Improved study on double closed-loop control of three-phase PWM rectifier based on induction heating rectifier side

With the development of power electronics technology, induction heating power supply becomes more applicable. The three-phase PWM rectifier is widely used in induction heating system because of its advantages of better power factor and bi-directional energy transfer, and often adopts the control method of voltage outer loop and current inner loop to improve its control performance. However, the traditional rectifier control structure in the application process will appear such as poor anti-interference ability, low fault tolerance and other outstanding problems. In this paper, an improved H∞ controller is designed for the induction heating system based on the rectifier-side power regulation by combining the robust control principle, establishing a state space model of the system with an equivalent series resonant load, firstly decoupling the linearization of the model, and then designing a double-closed-loop PI controller as well as an improved current inner-loop H∞ controller based on the decoupled model. In order to facilitate the analysis, the PI controller and the H∞ controller are simulated under two kinds of starting conditions, and the comparison further confirms that the improved system has better anti-interference ability and dynamic characteristics.


Introduction
With the concept of "carbon neutral" put forward in recent years, how to efficiently use energy and reduce carbon dioxide emissions has become the mainstream development direction of the energy industry.Induction heating utilizes the principle of electromagnetic induction to heat the device [1] , which is characterized by low loss and zero carbon emission, and is in line with the current energy development trend.
Literature [2] proposes a control strategy for PWM rectifier using double closed-loop PI control.However, since the PWM rectifier is a nonlinear system, when the system parameters change or perturbation occurs, the traditional control method is difficult to obtain good robustness of the PWM rectifier due to the fixed transfer function parameter settings.Literature [3,4] proposes an improved PR control, which is a strategy to improve the stability of the system by appropriately reducing the gain at the resonant frequency.However, the accuracy of this method in regulation is not easy to determine.Literature [5] proposes a fixed-frequency direct power control using a predictive controller, which makes the system robust to changes in capacitance parameters by incorporating a predictive controller, but is prone to reduce the stability of the PWM rectifier.Literature [6,7] used hysteresis loop current control by introducing a hysteresis loop comparator into the PWM rectifier, this control strategy can quickly track the supply side voltage, but its own properties will cause the converter device switching frequency is not fixed.Literature [8] applies the Lyapunov stability theory to the PWM rectifier control strategy by setting a Lyapunov function, which ensures that the rectifier system can still operate stably when it is subjected to large disturbances.
In order to overcome the traditional rectifier control structure in the application process, such as poor anti-interference ability, low fault tolerance [6] and other prominent problems, this paper combines the robust control principle, designed to meet the stability as well as specific tracking performance of the requirements of the H ∞ controller, and through the simulation waveforms to confirm the superiority of the rectifier side of the H ∞ power controller of the power regulation model.

Mathematical model of three-phase PWM rectifier
In order to analyze and design the power control module based on the rectifier side of the induction heating system, it is necessary to simplify the other parts of the induction heating system accordingly, and by considering the parameters of each part of the circuit, a simplified model of the system with an equivalent load is proposed.The load is assumed to be a pure impedance resistor during circuit modeling [7] .The main circuit topology of a three-phase voltage-based PWM rectifier is given in Figure 1 below.Based on Kirchhoff's voltage law, the equation of state of the three-phase voltage-based PWM rectifier in stationary coordinates can be obtained [9], and then the original three-phase stationary coordinate system equations are transformed in two phases by coordinate transformation to derive the equations in the two-phase stationary coordinate system, which are then transformed to the two-phase rotating coordinate system dq.
( ) The above equation type contains the product term of two variables, which belongs to the nonlinear model, which affects the control convenience of this heating system, which needs to be linearized in order to facilitate the control.Assuming that the switch does not produce energy consumption, the AC and DC side of the system has the same active power, respectively, with,   ,   to indicate that there: =   (2) Equivalent coordinate transformation can be used to obtain the transformed formula, the AC side of the output voltage of the dq-axis component of the substitution, due to the Udc in the system will not change the direction, so the   2 can be used as a state variable to replace the original system of the Udc and thus get the improved mathematical model for: The coil current flowing into the workpiece through electromagnetic induction in an induction heating system depends on the DC voltage at the input of the inverter [10] .

H∞ control and its basic models
The design of the controller in question is extremely critical in IH control systems.Fuzzy controllers and model predictive controllers, although an improvement over PI controllers, are difficult to apply in real systems due to the large number of calculus links implicit in these advanced control algorithms.Robust controllers have been considered to solve the above problems due to their relatively simple structure and their applicability to both nominal systems and systems with uncertainties.From the above, it can be seen that the robust controller ensures both the stability of the system and the fulfillment of the required performance in the presence of disturbances and noise, and the stability of the system and the maintenance of the required performance over the considered uncertainty range.The state variables [11]   = [ 1  2  3  4 ]  are selected according to the rectifier mathematical model equation (3), where each variable takes the value of respectively: The corresponding equation of state parameters are: Let the state feedback be [12] u=K(s)x and define the output signal to be , , then there is This is later solved by bringing into the Riccati equations [13] with the optimal control rate: 1.08 10 1.08 10

Simulation verification and analysis
According to the analysis above, this paper uses various mathematical simulation modules in the Simulink toolbox in Matlab to complete the construction of each control module of the system.The main circuit structure of the equivalent induction heating system simulation is shown in Figure 2. The simulation model of the H∞ double-closed-loop controller improved in this paper, as well as the logic block diagrams are shown in Figures 3 and 4. Figure 5 shows the output DC voltage response of an equivalent induction heating system under rated load conditions with conventional PI control and modified H∞ current inner loop control, respectively.From the figure 6, it can be seen that the improved H∞ current inner-loop control system still has better dynamic performance than the PI system in the presence of a sudden inductance change.From the figure 7, When starting the circuit to the steady state process, a voltage signal with an amplitude of 200 is suddenly added to the given signal to perturb the signal, it can be seen that the H∞ controller is more fault tolerant and has less impact on the system during the whole process.Figure 8, it is clear that the improved H∞ controller is able to recover the stability better and faster when the parameters of the circuit itself are regulated, compared to the PI controller which not only recovers slowly but also oscillates.

Conclusions
In this paper, the current inner-loop part of the original PI controller is improved by using the H∞ robust control principle.Finally, the improved system is simulated, and the comparison shows that the improved H∞ current inner-loop controller can have a better output response than the original controller under the normal rated operating condition and the change of the internal circuit parameters of the system, which confirms the superiority of the improved H∞ controller in the induction heating system.Although the research results in this paper have preliminarily verified the feasibility of the proposed scheme, due to the limitation of time and conditions, we have only simulated and analyzed the rectifier side control part of the induction heating system.Therefore, the next research can fabricate the physical object to verify the rationality of the design in this paper.

Figure. 2
Figure. 2 Simulation of the main circuit of the equivalent system.

Figure 3 Figure 4
Figure 3 Improved H∞ controller simulation module.start

Figure 5
Figure 5 Start-up response in two control modes.

Figure 6
Figure 6 DC voltage response of two control modes during sudden inductance change.

Figure 7
Figure 7Response in two control modes with sudden addition of perturbation.
Steady state response in two control modes with sudden inductance change.