Thomas Besselmann

A hybrid approach to modelling, control and state estimation of mechanical systems with backlash

Control of mechanical systems with backlash is a topic well studied by many control practitioners. This interest has been motivated by the fact that backlash in mechanical systems can cause severe performance degradation and lead to instability of the control system. Furthermore, high impact-forces in backlash-systems can lead to a lower durability of the components and to strokes and peaks in the output. In this paper a mechanical benchmark system is presented to provide facilities for testing the identification and control of systems with backlash. For controller design a hybrid model of the system was derived and used in a model predictive control (MPC) scheme. Observer-based state-estimation was used to recover unmeasured states, particularly the backlash angle. Explicit solutions of a tracking controller were computed to control the mechanical benchmark system in real-time. Simulation as well as experimental results are presented to show the applicability of this hybrid control approach.

Explicit MPC for LPV Systems: Stability and Optimality

This paper considers high-speed control of constrained linear parameter-varying systems using model predictive control. Existing model predictive control schemes for control of constrained linear parameter-varying systems typically require the solution of a semi-definite program at each sampling instance. Recently, variants of explicit model predictive control were proposed for linear parameter-varying systems with polytopic representation, decreasing the online computational effort by orders of magnitude. Depending on the mathematical structure of the underlying system, the constrained finite-time optimal control problem can be solved optimally, or close-to-optimal solutions can be computed. Constraint satisfaction, recursive feasibility and asymptotic stability can be guaranteed a priori by an appropriate selection of the terminal state constraints and terminal cost. The paper at hand gathers previous developments and provides new material such as a proof for the optimality of the solution, or, in the case of close-to-optimal solutions, a procedure to determine a bound on the suboptimality of the solution.

Power Electronic Traction Transformer: Efficiency Improvements Under Light-Load Conditions

Power electronic transformer (PET), a converter technology that utilizes power semiconductors in combination with medium-frequency transformers, is considered a promising solution for certain applications requiring flexible galvanic isolation. Among are those where space occupied by bulky low-frequency transformers is of concern and/or where advanced power quality control features are needed. In this paper, the PET for a single-phase traction on-board application is discussed with emphasis on the efficiency improvements and reductions of energy consumption during the operation on the vehicle. Several control algorithms devised to improve efficiency under light-load conditions are tested on a low-voltage prototype of the PET, and experimental results are presented demonstrating the effectiveness of the proposed algorithms.

Model Predictive Anti-Surge Control of Centrifugal Compressors with Variable-Speed Drives

In this article torque assisted anti-surge control (TASC), a compressor anti-surge control system based on model predictive control (MPC) is presented. TASC is implemented on an embedded system for the control of compressor stations with electrical variable-speed drives (VSD) which are used in applications such as natural gas transportation via pipelines. The manipulated variables of the proposed advanced controller are the electric motor torque and the position of a recycle valve, whereas the measured quantities are the same as those of a typical compressor control application including the pressure ratio and the gas flow. The TASC scheme uses the linear approximation of a nonlinear dynamic model to predict the behavior of the compression system. The information contained in the compressor map is incorporated into the nonlinear model as a 3rd order polynomial approximation. The surge line is taken into account as a constraint in the MPC formulation. Control action is calculated by solving an optimization problem in real-time at the control unit level with cycle times as low as 20 ms. The potential benefits of the proposed control strategy are evaluated in a simulation scenario corresponding to a potential deep surge event typically used in anti-surge control validation exercises. The simulations are carried out in a hardware-in-the-loop setting. In the evaluation, the performance of TASC is compared to a conventional anti-surge control approach. Due to the predictive capability and the manipulation of the motor torque, TASC is observed to achieve a safer and more efficient operation of the compressor station.

