This reserch focuses on *advanced torque control* of permanent magnet synchronous motor drives. A novel modular structure is introduced to simplify the design and implementation of **Model Predictive Control (MPC)**. The layout consists of the control and the control framework.

The dynamic control is the novel *virtual flux controller*, which is used to reach desired reference values, and the *state observer*, which is used to reduce effects of non-modeled system properties. The control framework consists of static mappings to simplify the control problem. Besides the αβ and dq transformations, a reference generation procedure is used to generate state references based on optimality criteria. Also, the actuation scheme is part of the control framework and defines the available input set and the resulting control properties.

The first method actuates directly switch states, i.e. voltage vectors, which yield an integer set named **Finite Control Set (FCS)**. The other method actuates duty cycles via modulation, which yield the **Convex Control Set (CCS)**.

A *stability analysis* is carried out for both, CCS-MPC and FCS-MPC. MPC is called stable, if it is feasible and convergent, which can be ensured using the main MPC stability theorem. However, stringent computation requirements make it difficult to apply the theorem in practice. Thus, the Lyapunov based MPC approach is applied to the motor drive, which provides stability guarantees independent of the prediction horizon. A stability constraint based on control Lyapunov functions (CLF) ensures convergence to the origin and the resulting optimal control problem is shown to be feasible for all time. In other words, a control input can be found at each sampling instant, which satisfies all constraints and yields a stable closed-loop system. The properties of CCS-MPC are derived using a nonlinear controller and the constrained closed-loop system is shown to be stable in the sense of Lyapunov. The stability properties of FCS-MPC are more complex due to the integer input set. Using set-theoretical methods, it is shown that a sufficiently large control error can be steered towards the origin. In other words, the proposed FCS-MPC is shown to be set stable, i.e. the control error is guaranteed to converge to a well-defined neighborhood of the origin.

MPC requires that a **Constrained Finite Time Optimal Control (CFTOC)** problem is solved at each sampling time. Small sampling periods and limited computation capabilities of embedded hardware require the CFTOC to be sufficiently simple, which is achieved using the virtual flux model in the static reference frame. The problem size is contained using a sufficiently small prediction horizon and efficient algorithms are necessary to provide a result within a sampling period. The CFTOC of the proposed CCS-MPC is a (convex) linear or quadratic programming problem, which can be solved using existing efficient algorithms. To provide a minimal approach, an efficient algorithm is introduced to solve the one-step-ahead prediction CFTOC analytically.

FCS-MPC results in a mixed integer programming problem and is therefore more difficult to solve with standard numerical methods. In practice, the CFTOC is solved by enumeration, which is combined with branch-and-bound, i.e. branch-and-cut,

techniques to improve the computational efficiency.

The control algorithms have been developed on a Software-in-the-Loop (SiL) platform based on Matlab/Simulink and the code is implemented without modification on an experimental test-bench. The evaluation confirms the design and implementation of CCS-MPC and FCS-MPC and shows good results in dynamic and steady-state operation. The two MPC approaches have complimentary properties, which can be used to target different applications. CCS-MPC achieves a constant switching frequency and is a promising alternative to proportional-integral (PI) vector control.

The concept can be combined with different modulation schemes, e.g. the Symmetric Space Vector Modulation (SSVM) and the Discontinuous Space Vector Modulation (DSVM) are used in this text. FCS-MPC takes the inverter switching into account

and achieves an approximately constant switching ripple but a variable switching frequency. The concept is most profitably applied to systems where a high sampling frequency compared to the switching frequency is desired, e.g. high power or servo drives. Moreover, FCS-MPC lacks Pulse Width Modulation (PWM) harmonics in its current spectrum. Consequently, it is advantageous in terms of acoustic noise since emphasized tones are missing. However, the distinguished PWM harmonics of

CCS-MPC are simpler to filter.

In summary, it can be said that the work on advanced torque control of permanent magnet synchronous motor drives has produced an innovative strategy. The introduction of a new structure has significantly simplified the model predictive control problem, the concept of stability in particular. Moreover, this structure results in the implementation of simple algorithms, which can be computed efficiently.

M. Preindl, S. Bolognani. «Model Predictive Direct Torque Control with Finite Control Set for PMSM Drive Systems, Part 2: Field Weakening Operation». IEEE Transactions on Industrial Informatics 9 (2013), 648–657. doi: 10.1109/TII.2012.2220353

M. Preindl S. Bolognani. «Model Predictive Direct Torque Control with Finite Control Set for PMSM Drive Systems, Part 1: Maximum Torque per Ampere Operation». IEEE Transactions on Industrial Informatics 9 (2013), 1912–1921. doi: 10.1109/TII.2012.2227265

M. Preindl S. Bolognani. «Model Predictive Direct Speed Control with Finite Control Set of PMSM Drive Systems». IEEE Transactions on Power Electronics 28 (2013), 1007–1015. doi: 10.1109/TPEL.2012.2204277

EDLab-PD triggered the new Serie of IEEE Workshops PRECEDE:

1st IEEE PRECEDE 2011 - Workshop on Predictive Control of Electrical Drives and Power Electronics - Oct 14-15, 2011, Munich (Germany)

2nd IEEE PRECEDE 2013 - Workshop on Predictive Control of Electrical Drives and Power Electronics - Oct 17-19, 2013, Munich (Germany)