Finite control set model-free predictive current control of permanent magnet synchronous motor

This thesis proposes finite control set model-free predictive current control (FCSMFPCC) algorithm of permanent magnet synchronous motor (PMSM). To address issue of degraded performance during motor operation due to parameter mismatch, a model-free predictive current control arithmetic is devised, which utilizes ultra-local model (ULM) of PMSM. This proposition takes sum of known and sealed disturbances of the system as an unknown quantity, and uses sliding mode observer (SMO) to take stock of sealed quantity. To address the issue of operation delay in predictive control, a two-step method is used to make up for the system. When using price function to choose the first-rank voltage vector, vector selection optimization link is added, which effectively simplifies the algorithm while optimizing the inverter switching action. The simulation outcomes highlight the advantages of the described control algorithm in terms of better dynamic response performance and stronger robustness.


Introduction
PMSM has been generally used in multitudinous occasions of production and life as a result of benefits of large power specific mass, high potency, broad speed area.To further fulfill the requirement of industrial development for the speed regulation performance of PMSMs, researchers have proposed many high-performance control approaches, such as predictive control, sliding mode control as well as neuronic network control [1].Model predictive control (MPC) can provide excellent dynamic performance and the structure is close to the controlled object, so it has widely attracted attention from scholars at home and abroad.
According to the different voltage vector control sets, MPC is able to be divided into continuing control set model predictive control (CCSMPC) and limited control set model predictive control (FCSMPC).The FCSMPC makes perfect use of incontinuous features of inverter switching device [2].Based on the predictive model of the control target, it directly traverses the voltage complexors matching to all possible on-off states of inverter, calculates matching predictive value, and identifies the first-rank voltage vector.The core concept of FCSMPC is to forecast future state of system as well as select most suitable regulating action to achieve the desired performance [3].In each control cycle, the controller needs to complete a state prediction calculation for the control target.The control strategy makes the cost function optimal and is chosen in a limited control set.Compared with the CCSMPC, the FCSMPC not only has the inherent advantages of the MPC strategy, but also is more concise and intuitive in principle, easy to implement in hardware and software, and does not need to use the modulation module, so it has better dynamic response performance.Therefore, the FCSMPC has become a study hotspot in the domain of motor control [4].
To maintain the advantages of FCSMPC and address the drawbacks of parameter sensitivity, domestic and foreign scholars have made many improvements based on parameter identification [5].This kind of method aims to achieve the effect of real-time correction of the controller model by online identification of changing parameters, such as stator resistance, stator inductance, etc.Nevertheless, due to the huge amounts of parameters of PMSM, identifying all parameters at the same time may lead to false convergence due to underrank, or require additional injection of excitation signals, resulting in reduced control performance.Therefore, individual main parameters are generally selected for identification [6].In addition, unmodeled nonlinear opportunities, for instance transverter dead time, magnetic coupling, etc., will firsthand impact on precision of recognition consequences.Moreover, the sophisticated parameter recognition algorithm will similarly enhance complexity of the forecasting control algorithm [7].With the deepening of the research on motor control theory, model-free control is implemented in speed control system of PMSM.The basic idea of model-free control is to establish ULM ground on import as well as export of system.Design of controller only needs to utilize input variables as well as output variables of controlled system.Due to introduction of ULM, the MPC does not need accurate mathematical model of controlled system.In addition, the ULM contains the unmodeled part of the system and the internal and external disturbance part.Therefore, model-free control has powerful robustness to inner and exterior disturbances, unmodeled dynamics, and measurement noise of the system.However, model-free control also has its limitations, which need to be continuously studied and improved.
The paper proposes an FCSMFPCC algorithm to address the control property deterioration issue on account of motor parameter incongruity.Model-free predictive control is realized by establishing ULM of motor.A vector selection optimization approach is devised to optimize the procedure of using price function to choose first-rank voltage vector.Rest of article is divided as follows.In second part, mathematical model of PMSM is established.In the third part, an FCSMFPCC algorithm is proposed.An SMO is constructed to observe the known and sealed total disturbances of the system in the ULM of the motor.In the fourth section, the devised algorithm is proven by simulation.In the fifth section, the work of the full text is summarized.

