A Hybrid MPC-PID Control System Design for the Continuous Purification and Processing of Active Pharmaceutical Ingredients
Abstract
:1. Introduction and Objective
1.1. Objectives
- Present a system-wide hybrid MPC-PID control scheme.
- Quantify the importance of a cascade control scheme in case of pharmaceutical unit operations.
- Present a comparative study between PID-only control and MPC-PID control schemes based on set point tracking and disturbance rejection criteria.
2. Background
3. Flowsheet Model Description
3.1. Numerical Technique
4. A Systematic Framework for Hybrid Control Design
- Identify the critical control variables.
- Identify suitable actuators or manipulating variables to be paired with the control variables.
- Obtain the response of the control variables by implementing a step change to the manipulating variables (from the actual flowsheet model, which has been developed in gPROMS™).
- Fit a transfer function model to relate the control and manipulating variables from the response obtained in the previous step. This has been done using the system identification tool box of MATLAB™.
- Group the control loops into two categories (i.e., MPC controlled and PID controlled)
- Design the hybrid MPC-PID control loops in Simulink™.
- Evaluate the performance of the designed control system in terms of set point tracking and disturbance rejection ability.
5. Design Strategy of the Control System
5.1. Selection of the Control Variables and Pairing with Suitable Actuators
Process | Control variable | Actuators (Manipulating variable) |
---|---|---|
Crystallization | Temperature cooling schedule | Coolant temperature |
Saturation concentration | ||
Drying | Drying gas temperature | Super-heated steam temperature |
Blending | API composition | Excipient flow rate |
Holdup | Weir height |
5.2. Design of Controller
6. Results and Discussion
6.1. Control System Design
PID parameters | |||
---|---|---|---|
Control loop | Gain | Reset Time | Rate |
Crystallization (slave loop) | −0.166 | 2.95 × s | 1.09 × s |
MPC parameters | |||
Control loop | Input Weight | Rate Weight | Output Weight |
Crystallization (master loop) | 0 | 0.1 | 1 |
Drying | 0 | 0.1 | 1 |
Mixing (API composition) | 0 | 0.1 | 1 |
Mixing (holdup) | 0 | 0.1 | 1 |
6.2. Comparison of the Hybrid MPC-PID Scheme with PID-only Scheme
Set point tracking | ||
---|---|---|
Control loop | MPC-PID | PID-only |
Saturation concentration | 6.322 × | 2.935 × |
Drying gas temperature | 7.371 × | 2.068 × |
API composition | 1.584 × | 1.892 × |
Disturbance rejection | ||
Control loop | MPC-PID | PID only |
Saturation concentration | 3.317 × | 4.540 × |
Drying gas temperature | 1.556 × | 6.193 × |
7. Conclusions
Acknowledgments
Nomenclature
Symbol | Description | Units |
Ac | Area of heat transfer | m2 |
B0 | Primary nucleation term | particles/(m3/s) |
b | Kinetic parameter for crystallization | Dimensionless |
C | Solute concentration in crystallization | moles/m3 |
Csat | Saturation concentration of solute | moles/m3 |
Cpw | Specific heat constant for water | J/K |
Dp | Crystal diameter | μm |
F | Particle density | particles/m3 |
G1 | Growth rate | m/s |
G2 | Growth rate | m/s |
g1 | Kinetic parameter for crystallization | Dimensionless |
g2 | Kinetic parameter for crystallization | Dimensionless |
kg1 | Kinetic parameter for crystallization | m/s |
kg2 | Kinetic parameter for crystallization | m/s |
kb | Kinetic parameter for crystallization | particles/(m3/s) |
L1 | Internal coordinate for length of solid | m |
L2 | Internal coordinate for length of solid | m |
L3 | Internal coordinate for length of liquid | m |
Mw | Cooling water flow rate | kg/s |
T | Temperature (cooling schedule) | Kelvin |
Tc | Temperature of cooling water | Kelvin |
Tin | Inlet temperature of water | Kelvin |
U | Overall heat transfer coefficient | W/(m2·K) |
ϵ | Porosity of the cake | Dimensionless |
ρavg | Average density of wet particles | kg/m3 |
ρs | Density of solid | kg/m3 |
∆P | Filter pressure difference | kPa |
μ | Fluid viscosity | kg/(m·s) |
α | Specific cake resistance | m/kg |
A | Filter surface area | m2 |
CF | Concentration of solutes in slurry | moles/m3 |
c | Mass of solute deposited on filter per unit volume of filtrate | kg/m3 |
mF | Mass of wet cake | kg |
mc | Mass of dry cake | kg |
mv | Rate of evaporation during drying | kg/s |
Na | Avogadro number | Dimensionless |
Rm | Filter medium resistance | 1/m |
V | Filtrate volume | m3 |
Vp | Particle volume | m3 |
As | Area of heat transfer | m2 |
Cps | Specific heat capacity | J/(kg·K) |
Cpsteam | Specific heat constant for steam | J/K |
k | Mass transfer coefficient | m/s |
hfg | Specific heat of evaporation | J/kg |
h | Heat transfer coefficient | W/(M2·K) |
Ts | Temperature of steam | Kelvin |
Tp | Temperature of particle | Kelvin |
Tg | Drying gas temperature | Kelvin |
Tin-steam | Inlet temperature of steam | Kelvin |
massout | Outlet flow rate of API crystals from dryer | kg/s |
Ms | Steam flow rate | kg/s |
Nu | Nusselt’s Number | Dimensionless |
Pr | Prandtl Number | Dimensionless |
Re | Reynolds Number | Dimensionless |
Sh | Sherwood Number | Dimensionless |
U | Overall heat transfer coefficient | W/(m2·K) |
xp | Liquid content of solid particle | Dimensionless |
xeql | Liquid content of solid particle at equilibrium | Dimensionless |
n | Counter for number of components | Dimensionless |
nmax | Maximum number of components | - |
t | Time | s |
Vf | Forward axial velocity | m/s |
Vb | Backward axial velocity | m/s |
Vr | Radial velocity | m/s |
x | Spatial coordinate in axial direction | - |
xmax | Maximum number of axial compartments | - |
y | Spatial coordinate in axial direction | - |
ymax | Maximum number of radial compartments | - |
yAPI | Fractional API composition at mixer outlet | Dimensionless |
yavg | Average spatial composition of component A | moles/m3 |
yi | Composition of component A in i-th compartment | moles/m3 |
Appendix: Process Model Integrated with the Hybrid MPC-PID Scheme
Crystallizer
Filtration Process
Drying Process
Mixer
MPC-PID Controller Equations
Conflicts of Interest
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Sen, M.; Singh, R.; Ramachandran, R. A Hybrid MPC-PID Control System Design for the Continuous Purification and Processing of Active Pharmaceutical Ingredients. Processes 2014, 2, 392-418. https://doi.org/10.3390/pr2020392
Sen M, Singh R, Ramachandran R. A Hybrid MPC-PID Control System Design for the Continuous Purification and Processing of Active Pharmaceutical Ingredients. Processes. 2014; 2(2):392-418. https://doi.org/10.3390/pr2020392
Chicago/Turabian StyleSen, Maitraye, Ravendra Singh, and Rohit Ramachandran. 2014. "A Hybrid MPC-PID Control System Design for the Continuous Purification and Processing of Active Pharmaceutical Ingredients" Processes 2, no. 2: 392-418. https://doi.org/10.3390/pr2020392