Design of a Current Mode PI Controller for a Single-phase PWM Inverter

S. M. Cherati1, N. A. Azli2, S. M. Ayob and A. Mortezaei

Power Electronics and Drive Research Group (PEDG), Energy Research Alliance Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Malaysia

sam.mcherati@fkegraduate.utm.my1 naziha@ieee.org2

Abstract- This paper presents the design of current mode PI controller for single-phase PWM inverter. The controller is comprised of inductor current as the inner loop and output voltage as the outer feedback loop. The control design is carried out using Sisotool, which is provided in Matlab. By using this tool, users can examine the effects of changing the gain control values to system’s transient response and stability, simultaneously. Hence, simplify and speed up the control design process. To evaluate the performance of the designed controller, the inverter is simulated under several types of load disturbances. From the result, it is shown that the designed controller exhibits a good transient response i.e. fast rising and settling time with small overshoot when subjected to step load disturbance.

I. INTRODUCTION Power inverter is an important part of many DC to AC conversion equipments such as uninterruptible power supply (UPS), induction motor drive and automatic voltage regulator (AVR) systems. In these systems, it is the major requirement for the power inverter to be capable of producing and maintaining a stable and clean sinusoidal output voltage waveform regardless of the type of load connected to it. The main key to successfully maintain this ability is to have a feedback controller [1]. Currently, there are various control methods that have been proposed for inverter. Among the prevalent methods are the Voltage Mode Control (VMC) and Current Mode Control (CMC). In VMC method, the control parameters design is easy. The implementation can be considered as inexpensive since it requires only one voltage sensor. However the main drawback of VMC is that the system is prone to instability and very sensitive to large input variations. Moreover, VCM also does not control the current. Thus, power electronic switches are vulnerable to over-current damage or overloads. To achieve better performance, robustness and also immune to input disturbance and current protection, current mode (CMC) is more preferable. Unlike VMC, CMC has an additional inner loop. Usually, the inductor current is used as the inner loop. The inductor current is sensed and used to control the duty cycle.

In this paper, accurate design of PI parameter is discussed for voltage and current loop and their proper bandwidth and phase margin are calculated. Both the transfer function and the state-space models of the inverter are provided.

II. DYNAMIC MODEL OF SINGLE-PHASE INVERTER

Fig. 1, shows the equivalent circuit of a single-phase full bridge inverter with connected load. In this study, control based on the linear strategy theory is presented. Solid-state switches and connected rectifier are nonlinearity source of a system, so for proper control design, the system must be linearized around its operating point. If the designed controller is robust enough, the system can work around its operating point with high performance which means a wide range of bandwidth is required [2]. In this work, a nominal resistive load of 10 Ω is set as the operating point for linearization.

Fig. 1. Full bridge single-phase inverter

A. State-Space Model

The resistive load and its related filter operate as a continuous time second-order system. The state variables of the system are capacitor voltage ( ) and inductor current ( ). The dynamic model of Fig. 1, can be represented by the following equations.

′

′ ⁄ ⁄ 0 (1)

(2) One of the important factors of load effect on the inverter is output impedance which in this case as rectifier is a load with nonlinear nature; the output voltage will be highly distorted. For determining the output impedance, circuit laws can be applied as shown in Fig. 2.

2011 IEEE Applied Power Electronics Colloquium (IAPEC)

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Fig. 2. Equivalent circuit of a single-phase inverter

(3)

and are ignored in many modeling since they are generally very small but in this paper only is disregarded ( =0 ). By using ω and determining as output impedance in ,

ωω ω

(4) It can be clearly seen in (4) that, by increasing the switching frequency, the output impedance will be reduced. This means that lower component values of the LC filter are required [3]. By ignoring the internal resistance of the filter capacitor ( = 0), (1) and (2) can be simplified as (5) and (6).

′

′ 0 (5)

0 1 (6)

B. Analysis of multiple feedback loop control

A DC motor has some similarity to an inverter in terms of using cascade control (multi-loop control) [4]. In a DC motor system, the armature current and stator voltage are used as current and voltage feedback loop for achieving sufficient steady-state and good transient performance. A single-phase inverter has the same scenario. The inductor current of the filter acts as an inner loop parameter while the output voltage is the outer loop parameter. Fig. 3 illustrates the voltage and current loop [5].

