Applications
- Power Electronics and Drives
- Power Systems
- Automotive Applications
- Active Damping
- Hydropower Applications
Power Electronics and Drives
Power electronics systems represent a well-established technology that has seen significant performance improvements over the last two decades. In general, they involve applications of transforming electrical power from one usually unregulated form, to another that is regulated to some reference (e.g. consider the problem of unregulated dc to regulated dc conversion). This transformation is achieved by the use of semiconductor devices that operate as power switches, turning on and off with a high switching frequency. From the control point of view, power electronic circuits and systems constitute excellent examples of hybrid systems, since the discrete switch positions are associated with different modes of continuous time dynamics. Moreover, both physical and safety constraints are present that make the underlying mathematical problems complex and difficult to solve.
Direct Torque Control (DTC) of Induction Machines
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| The equivalent representation of a three-phase three-level inverter driving an induction motor | The voltage vectors produced by a three-level inverter on the dq plane and the corresponding values of the integer variables (switch positions) |
In adjustable speed induction motor drives dc-ac inverters are used to drive induction motors as variable frequency three-phase voltage or current sources. The basic principle of DTC is to directly manipulate the stator flux vector such that the desired torque is produced. This is achieved by choosing an inverter switch combination that drives the stator flux vector by directly applying the appropriate voltages to the motor windings. The equivalent representation of a three-phase three-level inverter driving an induction motor is shown in the above figure. The switch positions of the three-level inverter are described using the integer variables ua, ub, uc in {-1, 0, 1}. Each variable corresponds to one phase of the inverter, and the values -1, 0, 1 correspond to the phase potentials -Vdc/2, 0, Vdc/2, respectively. There exist 3^3 = 27 different vectors of the form uabc = [ua ub uc]T, which are commonly referred to as voltage vectors. These can be mapped into the dq plane, as shown above. This provides a geometric interpretation of the voltages that can be produced by the inverter.
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| The basic scheme of classic DTC | The principle of DTC. A voltage vector is chosen that positions the stator flux vector in the target window, which is defined by the hysteresis bounds |
The choice of the appropriate voltage vector addresses a number of different control objectives. Primarily, the stator flux and the torque need to be kept within pre-specified bounds around their references. In high power applications, where three-level inverters with Gate Turn-Off (GTO) thyristors are used, the control objectives are extended to the inverter and also include the minimization of the average switching frequency and the balancing of the inverter's neutral point potential around zero. We aim at deriving Model Predictive Control (MPC) schemes that keep these three controlled variables (torque, stator flux, neutral point potential) within their given bounds, minimize the (average) switching frequency, and are conceptually and computationally simple yet yield a significant performance improvement with respect to the state of the art. More specifically, the term conceptually simple refers to controllers allowing for straightforward tuning of the controller parameters or even a lack of such parameters, and easy adaptation to different physical setups and drives, whereas computationally simple implies that the control scheme does not require overly excessive computational power to allow for an implementation on DTC hardware that is currently available or at least will be so within a few years.
We have proposed three such novel control approaches to tackle the DTC problem, which are inspired by the principles of MPC and tailored to the peculiarities of DTC. Focusing on the third scheme, which ABB has decided to implement and has protected with a European Patent application, the major benefits achieved is its superior performance in terms of switching frequency, which is reduced over the whole range of operating points by up to 50%, while the average reduction amounts to 25%. Furthermore, the controller needs no tuning parameters. As the computation of an explicit solution is avoided, all quantities may be time-varying including model parameters, set points and bounds. Those can be adapted on-line.
Paper 1, Paper 2, Paper 3Control of Fixed Frequency DC-DC Converters
In fixed-frequency switch-mode dc-dc converters, the switching stage comprises a primary semiconductor switch that is always controlled, and a secondary switch that is operated dually to the primary one. The switches are driven by a pulse sequence of constant frequency (period), the switching frequency fs switching period Ts). The dc component of the output voltage can be manipulated through the duty cycle d, defined by d=ton/Ts, where ton represents the interval within the switching period during which the primary switch is in conduction.
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| Topology of the step-down synchronous converter | Driving signal for a fixed-frequency dc-dc converter |
The control objective for dc-dc converters is to regulate the dc component of the output voltage to its reference. This objective has to be achieved subject to the constraints that are present, resulting from the converter topology. In particular, the manipulated variable (duty cycle) is bounded between zero and one, and in the discontinuous current mode a state (inductor current) is constrained to be non-negative. Additional constraints are imposed as safety measures, such as current limiting or soft-starting, where the latter constitutes a constraint on the maximal derivative of the current during start-up. Moreover, the regulation has to be maintained despite gross changes in the load and the input voltage. We aim at developing novel control schemes that account for the hybrid properties of these systems and address the aforementioned control objectives.
