Introduction to Model Predictive Control

Model Predictive Control (MPC), also known as receding horizon control, is an advanced control strategy widely implemented in diverse industrial processes and systems, including power electronic systems. MPC is an optimal control approach that employs a mathematical model of the system to forecast its future behavior within a specified prediction horizon. By solving an optimization problem at each time step, MPC determines the optimal control actions that minimize a cost function, which is typically composed of a combination of performance and control effort criteria.

MPC has gained considerable attention in power electronics because of its capacity to manage constraints, multiple inputs and outputs, and nonlinearities while delivering exceptional performance and resilience. The key distinguishing features of MPC from other control techniques lie in its explicit consideration of system constraints and its ability to optimize control actions over a prediction horizon based on a mathematical system model. Consequently, MPC yields improved performance, reduced energy consumption, and enhanced reliability in various power electronic applications.

Recent developments in computational capabilities, algorithms, and hardware have facilitated the real-time application of MPC in fast dynamic systems such as power converters and motor drives. The versatility and adaptability of MPC make it an appealing option for various power electronic systems, including DC-DC converters, AC-DC rectifiers, inverters, and motor control.

Principle of Operation

Model Predictive Control (MPC) is based on optimizing a cost function while taking into account system constraints, using predictions of future system behavior over a defined horizon. The primary stages of MPC operation include prediction, optimization, and control action, which are repeated at each control step. In the following, we will delve into each of these steps in greater detail.

Prediction: MPC utilizes a mathematical model of the system to forecast the future behavior of system states and outputs over a specified prediction horizon. This prediction is based on the current system state and possible future control actions. The prediction horizon is the number of future time steps the controller considers, and it plays a crucial role in the controller's performance. A longer horizon provides more accurate predictions but increases the computational complexity.

Optimization: At each time step, MPC solves an optimization problem to determine the optimal control actions that minimize a predefined cost function. The cost function typically includes terms related to tracking error, control effort, and other objectives such as energy consumption or system robustness. The optimization problem also incorporates constraints on system states, outputs, and control inputs. These constraints reflect physical limitations, safety requirements, or desired performance specifications. By solving the optimization problem, MPC generates a sequence of control actions that minimize the cost function while satisfying the constraints.

Control Action: After the optimization problem is solved, the first control action from the optimal sequence is implemented in the system. The system then proceeds to the next time step, and the process repeats, with the optimization problem being solved again. This receding horizon approach allows MPC to continually adapt to new information and changing operating conditions, enhancing both performance and robustness. MPC's effectiveness in power electronic systems is due to its ability to handle multiple inputs and outputs, nonlinearities, and constraints explicitly. By including system constraints and forecasts of future behavior, MPC can achieve high-performance control with improved robustness and adaptability compared to traditional control methods, making it ideal for various power electronic applications.

Optimization Techniques in MPC

Model Predictive Control (MPC) depends on optimizing a cost function to determine the best control actions for a given system. The selection of the optimization method is critical since it directly affects the controller's performance, computation time, and robustness. This section will explore several optimization techniques commonly utilized in MPC for power electronic systems.

Quadratic Programming (QP): QP is a popular optimization method used in linear MPC problems where the cost function is quadratic and the constraints are linear. QP solvers are efficient and well-established, providing fast and accurate solutions for medium-sized problems. However, for larger or nonlinear problems, QP may become computationally expensive or impractical.

Nonlinear Programming (NLP): NLP is commonly employed for nonlinear MPC problems. NLP solvers can handle nonlinear cost functions and constraints, offering more precise solutions for complex systems. However, the computational complexity of NLP is typically higher compared to QP, making it less suitable for real-time applications with strict computation time requirements.

Mixed-Integer Linear Programming (MILP) and Mixed-Integer Nonlinear Programming (MINLP): In certain power electronic applications, discrete or integer variables are present, such as switching states in converters. For such problems, mixed-integer programming techniques are necessary. MILP and MINLP solvers can handle both integer and continuous variables, and linear and nonlinear constraints respectively. However, these solvers can be computationally demanding, particularly for large-scale problems.

Sequential Quadratic Programming (SQP): SQP is an iterative optimization method commonly used for solving non-linear MPC problems. It approximates the original nonlinear problem by a series of quadratic programming subproblems, which are solved iteratively. SQP can perform well for moderate-sized nonlinear systems but may encounter challenges with large-scale or highly nonlinear problems.

Model Predictive Control with Approximate Dynamic Programming (ADP) or Reinforcement Learning (RL): In certain cases, MPC can be combined with machine learning techniques like ADP or RL to reduce the computational burden of optimization. These methods leverage on learning algorithms to approximate the optimal control policy, enabling more efficient real-time control solutions. By training a model or reinforcement learning agent, the control actions can be approximated without the need for extensive online optimization.

The choice of an optimization technique in MPC depends on some characteristics of the power electronic system, they include the system's size, linearity, presence of integer variables, computational resources, and real-time requirements. It is crucial to strike a balance between control performance, computation time, and robustness to achieve the desired system behavior.

