Linear Control Techniques

Linear controllers are designed and applied based on the linear model of the controlled plant. Linear control methods are crucial for maintaining the desired output voltage in power electronic systems while minimizing deviations caused by disturbances or changes in the load. This section examines four commonly used linear control techniques: Proportional-Integral (PI) control, Proportional-Integral-Derivative (PID) control, pole placement control, and deadbeat control.

Proportional-Integral (PI) Control

Proportional-Integral (PI) control is extensively used in power electronic systems due to its simplicity and effectiveness. It combines a proportional term (P) and an integral term (I). The proportional term responds to the difference between the desired output voltage and the actual output voltage, while the integral term accumulates the error over time.

The PI controller adjusts the control signal based on the sum of the components mentioned earlier. The proportional term provides a fast response to changing errors, while the integral term eliminates steady-state errors and ensures long-term maintenance of the desired output voltage. PI controllers are suitable for applications with small disturbances and slow dynamics.

The transfer function of PI controller in the continuous domain can be expressed as:

$$G_{pi}(s)=k_p+\frac{k_i}{s}$$

where k_p and k_i are the proportional and integral gains, respectively.

The controlled plant in power electronic systems is frequently a three-phase two-level voltage source converter (VSC). Figure 1 displays the control diagram of the PI controller used for current control in VSC. The grid voltage of the point of common coupling is U_gabc ,the grid current is I_gabc , Z_f is the impedance of filter which can a simple L filter or LCL filter, Z_g represents the impedance of weak grid, v_cabc is the converter voltage, v_dc is the DC voltage, and C is the DC capacitance.

Figure 1: Control diagram of proportional and integral controller applied in a three-phase voltage source converter to control the current

Proportional-Integral-Derivative (PID) Control

Proportional-Integral-Derivative (PID) control is an extension of the PI control technique that adds a derivative term (D) to the control law. The derivative term is proportional to the rate of change of the error, enhancing the controller's performance and understanding of the system's dynamics.

The PID controller adjusts the control signal by based on the sum of the proportional, integral, and derivative components. The addition of the derivative term enables the controller to respond faster to system changes, resulting in improved transient performance. PID control is extensively applied in power electronic systems that demand precise voltage regulation and enhanced dynamic performance.

Pole Placement Control

Pole placement is a feedback control method that allows for positioning the dominant closed-loop poles of a plant at a desired location in the s-plane. When all system state variables are measurable and controllable, state feedback with an appropriate gain matrix enables pole placement. The pole locations determine the roots of the system characteristic equation, which dictate the system's response characteristics. By regulating the dominant closed-loop poles, the damping ratio and undamped natural frequency can be adjusted, offering flexible design of dynamic and steady-state performance.

Deadbeat Control

Deadbeat control is a discrete-time control technique that strives to reduce the tracking error of the controlled current to zero within a short time, typically one or two sampling intervals. It calculates the control action based on the difference between the desired and actual current values, as well as system parameters.

Deadbeat control provides a quick transient response and a fixed switching frequency, simplifying the design of filtering elements. However, it can be sensitive to parameter variations and measurement noise. To ensure stability and performance, accurate system modeling and robust control algorithms are necessary.

Non-Linear Control Techniques

Linear control methods may not be effective when dealing with hostile environments such as unbalanced or distorted grid voltage. Additionally, nonlinear controllers are better suited for improving robustness and adaptability to different situations when considering system parameter variation and disturbance uncertainty. Nonlinear control techniques are utilized in power electronic systems to regulate current flow through various components, ensuring stability and optimal performance. This section examines three commonly used nonlinear control techniques: Hysteresis control, Model predictive control, and artificial intelligence.

Hysteresis Control

Hysteresis control, also known as bang-bang control, is a widely used and simple current control technique. It compares the actual current waveform with reference current waveforms and keeps the current within a predefined hysteresis band. When the current exceeds the upper or lower limit of the band, the controller switches the power device's state to bring the current back within the band.

Hysteresis control offers a quick response and is relatively straightforward to implement. However, its performance can be impacted by the varying switching frequency, which may introduce harmonic distortion and complicate the design of filtering elements.

The control logic for the hysteresis controller per phase is shown in Figure 2.0.

Figure 2: Hysteresis control scheme applied in a three-phase voltage source converter

To generate pulses, the reference inverter current is compared to the actual inverter current I_gabc, and the pulses are generated based on the error. The switching logic is expressed as:

$$S_{abc}=\begin{cases} -1, I_{gabc} \geq I_{abc_{\text{ref}}} + h \\ 1, I_{gabc} \leq I_{abc_{\text{ref}}} - h \end{cases} $$

where S_abc is the switching signal, with 1 indicating the upper switch is on and -1 indicating the lower switch is on. The hysteresis band is represented by h. The actual current is controlled to match the reference current by ensuring that the actual current remains within the hysteresis band.