For this, we derive a hybrid model that is valid for the whole operating regime and captures the evolution of the state variables within the switching period. Based on the converter's hybrid model, we formulate and solve an MPC problem that allows for a systematic controller design that achieves the aforementioned control objectives. The developed scheme tackles the control problem in a complete manner and features very favorable performance properties. In particular, the control performance does not degrade for changing operating points. Regarding the implementability of the controller, we derived off-line the explicit PWA state-feedback control law , which can be easily stored in a look-up table and used for the practical implementation of the proposed control scheme. Moreover, an a posteriori analysis step shows that the considered state space is a control invariant set. Most importantly, a Piecewise Quadratic (PWQ) Lyapunov function can be computed that proves exponential stability of the closed-loop system for the whole range of operating points.
Main Paper (Chapter 8)
4-bus and 12-bus Power Systems
Modern power systems typically feature a large and diverse set of elements featuring both continuous and integer dynamics; additionally, in the face of internationally changing market conditions power grids are being evermore operated at their physical and technical limits. The resulting scenario requires an adequate control scheme to take into account the ensuing behavior of hybrid components such as on line tap changers, reactive power banks, automatic voltage regulators and thermostatic load recovery controllers interacting across the physical network governed by the classic Kirchhoff equations.
Following an outage of a transmission line in the network, voltages across the network will typically tend to progressively drop; below a certain threshold, there is a serious risk of the entire network breaking down, as numerous recent reports in the news concerning nation-wide blackouts bear witness to. Initially the synchronous machines will try to locally sustain the voltages in their vicinity but once their physical limit has been exceeded appropriate actions must be taken on the inputs to avert system collapse. Typical available controls include varying the ratio of the OLTCs, injecting reactive power into the network by means of capacitor banks and shedding load to relieve the network stress; all these inputs can be varied in discrete steps and are therefore an intrinsic part of the system's hybridism. The primary objective is to maintain all voltages above 0.9 per unit. The secondary objective is to minimize the amount of load shedding necessary to achieve this; additionally a third objective may also be to maintain voltages as close as possible to 1 per unit.
Hybrid Model Predictive Control (MPC) schemes have been successfully applied to 4 and 12-bus network models, developed and analyzed in conjunction with ABB Corporate Research within the framework of the Control and Computation (CC) Project.
Main paperCombined Cycle Power Plants
Modern, progressively more market-oriented electric power utilities push for optimally scheduling the future commitment and dispatch of energy production facilities to reap the maximum economical advantage. The scheduling optimization of a combined cycle power plant requires to take into account its intrinsically hybrid characteristics. Discrete features of a power plant are, for instance, the possibility of turning on/off the turbines, operating constraints like minimum up and down times and the different types of start up of the turbines; vice versa, features with continuous dynamics are power and steam output, the corresponding fuel consumption, etc. The union of these properties characterizes the hybrid behavior of a combined cycle power plant.
The economically optimal scheduling of a combined cycle power plant can be conveniently recast as a hybrid Model Predictive Control (MPC) scheme that allows to optimize the plant's scheduling by taking into account the time variability of both prices and electricity/steam demands. Economic optimization is achieved by designing the inputs of the plant that minimize a cost functional representing the operating costs
As shown in [Paper] hybrid systems in the MLD form provide a suitable framework for capturing the dynamics of combined cycle power plants and MPC allows to naturally implement a scheme for determining optimal schedules for combined cycle power plants. Other characteristics like ramp constraints on the power output, dynamics of the heat recovery steam generators and additional boilers, or nonlinear input/output relationships (approximated by piecewise affine (PWA) functions) can also be taken into account and conveniently incorporated in the MLD description in a more extensive and in-depth model formulation.
Main paperTraction Control
Traction control systems are amongst the best studied mechatronic systems in automotive applications. They are used to improve a driver's ability to control a vehicle under adverse external conditions such as wet or icy roads.
The traction controller aims at maximizing the traction force between the vehicle's tire and the road, thus preventing the wheel from slipping and at the same time improving vehicle stability and steerability.
The traction force function exhibits a strongly nonlinear and uncertain behavior; we therefore applied hybrid modeling techniques to the problem. A controller was devised to optimally control the slip. The explicit solution to the optimal control problem was computed and verified in simulation and real experiments. Compared to other methods (sliding mode, fuzzy), this method does not need ad-hoc tuning at all, its only tuning parameter is the prediction horizon.
Main paperAdaptive Cruise Control
Cruise control is a common and well known automotive driver assistance system. The driver sets a reference speed and the engine is controlled so that this reference speed is maintained regardless of external loads such as wind, road slope or changing vehicle parameters. Further development led to the so called Adaptive Cruise Control (ACC) that takes into account the traffic in front of the car by using a multitude of sensory information.