(a)

(b)

(c) Fig. 3. Control schemes for a single-phase inverter. (a) Voltage feedback loop control. (b) Current feedback loop control. (c) Outer voltage and inner current feedback loop control Kv and KI of Fig. 3, represent voltage and current sensors gain respectively. Fig. 3(c), shows the overall current mode control structure. The variable KPWM is the PWM gain, which

is defined as . The controller for the loops can be either

PI, Sliding mode, Fuzzy, Deatbeat etc. [6]-[9]. For this work, a conventional PI controller is used.

III. CONTROL SYSTEM DESIGN The design of PI controller can be done using several methods. It can be designed using Ziegler-Nicholas, Pole-placement method and Frequency response [10]. However, the latter method will be used to design the controller. For simplicity, Sisotool from MATLAB/SIMULINK is used to tune the controller and evaluate the suitability of bandwidth and stability. As mentioned earlier, the control system is designed for a linear load (R = 10 Ω) and tested on a nonlinear load such as a rectifier. The simulation testing parameters are as given in Table 1.

TABLE 1. SIMULATION TESTING PARAMETERS

215 V

200 Vp-p

0.3 Ω

1.2 mH

13.2 µF

10 Ω

40 kHz

0.06

0.01 R = 100 Ω

C = 500 µF

1 V

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Fig. 4. The single-phase circuit with its control system

Fig. 5. The single-phase inverter simulation model PI controllers are used as the voltage and current controllers. The PI controller transfer function is represented as: ⁄ (7)

For obtaining accurate value of and , the Sisotool in MATLAB/SIMULINK can be used. Since the voltage loop and current loop are decoupling, each PI controller can be designed separately. In this work, the inner loop will be firstly designed. The control bandwidth for the inner loop should be larger than the outer loop, since the inductor current has faster response compared to the output voltage. Since the switching frequency is 40 kHz, the control bandwidth for the current loop should be within 4 kHz. The bandwith for the voltage loop is set to be within 400 Hz. Both loops should be designed with phase margins of within 65o.

The PI controller for the current loop can be designed by using the transfer function between the inductor current and the current reference. Based on Fig. 3(b), the transfer function

of can be obtained as follows:

(8)

(9)

The complete transfer function by incorporating the PI controller can be expressed as in (10). ⁄

(10) From (10), it can be shown that the controller adds a zero at the left side of s-plan and zero at the origin to compensate the second-order transfer function. Fig. 6 shows the resulting bode-plot of the closed-loop current mode.

Fig.6. Bode plot of current loop system

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From Fig. 6, the bandwidth of the current loop is 3.6210 while the phase margin is 65 , which are acceptable values. To design the outer loop controller, it is assumed that the inner loop is unity as illustrated in Fig. 7. Equation (11) expresses the complete transfer function of Fig. 7 with PI controller. ⁄ (11) It should be noted that the outer loop should have a bandwith of 400 Hz. Fig. 8 shows the resulting bode plot and root locus of the voltage loop.

Fig. 7. Voltage loop block diagram with the designed current loop.

Fig.8. Bode plot and root locus of the voltage loop

It can be clearly seen that, the bandwidth is lower than the inner loop (942 Hz) while its phase margin is 63o.

IV. SIMULATION RESULTS The control system has been designed for a linear load (R = 10 Ω). The following figures (Fig. 9 and Fig. 10) illustrate the voltage and current waveforms of the load when the system becomes no-load at t = 0.004.

Fig. 9. Output voltage

Fig. 10. Load current

V. CONCLUSION

In this paper a current mode PI controller for a single-phase PWM inverter has been designed. The control structure is comprised of two loops and has been arranged in a cascaded fashion. Two systems variables namely the inductor current and the output voltage are sensed as the feedback variables. The Sisotool from MATLAB/SIMULINK has been used to tune and design the PI control parameters for both loops. The performance is verified by subjecting the inverter system with different types of load. The simulation results have shown that the controller is capable of producing good output voltage regulation.

0 0.005 0.01 0.015 0.02

-100

-50

0

50

100

Time Second

Vo

ltag

e (V

olt

)

Output Voltage

0 0.005 0.01 0.015 0.02-15

-10

-5

0

5

10

15

Time (second)

Cu

rren

t (A

mp

)

Load Current

183

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