Model Predictive Control

Predictive control, also referred to as Model Predictive Control (MPC), is an advanced current control technique that utilizes a mathematical model of the power electronic system to anticipate future current behavior. Using these predictions, the controller determines the optimal control actions to minimize a predetermined cost function, such as current tracking error or switching losses.

Predictive control offers exceptional performance and is capable of adapting to variations in system parameters. However, it necessitates substantial computational resources and may pose implementation challenges compared to other control techniques.

Artificial Intelligence

Fuzzy Logic Control and Neural Network Control are Artificial Intelligence (AI) techniques that have become significantly popular in the control of Power Electronic Systems. These methods provide robust and adaptable control, allowing systems to effectively manage uncertainties and complexities that are typical in power electronics.

Fuzzy Logic Control:

Fuzzy Logic Control provides a systematic approach to handling uncertain and imprecise systems that are difficult to model mathematically. By incorporating degrees of truth, it enables approximate reasoning, which is vital for complex power electronic systems. Fuzzy Logic Control utilizes membership functions and linguistic rules to convert fuzzy sets into output action, allowing for the management of nonlinear and variable power electronic systems.

Neural Network Control:

Neural Network Control draws inspiration from the interconnected neural structure of the human brain. It employs artificial neural networks (ANNs) for system control. ANNs learn and adapt based on experience, making them valuable in controlling nonlinear and complex power electronic systems where precise mathematical models may be challenging to obtain. By comprehending system behavior through input-output data pairs, ANNs generate suitable outputs for a given set of inputs, offering robust solutions to the dynamic and evolving challenges of power electronic system control.

Comparison of Linear and Non-Linear Control Techniques

Control techniques play a critical role in power electronic systems as they influence the dynamic response and steady-state performance. Linear and non-linear control techniques are the two primary categories utilized in these systems. However, each approach has unique features that may make one more appropriate than the other for a particular application.

Linear control techniques, such as PI control, PID control, pole placement control, and deadbeat control, are rooted in linear system theory. They offer reliable control in stable operating conditions and are relatively simple to design and implement. However, their performance tends to degrade when confronted with significant non-linearity or variable parameters, such as during large disturbances or rapid load changes.

On the other hand, non-linear control techniques, such as hysteresis control, model predictive control, and artificial intelligence methods like fuzzy logic and neural networks, are specifically designed to handle non-linear systems. These techniques exhibit flexibility and adaptability, making them suitable for complex power electronic systems characterized by non-linear behaviors and variable operating conditions. Non-linear control techniques excel in managing large disturbances and rapid changes in system states or operating conditions. Nonetheless, their design and implementation are typically more intricate compared to linear control techniques.

In addition, artificial intelligence methods bring a learning component to the control system, enhancing its adaptability. These methods excel at handling system uncertainties and complexities that can pose challenges for traditional linear and non-linear techniques.

To summarize, the selection between linear and non-linear control techniques depends on the application and system characteristics. Linear methods are well-suited for systems operating near a fixed point, while non-linear methods are more suitable for systems with pronounced non-linear characteristics or variable operating conditions. The complexity of the control technique should also be taken into account, weighing the performance advantages against the design and implementation complexities.

Applications in Various Power Electronic Converters

Linear and Non-Linear Control Techniques play an essential role in the operation of power electronic converters, optimizing stability, performance, and efficiency. This section delves into the applications of these control techniques in various power electronic converters, including DC-DC converters, AC-DC rectifiers, DC-AC inverters, and AC-AC converters.

DC-DC Converters: DC-DC converters are essential for voltage regulation and conversion in power supplies, battery chargers, and renewable energy systems. Linear control techniques, such as PI and PID controllers, are commonly used in these converters to maintain a stable output voltage despite fluctuations in input voltage and load conditions. Non-linear control techniques, such as hysteresis and model predictive control, govern the inductor current, improve transient response, and reduce output voltage ripple.

AC-DC Rectifiers: AC-DC rectifiers convert AC input voltage to regulated DC output voltage and are crucial in power supplies, motor drives, and battery charging applications. Linear control techniques, such as PI controllers and pole placement control, are used to regulate the output voltage. Non-linear control techniques, such as predictive control and hysteresis control, shape the input current waveform, reduce harmonic distortion, and achieve power factor correction.

DC-AC Inverters: DC-AC inverters convert DC input voltage to AC output voltage and find applications in motor drives, renewable energy systems, and uninterruptible power supplies. Linear control techniques are employed to control the output voltage magnitude and frequency, ensuring proper operation of connected loads. Non-linear control techniques, such as hysteresis control and predictive control, govern the output current, improve dynamic performance, and mitigate harmonic distortion.

AC-AC Converters: AC-AC converters are utilized for voltage and frequency conversion in applications like motor speed control, power quality enhancement, and voltage regulation. Linear control techniques, such as PI and pole placement control, are implemented to oversee the output voltage magnitude and frequency. Non-Linear control techniques like hysteresis control and predictive control are applied to control the output current, minimize harmonics, and ensure peak performance.