A parametric branch and bound approach to suboptimal explicit hybrid MPC

In this article we present a parametric branch and bound algorithm for computation of optimal and suboptimal solutions to parametric mixed-integer quadratic programs and parametric mixed-integer linear programs. The algorithm returns an optimal or suboptimal parametric solution with the level of suboptimality requested by the user. An interesting application of the proposed parametric branch and bound procedure is suboptimal explicit MPC for hybrid systems, where the introduced user-defined suboptimality tolerance reduces the storage requirements and the online computational effort, or even enables the computation of a suboptimal MPC controller in cases where the computation of the optimal MPC controller would be intractable. Moreover, stability of the system in closed loop with the suboptimal controller can be guaranteed a priori.

Explicit model predictive control for linear parameter-varying systems

In this paper we demonstrate how one can reformulate the MPC problem for LPV systems to a series of mpLPs by a closed-loop minimax MPC algorithm based on dynamic programming. A relaxation technique is employed to reformulate constraints which are polynomial in the scheduling parameters to parameter-independent constraints. The algorithm allows the computation of explicit control laws for linear parameter-varying systems and enables the controller to exploit information about the scheduling parameter. This improves the control performance compared to a standard robust approach where no uncertainty knowledge is used, while keeping the benefits of fast online computations. The off-line computational burden is similar to what is required for computing explicit control laws for uncertain or nominal LTI systems. The proposed control strategy is applied to an example to compare the complexity of the resulting explicit control law to the robust controller.

Hybrid Parameter-varying Model Predictive Control for Autonomous Vehicle Steering

In this paper the concept of Hybrid Parameter-Varying Model Predictive Control (HPV-MPC) is applied for autonomous vehicle steering. Parameter-varying in the MPC context means that a prediction model with non-constant, parameter-varying system matrices is employed. In the investigated scenarios, the displacement of a car on an icy road due to a side wind gust shall be mitigated, and a double lane-change maneuver shall be performed autonomously. In order to explore a possible reduction of online computations and the inherent degradation of control performance, the nonlinear model of the lateral dynamics is approximated in various ways. A comparison between controllers using prediction models varying from the full nonlinear model, as an indication for the maximal achievable performance, to a linear model was performed. Particular emphasis was put on the hybrid parameter-varying prediction model, to investigate their potential in terms of computational effort and control performance.

Model Predictive Control in the Multi-Megawatt Range

This paper presents an application of model predictive control to a variable-speed drive system operating in the multi-megawatt range. The variable-speed drive system comprises a synchronous machine fed by a line-commutated rectifier and a load-commutated inverter. The control task is to regulate the dc-link current, and hence the machine torque, to ensure the machine speed follows a given reference. The proposed control approach is model predictive control, where both the rectifier- and inverter-firing angles are considered as control inputs. The nonlinear model predictive torque controller has been implemented on an embedded system and applied in an industrial-scale pilot plant installation. The experiments show the successful operation of model predictive control on a plant with more than 48 MW power.

Model Predictive Control of Load-Commutated Inverter-Fed Synchronous Machines

This paper considers torque regulation of a variable-speed synchronous machine fed by a line-commutated rectifier and a load-commutated inverter. The proposed control approach is model-predictive control where both the rectifier and inverter firing angles are considered as control inputs. Conventional controllers assign different tasks to the rectifier and inverter firing angle. In contrast, the model-predictive controller coordinates the firing angles and this improves the dynamic performance and disturbance rejection. In particular, the proposed controller handles line side under voltage conditions better than a conventional PI controller. The nonlinear model-predictive torque controller has been implemented on an embedded system and applied in an experimental test bed. The experiments confirm that the controller is able to successfully ride through line side under voltage conditions.

Max–Min Optimal Control of Constrained Discrete-time Systems

Abstract This paper considers the optimal control problem for constrained discrete–time systems affected by measured and bounded disturbances and uncertainties in the underlying system equations. This problem setting leads to the sup–inf robust optimal control problems. Three classes of discrete–time systems permitting the characterization of the sup–inf value functions and robust optimal control policies are examined. The corresponding max–min optimal control problems are solved by using the dynamic programming.