Good acceleration and deceleration control is essential for the ACC systems. It was our aim to develop a controller which can cope with complex traffic scenes, computing the optimal acceleration and deceleration commands. Safety constraints are also to be considered.
We developed a hybrid model of the car to accurately capture the inherent hybridness of the system. A quadratic cost function was used and the constrained finite horizon optimal control (CFTOC) problem was posed. The explicit controller was computed by applying dynamic programming techniques. Experimental results were presented for the car-following scenario.
Electronic throttle
The electronic throttle has gradually become an essential element of many engine control systems. Compared to its mechanical counterpart, the electronic throttle leads to significant improvements in vehicle emission, fuel economy and drivability, if it is well controlled. Unfortunately, it exhibits a strong nonlinear behavior due to its being built of cheap components inducing a high friction. Additional obstacles are the so-called Limp Home position nonlinearity and the fast sampling needed for good control.
In spite of these difficulties, a good tracking controller is vital for the system in terms of responsiveness to driver's inputs. The goal was thus to create a controller which handles the nonlinearities and can be implemented efficiently.
A hybrid PWA model was developed, incorporating the nonlinearities. The optimal state feedback control law was computed explicitly, allowing for a very fast controller implementation. The controller was verified in simulation and experiment, yielding very satisfying results. The strength of this approach lies in the nonlinearities being included in the model directly. No ad-hoc tuning is necessary, as opposed to other controllers used for this task.
Main paperSmart Damping Materials
Smart materials have long been heralded as the dawn of a new era in the construction of automotive vehicles, airplanes and other structures that have to meet ever more demanding performance requirements. This has largely not happened, at least not in the commercial arena. In this context dynamic behavior is one main design criterion for many kinds of load-carrying structures, as undesirable large-amplitude vibrations often impede the effective operation of various types of mechanical systems, including antennae, spacecrafts, rotorcrafts, automobiles, and sophisticated instruments. It is therefore desirable to introduce structural damping into a system to achieve a more satisfactory response and to delay fatigue damages.
The large instrumentation overhead of conventional vibration control can be significantly reduced by a new method that involves attaching an electrical shunt controller across the terminals of one piezoelectric transducer with the view to minimizing structural vibrations. This approach is referred to as piezoelectric shunt damping and is known as a simple, low-cost, lightweight and easy-to-implement method for vibration damping.
We are developing new adaptive resonant shunt circuits that can efficiently damp several structural modes and do not require power for operation.
Main paperAutonomous Switching Shunts
A completely autonomous shunt circuit was developed and implemented. It does not require any power for operation and its size is tiny. Experiments showed a vibration suppression of around 60%-70%.
The described shunt circuit is based on so called Switching Shunts. An optimal switching law was derived using the Hybrid System Framework. The obtained switching law was implemented with a few analog electronic components, such that the resulting circuit does not require power for operation. Additionally, the circuit can tune itself automatically [1].
Modeling and Optimal Control of a Hydropower Plants
We consider a hydro power plant that includes three types of water outflow units: Four gates, four flaps and two turbines. The total outflow of the dammed river is determined both by the water level in the reservoir and by the opening of the units. The manipulated variables are the openings of each outflow element and the measured variables are the total outflow and the power generated.
In this work the outflow units are modeled as hybrid systems in the Mixed Logic Dynamical (MLD) form. For systems in MLD form the control synthesis problem can be formulated and solved in a systematic way using a Model Predictive Control (MPC) scheme. However, no control objective and controller were derived for this system so far.
The MLD model was capable of accurately reproducing the water level control behavior of the power plant. The detailed models of each unit considered not only standard operating conditions, but also emergencies and startup and shut-down procedures.
Main paperWater Level Control for Cascaded River Power Plants
The discharge through a cascade of river power plants needs to be adjusted to control the water level at a pre-specified point. The common control method often yields large unnatural discharge variations resulting in unsatisfactory control performance. In cascades of river power plants, these discharge variations are unpredictably amplified affecting nature and imposing problems on navigation.
A supervisory controller for cascaded river power plants was conceived. The controller is based on Model Predictive Control (MPC). The required linear discrete time model of the power plant cascade is derived from the Saint Venant equations. The objective of the controller is to keep the pre-specified water levels within given bounds and to dampen the discharge variations. This is expressed in a quadratic cost function subject to constraints. A Kalman filter is used to estimate the current values of the state variables from available water level measurements.
The proposed scheme results in a coordinated control of the power plant cascade. It takes interactions between the power plants into account, issues preemptive control moves for anticipated disturbances, and includes explicit constraint handling and straightforward tuning. Compared with the currently employed PI-type controllers enhancements are achieved. In particular, the damping of disturbances is significantly improved while the water level constraints are met.
Main paper