Continuous Stirred Tank Reactor Temperature Control — Simulation & Power Modeling

Abstract — Continuous Stirred Tank Reactor Temperature Control

Continuous Stirred Tank Reactor Temperature Control: Power Electronics, MATLAB/Simulink & Circuit Modeling Integrated Analysis: MATLAB/Simulink · MOSFET/IGBT Gate Drivers · SPWM/SVPWM · THD Spectrum · ~4721 Words Chapter 1: Power Electronics Overview, System Specifications & Topology Modeling Open an interactive online Jupyter Notebook with this content on Binder: The example consists of the three modules template_model.py , which describes the system model, template_mpc.py , which defines the settings for the control and template_simulator.py , which sets the parameters for the simulator. The modules are used in main.py for the closed-loop execution of the controller. The file post_processing.py is used for the visualization of the closed-loop control run. One exemplary result will be presented at the end of this tutorial as a gif.

Analytical & State-Space Control Methodology

In the following the different parts are presented. But first, we start by importing basic modules and do-mpc . In the following we will present the configuration, setup and connection between these blocks, starting with the model . The considered model of the CSTR is continuous and has 4 states and 2 control inputs. The model is initiated by: The four states are concentration of reactant A ( \(C_{\text{A}}\) ), the concentration of reactant B ( \(C_{\text{B}}\) ), the temperature inside the reactor ( \(T_{\text{R}}\) ) and the temperature of the cooling jacket ( \(T_{\text{K}}\) ): \begin{align} \dot{C}_{\text{A}} &= F \cdot (C_{\text{A},0} - C_{\text{A}}) - k_1 \cdot C_{\text{A}} - k_3 \cdot C_{\text{A}}^2, \\ \dot{C}_{\text{B}} &= -F \cdot C_{\text{B}} + k_1 \cdot C_{\text{A}} - k_2 \cdot C_{\text{B}}, \\ \dot{T}_{\text{R}} &= \frac{k_1 \cdot C_{\text{A}} \cdot H_{\text{R},ab} + k_2 \cdot C_{\text{B}} \cdot H_{\text{R},bc} + k_3 \cdot C_{\text{A}}^2 \cdot H_{\text{R},ad}} {-\rho \cdot c_p}\\ &+ \cdot (T_{\text{in}} - T_{\text{R}}) + \frac{K_w \cdot A_{\text{R}} \cdot(T_{\text{K}}-T_{\text{R}})}{\rho \cdot c_p \cdot V_{\text{R}}}, \\ \dot{T}_{\text{K}} &= \frac{\dot{Q} + K_w \cdot A_{\text{R}} \cdot T_{\text{dif}}}{m_k \cdot C_{p,k}}, \end{align} \begin{align} k_1 &= \beta \cdot k_{0,\text{ab}} \cdot \exp\left(\frac{-E_{\text{A},\text{ab}}}{T_{\text{R}}+273.15}\right), \\ k_2 &= k_{0,\text{bc}} \cdot \exp \left( \frac{-E_{\text{A},\text{bc}}}{T_{\text{R}}+273.15} \right), \\ k_3 &= k_{0,\text{ad}} \cdot \exp \left( \frac{-\alpha \cdot E_{\text{A},\text{ad}}}{T_{\text{R}}+273.15} \right). \end{align} The parameters \(\alpha\) and \(\beta\) are uncertain while the rest of the parameters is considered certain: Additionally, we define an artificial variable of interest, that is not a state of the system, but will be later used for plotting: Chapter 2: Semiconductor Dynamics: MOSFET & IGBT Switching Characteristics & Losses WIth the help ot the \(k_i\) -s and \(T_{\text{dif}}\) we can define the ODEs: Next, the model predictive controller is configured. First, one member of the mpc class is generated with the prediction model defined above: We choose the prediction horizon n_horizon , set the robust horizon n_robust to 1. The time step t_step is set to one second and parameters of the applied discretization scheme orthogonal collocation are as seen below: Because the magnitude of the states and inputs is very different, we introduce scaling factors: The goal of the CSTR is to obtain a mixture with a concentration of \(C_{\text{B,ref}} = 0.6\) mol/l. Additionally, we add a penalty on input changes for both control inputs, to obtain a smooth control performance.

Simulink Waveforms & Power Quality Findings

In the next step, the constraints of the control problem are set. In this case, there are only upper and lower bounds for each state and the input: If a constraint is not critical, it is possible to implement it as a soft constraint. This means, that a small violation of the constraint does not render the optimization infeasible. Instead, a penalty term is added to the objective. Soft constraints can always be applied, if small violations can be accepted and it might even be necessary to apply MPC in a safe way (by avoiding avoiding numerical instabilities). In this case, we define the upper bounds of the reactor temperature as a soft constraint by using mpc.set_nl_cons() .

Scope & Practical Applications

• High-efficiency DC-DC converters and isolated resonant topologies (LLC / DAB)
• Sinusoidal and Space Vector PWM inverters for grid integration & industrial motor drives
• MOSFET / IGBT gate driver optimization with active Miller-clamp shoot-through protection
• Power quality conditioning with Total Harmonic Distortion (THD) strictly compliant with IEEE 519
• Complete Simscape .SLX model files, parameter calculation scripts, and IEEE dissertation reports