PROJECTS / MPC · CSTR · State-space
Model Predictive Control for a Non-Isothermal CSTR
Development and evaluation of a predictive controller for a non-isothermal Continuous Stirred-Tank Reactor, covering process analysis, operating-point stability, linearization, discretization, state-space properties, multivariable structure and constrained MPC implementation.
PROJECT OBJECTIVE
From process dynamics to predictive control
The work progressed from analysing the non-isothermal CSTR and its operating points to proposing a discrete-time multivariable control structure and implementing an MPC controller. The final evaluation considered both servo and regulatory problems.
A coupled non-isothermal process
Six operating points were analysed before the detailed control design.
Multiple operating points
Six operating points were analysed as part of the steady-state and stability assessment.
All points stable
The eigenvalue analysis reported all six analysed operating points as stable.
Coupled variables
The model and transfer functions indicated coupling between process variables, motivating a multivariable control structure.
| Point | Eigenvalue 1 | Eigenvalue 2 | Status |
|---|---|---|---|
| 1 | -0.0787 | -0.0787 | Stable |
| 2 | -0.0568 | -0.0568 | Stable |
| 3 | -0.0382 | -0.0382 | Stable |
| 4 | -0.0224 | -0.0224 | Stable |
| 5 | -0.0090 | -0.0090 | Stable |
| 6 | -0.0176 | -0.0408 | Stable |
From continuous dynamics to a discrete control model
Process model
Non-isothermal CSTR dynamics.
Operating points
Steady-state and stability analysis.
Linearization
Local model around the selected point.
Discretization
Continuous to discrete domain.
Control structure
Multivariable formulation.
Operating point 3
Point 3 was selected for detailed control analysis. The presentation reports that this point was both controllable and observable.
Z-domain analysis
The transfer functions confirmed coupling between the variables and supported the proposed multivariable control structure.
Building the predictive controller
Scaling
Normalize variables and limits.
Incremental form
Formulate control moves.
Prediction
Generate future predictions.
Objective
Define optimization objective.
QP solution
Solve constrained optimization.
Offline preparation + online updates
Offline calculations
Import model matrices, operating points and scaling parameters; construct prediction, objective and constraint structures.
Online loop
Read process information, build and solve the optimization problem, apply the control action, simulate the process and store results.
Servo and regulatory problems
Setpoint tracking
The reported result was satisfactory, with good controller performance around the selected operating point.
Disturbance rejection
The reported regulatory result generated an offset, especially regarding the concentration disturbance.
What the study demonstrated
Process
Multiple steady-state operating points were identified.
Stability
All analysed points were classified as stable.
Control
Process coupling supported the proposed multivariable strategy.
MPC
The controller showed good performance around the selected operating point.
Explore the full implementation on GitHub
Model, discretization routines, MPC formulation and simulation scripts used throughout this project are available in the public repository.
View project on GitHub