of initial excitement. By employing the finite element model, the performance of the controller is validated for strong wind blow load and concentrated impact excitement of the particular point of one of the beams. For each of the excitations, the closed loop control outperforms the optimal passive damping case by over 27% for the considered energy metric.

Influence of Various Control Strategies on Transient Torsional Vibrations of Rotor-Machines Driven by Asynchronous Motors

In the paper, a dynamic electromechanical interaction between the selected kind of rotating machines and their driving electric motors is investigated. These are the high-speed beater mills and crushers as well as blowers, pumps and compressors, all driven by the asynchronous motors through elastic couplings with linear and non-linear characteristics. In particular, there is considered an influence of negative electromagnetic damping generated by the motor on a possibility of excitation of resonant torsional vibrations. Moreover, for the asynchronous motor in transient and steady-state operating conditions, there are tested several control strategies which are based on the closed-loop vector and scalar principles. The theoretical calculations have been performed by means of the advanced structural mechanical models. Conclusions drawn from the computational results can be very useful during a design phase of these devices as well as helpful for their users during a regular maintenance.

Adaptive optimal control algorithm for vibrational systems under nonlinear friction

In this paper a novel control algorithm for vibration attenuation is presented. Proposed scheme is developed to control linear systems with presence of external disturbance. The goal of the control is to steer the system to prescribed reference trajectory by minimizing associated quadratic performance index. The synthesis of the control law consists of two steps. At the first step, past measures of disturbance are used to develop local linear approximation of dynamics of disturbance signal. Weights of the associated auto-regressive model are calculated by the least-square algorithm. At the second step, calculated model is used to obtain linear time-invariant approximation of the control system. The receding horizon control law is then calculated by using finite horizon Linear Quadratic Regulator. The algorithm is verified numerically for torsional vibrating system under nonlinear, time-varying friction. The results of simulation are compared to a standard Linear Quadratic Gaussian control.

Collaborative control for structures subjected to traveling loads

The paper presents a novel collaborative control method that adapts the structures subjected to traveling loads. The adaptation is realized by changes of the damping of the structures supports. The control objective is to provide smooth passage of vehicles and to extend the safe life-time of the carrying structures. The control method utilizes a distributed architecture where the local controllers communicate along the circular graph. The proposed controller is validated experimentally. It is simple for practical realization and exhibits the performance comparable to that provided by the optimal centralized strategies presented in [1] and [2].