Application of direct MRAC in PI controller for DC-DC boost converter

Received Jul 27, 2019 Revised Oct 22, 2019 Accepted Jan 9, 2020 Almost all electronic components require a DC power supply at present days. The needs of DC power supplies from low voltage scales, medium voltages such as generators, to high voltage scales for high voltage electricity transmission. The improvement of PI controller performances is presented in this paper. The adaptation gains improve transient response of DC-DC Boost Converter several operating conditions. Massachusetts Institute of Technology (MIT) rule is applied as an adaptive mechanism to determine the optimal control parameters in some conditions. The used adaptive control technique is Direct Model Reference Adaptive Control (MRAC), this method as able to control system in some various input voltage. The proposed method has a stable response and able to reach the model reference smoothly. However, the response of the system has instantaneously overshoot and follows the response back of model reference. The responses of proposed controller have short period of rise time, settling time, and overshoot.


INTRODUCTION
Nowadays, the high efficiency is suitable to build the electronic devices and power converter has an important role in this system. The stepped up or down DC voltage is the purpose of power converter, even though using a transformer are commonly used in AC voltage. A conventional power converter still an option in industry such as industry of battery charger, uninterrupted power supplies, and other energy conversion systems [1][2][3][4][5][6][7].
It is required electronic components to reach the desired voltage. Recent power converter components have high quality and high efficiency. One of them is DC-DC boost converter which have utilization to step the output voltage up [8,9]. In order to create the DC-DC boost converter rapid changes of rensponse, it must work in high frequency [10,11]. In this condition, DC-DC boost converter requires controller to manage the desired value.
Adaptive controls are widely used by researchers to solve dynamic problems [12][13][14][15][16][17][18] and some of them use PID as its control structure. Conventional PID is based on a mathematical model, such that it has stability, reliability and control capabilities. Conventional PID controllers are effective in linear systems, but it is not suitable for non-linear systems and high-order systems. Determination of PID parameters has been used in many ways [19]. Several methods have their own advantages and drawbacks to determine PID parameters for reaching stable system. The fixed parameter in PID controller is not quite robust or not able to adapt and therefore the adaptive controller techniques is required improve system response [20,21]. Several  [22,23]. DMRAC performances are provided by model as reference, it means the plant response must follow model response. The following parameter adjustment mechanism is calculated by using Massachusetts Institute of Technology (MIT) rule [24,25]. In order to find out the response of boost converter as a non-linear system, the paper offers DMRAC in PI controller as an alternative controller to compensate for input voltage variations.

PROPOSED METHOD
This section describes a DC-DC boost converter model and derivation of adaptation gain using DMRAC.

DC-DC Boost Converter Model
DC-DC boost converter is commonly used in DC system and also known as step up DC converter. It has simple configuration and one of non-isolated power converter as shown in Figure 1. The output voltage demand must be greater than the input voltage and continuous. It utilizes two semiconductors such as a controlled power device, and an uncontrolled device. They consist basically of an inductor in series and capacitor in parallel.
During the switch is OFF, the inductor releases the charge to the capacitor and load. The condition According to the ON and OFF state, the average value of model for boost converter is shown in state space as (5).
In order to define the small signal model of boost converter, substituting every variable is required. Each parameter is presented in steady state part and small signal variation as follows, The steady state variables become zero by deriving these terms and the multiplication results of small signal variation are neglected. The small signal model for inductor current and capacitor voltage of boost converter as given by (8).
The derived transfer function (9) from the output voltage to the duty cycle shows the effect of the duty cycle modify the capacitor voltage when the duty cycle performs.

Direct Model Reference Adaptive Control with PI Controller
Adaptive control system is a control system that has adjusted control parameters according to some disturbances. In DMRAC, the desired system performance is stated in a reference model. Figure 2 shows the block diagram of the DMRAC. The control parameters are changed based on error feedback, which is the difference between the output system and the output of reference model. The structure of DMRAC is divided in two loops, the inner loop and outer loop. The PI controller is employed in this research because the structure of PI controller is simple to execute in implementation. PI controller is one of single input single output (SISO) method, this controller has no ability to follow the diversity of environment. The boost converter is 2nd order system, such that the described system by 2nd order model as: The reference model in 2nd order system given by: The term of PI controller as: Transfer function of boost converter and PI controller is The difference between the output system and reference model:  Where  indicates the error between plant output and model reference output. The  has no fix value and it is set in such a way such that J is minimized to zero. In MIT rule, Negative gradient of J is needed to determine time rate of change of  as shown in (17).
Parameters p K and i K are determined by applying MIT gradient rules (19).

RESEARCH METHOD
The research is based on the output voltage generated by the boost converter which has not been properly regulated. This problem occurs when there are changes in input voltage, reference voltage, and the load. This research that will be carried out in a boost converter using a PID controller and a boost converter simulation using DMRAC. The conventional controller PID is utilized to compare the proposed controller that verified by varying input voltage. Table 1 presents the parameters of boost converter. By using these pasameters, the model of DC-DC boost converter (5) is utilized as a plant of the system. The derivation DMRAC based on PI controller obtain (22) and (23), these equations are the adaptive controller model. The value of gammas is specified to achieve the appropriate response. Some scenarios for changing the input voltage and load are set to find out the response of the proposed controller.

RESULTS AND ANALYSIS
The performance of boost converter in proposed controller is proven in simulation such that any changed responses are able to be observed. The input voltage and resistor load of boost converter are 12 V and 100 Ω, respectively. Reference voltage is set to be 48 V and the value of gammas as following,   In second scenario, the load is changed to 300 Ω at 0.3 s, a small oscillation occurs and finally follows the reference model. The transient response of the proposed controller shows it has fast response to achieve the voltage reference, the load change makes conventional PID requires more time. The voltage deviation in proposed controller by 6.25% for 0.01 s, this response is quite fast than conventional PID controller. The output voltage of the changing load is shown in Figure 4. However, the proposed controller has shorter oscilation compared to conventional PID controller, the voltage deviation in less than PID controller.

CONCLUSION
In this paper, DMRAC is chosen for controlling DC-DC boost converter, this method is satisfied for its controller structure and good performance in various input voltages and loads. The proposed system is stable and able to reach model reference perfectly with shorter recovery time. However, the response of the system has instantaneously overshoot and voltage deviation. The rise time, settling time, and overshoot for step response to follow the response of model reference are some objectives that determine whether the adaptation gains work properly. The adaptation gains determine the success of adaptive control. The adaptation gains of the proposed controller are obtained by empirical gains.