Implementation of MPC in Power Electronic Systems

To achieve the desired performance and robustness, implementing Model Predictive Control (MPC) in power electronic systems requires a systematic approach. In this section, we will examine the primary stages involved in implementing MPC for power electronic systems.

System Modeling: For MPC to be successful, developing an accurate model of the power electronic system is critical. This model must encompass the system's dynamic behavior, including its electrical, mechanical, and thermal properties. Linear, nonlinear, or switched models can be utilized, depending on the system's complexity and the desired control performance.

Controller Design: The MPC controller needs to be designed based on the system model and the chosen optimization technique. This involves defining the control objectives, such as voltage or current regulation, power factor correction, or efficiency maximization, and formulating them into a cost function. The control constraints, such as voltage and current limits or switching frequency restrictions, should also be incorporated into the controller design to ensure safe and reliable operation.

Optimization Solver Selection: The selection of an appropriate optimization solver depends on the problem's characteristics and the available computational resources. The solver should be chosen based on its ability to handle the specific problem size, linearity, and real-time requirements.

Sampling Time and Prediction Horizon: Determining the appropriate sampling time and prediction horizon is crucial for achieving the desired control performance. The sampling time should be sufficiently small to capture the system's dynamics accurately and ensure stability. The prediction horizon should be long enough to incorporate the desired control objectives but short enough to reduce computational complexity.

Real-time Implementation: MPC controller is typically implemented in real-time on the chosen digital platform, such as microcontrollers, digital signal processors (DSPs), or field-programmable gate arrays (FPGAs). The chosen platform must have sufficient processing power and memory to handle the real-time optimization solver and control algorithm. Efficient programming and algorithmic techniques should be employed to reduce computation time and ensure robust operation.

Testing and Validation: Before deploying the MPC controller in a power electronic system, extensive testing and validation should be performed. This includes simulation studies, hardware-in-the-loop testing, and experimental validation on the actual hardware. These tests help to identify potential issues and fine-tune the controller's performance.

Performance Monitoring and Adaptation: Once the MPC controller is deployed in the power electronic system, ongoing performance monitoring is necessary to ensure its continued effectiveness. This involves tracking key performance indicators, such as settling time, overshoot, and steady-state error. If any deviations or performance degradation are observed, the controller may need to be adapted or re-tuned to maintain optimal performance in changing system conditions or requirements.

Applications and Benefits of MPC in Power Electronics

MPC has become a potent control strategy for power electronic systems, providing several benefits regarding performance, efficiency, and reliability. In this section, we will explore some of the primary applications of MPC in power electronics and underscore its advantages over traditional control methods.

Voltage and Current Regulation: MPC can be utilized to control and maintain voltages and currents in different types of power electronic converters, including DC-DC, DC-AC, and AC-DC converters. By anticipating the future behavior of the system and optimizing control actions, MPC enables faster transient response, decreased overshoot, and improved performance at steady-state. These benefits surpass those offered by traditional PI or PID controllers.

Active Power Filtering: Within power distribution systems, MPC can control active power filters, serving the purpose of mitigating harmonics and correcting power factors. MPC's capacity to address multiple control objectives and constraints results in better harmonic compensation, enhanced power quality, and increased efficiency in utilizing filter components.

Motor Drives: MPC has demonstrated successful implementation in controlling a wide range of motor drives, this includes induction, permanent magnet synchronous, and switched reluctance motors. The utilization of MPC in motor drives offers several advantages, including improved dynamic performance, minimized torque and current ripples, and increased efficiency through optimal optimization of the motor's operating points.

Renewable Energy Systems: Within renewable energy systems like photovoltaic (PV) and wind energy conversion systems, MPC has the potential to optimize power extraction and facilitate maximum power point tracking (MPPT). MPC is also capable of coordinating the functioning of multiple energy sources, energy storage devices, and loads to achieve optimal performance and reliability of the system.

Grid-Connected Inverters: MPC is applicable in managing grid-connected inverters across various applications, including distributed generation, energy storage, and microgrids. By taking into account voltage and frequency fluctuations within the grid, as well as the current and power constraints of the inverter, MPC can offer enhanced grid synchronization, power quality, and system stability.

Multi-converter Systems: In complicated power electronic systems featuring multiple interconnected converters, MPC can be employed to effectively coordinate the operation of individual converters and optimize the overall system performance. As a result, MPC can lead to enhanced power sharing among converters, decreased circulating currents, and improved system reliability.

Benefits Of Using MPC

The advantages of utilizing MPC in power electronics applications can be summarized as follows:

• Enhanced dynamic performance, such as quicker transient response and diminished overshoot.
• Improved steady-state performance with decreased steady-state errors and reduced output ripples. Simultaneous handling of multiple control objectives and constraints.
• Optimal operation of power electronic systems, leading to increased efficiency and reliability
• Improved adaptation to changing system conditions or requirements.

In conclusion, MPC offers notable advantages in power electronic systems, positioning it as a promising control strategy across diverse applications. By harnessing the predictive capabilities of MPC and addressing the distinctive challenges posed by power electronics, engineers can devise advanced, robust, and efficient control solutions for a broad spectrum of applications.