Mathematic model of PMSM
Mathematic model of PMSM in a dq − rotating coordinate system can be established as follows State equation of stator current of motor obtained from Equation ( 1) is 1 11

FCSMFPCC model of PMSM
The first-order ULM of unitary-input unitary-output system is depicted as where y and u represent output and input of system, separately;  represents the proportion factor determined by projector; F signifies sum of decided and sealed disturbances of system.On the basis of input and output of PMSM system, mathematic model of PMSM based on ULM can be overwritten as where response speed but can cause overshoot.Therefore, it is necessary to adjust the value of  to balance the response speed and overshoot.
In order to convert the continuous time model into a discontinuous time model, forward Euler discretization approach is applied to discretize Equation ( 4), and predicted current formula of the PMSM is obtained as There is a computational delay in the digital control system.To eliminate computational delay, a twostep method is put into use to make up for the system.The current time 2 k + is forecasted as Cost function is stipulated as To obtain the optimal switch state combination of inverter using enumeration method, 8 basic voltage vectors need to be predicted 8 times respectively.In practical applications, this method may cause unnecessary switching actions in the inverter, leading to an increase in the inverter switching frequency.It can also lead to an enhancement in dead time, which directly impacts the control capability of the system.To address this issue, this article optimizes vector selection.The principle of vector selection optimization is to allow at most one set of inverter switches to operate within the same cycle.The principle scheme of vector selection optimization is given in Figure 1.Predictive control based on vector selection optimization only needs to substitute 4 basic voltage vectors into the cost function for calculation when using the enumeration method for optimization.It reduces the computational time of the algorithm by nearly half.It effectively simplifies the algorithm while optimizing the switching action of the inverter.

Design of SMO
In the proposed FCSMFPCC, accurate estimation of d F and q F values is crucial.This paper designs an SMO to observe the values of d F and q F .The SMO can be constructed as where the superscript ^ indicates that the term is an estimated value; d y and q y are designed for sliding mode control laws.The sliding surface is designed as The control law is designed as where  is the sliding mode gain coefficient.Equation (11) can be obtained from Equation (4) and Equation (8) ( ) ( )

Simulation analysis
To validate the devised algorithm, the emulation model is set up in Matlab/Simulink for emulation validation.Figure 2 is the functional chart of the motor control system.The simulation uses a surfacemounted three-phase PMSM as the control object.The first-rank switching condition combination of the inverter at the next moment is directly predicted by the prediction algorithm.The inverter inverts the 311 V voltage on the DC side into a 220 V three-phase alternating current to drive the PMSM.The simulation time is deployed to 1 s.The fixed step size ode3 algorithm is put into use.The simulation step size is deployed to 2×10 -6 s.
Figure 3 shows the simulation consequences of conventional limited control set model predictive current control (FCSMPCC).Figure 4 shows the simulation consequences of the devised FCSMFPCC.In the simulation, motor initiates without load, and the load of 10 N•m is abruptly added at 0.5 s.It can be obtained from the simulation consequences that the devised FCSMFPCC has a quicker reaction velocity at start-up, and the velocity can be stabilized quickly.When load is abruptly applied, speed vibration of the devised FCSMFPCC is lesser, and the velocity bight can be restored to steadiness quicker.On the side, the deviation of d and q axis currents of devised FCSMFPCC is greater.Therefore, the devised FCSMFPCC has better actional response capability as well as stronger robustness.Figure 5 shows the simulation consequences of the conventional FCSMPCC when the parameters are unmatched.Figure 6 shows the simulation consequences of the devised FCSMFPCC when the parameters are unmatched.In the simulation of parameters incongruity, values of resistance and inductance are 2 s R and 2 s L , respectively.Contrasting emulation consequences of Figure 3 and Figure 5, we can obtain that parameter mismatch has a tremendous impact on the control effect of the traditional FCSMPCC.Contrasting emulation consequences of Figure 4 with Figure 6, we can obtain that when parameters mismatch occurs, velocity and d, q axis current curves of devised FCSMFPCC are nearly unchanged.Therefore, the proposed FCSMFPCC effectively overcomes the dependence on the accuracy of model parameters.

Conclusion
In this thesis, an FCSMFPCC arithmetic is devised.The problem that the control performance of the traditional FCSMPCC decreases when the parameters are mismatched is solved.The ULM of the motor is built, and the SMO is put to use to observe the total disturbance in the ULM, which effectively eliminates the effect of parameter incongruity on the system's current control.The vector selection optimization approach is put into use to improve the optimal voltage vector selection process, which effectively optimizes the algorithm and reduces the amount of calculation.The control performance of the devised arithmetic and the conventional FCSMPCC is compared by simulation.The simulation consequences display that the devised arithmetic has better actional response capability and stronger robustness, and overcomes the dependence on the accuracy of model parameters.

F
at time k , respectively; s T is the sampling time.

Figure 1 .
Figure 1.Schematic diagram of vector selection optimization.

Figure 2 .Figure 3 .Figure 4 .
Figure 2. The functional chart of the motor control system.

Figure 5 .Figure 6 .
Figure 5.The emulation consequences of conventional FCSMPCC when the parameters are unmatched.