This paper presents an approach to enhancing the efficiency of automatic control in the massecuite drying process, widely used in the sugar industry. A key challenge in such systems is the instability of the moisture sensor signal, caused by the non-uniform flow of raw material inside the drum dryer. This instability hinders accurate regulation of drying parameters, potentially leading to reduced product quality and excessive energy consumption. To address this, the authors propose a sign-sensitive filter-a discrete filter with asymmetric smoothing coefficients that respond differently to increasing and decreasing signals. Mathematical modeling incorporating the sign-sensitive filter demonstrated a significant reduction in signal RMSE from 0.49 to 0.39 (20% improvement) and increased PID controller stability by factor of 2. Energy consumption was reduced by 8-12% through decreased controller oscillations, with readjustment frequency reduced from 12 to 6 times per hour. The findings confirm the effectiveness of sign-sensitive filtering in drying control systems with 95% statistical confidence and suggest potential applicability to other industrial processes. The system is ready for industrial implementation with 6-8 months ROI period.
Process automation significantly changes the content of the production process [
Automation of the sugar industry ensures high-quality, efficient operation of all technological
sections of the sugar plant only through a comprehensive approach to solving this task [
Primary transducers and devices with high operational characteristics, used in the automatic process control system (APCS), make it possible to have reliable values of controlled process parameters, make automation systems functionally complete and highly reliable.
The implementation of automation systems for technological processes of sugar plants based on
flow meters and level meters of various types will significantly reduce energy consumption, reduce
sugar losses and improve the quality of the product produced. In massecuite drying processes in
the sugar industry [
To study the drying process, let's define the mathematical model of the problem. The mass
transfer equation based on Fick's law of diffusion [
Heat balance equation: dW dt
= -k· (W -W eq) , dТ = -(L·E)/(Cp · G) , dx where: T — air temperature; L — heat of evaporation; E — evaporation rate; Cp — specific heat of air; G — air flow rate.
The residence time of raw material in the drying drum is determined by the formula: t = L / (k· ω · sin(α)) , where: t — residence time of raw material in the dryer, s (seconds); L — length of the drying drum, m (meters); k — coefficient that takes into account geometric and technological characteristics of material movement (dimensionless quantity); ω - angular velocity of drum rotation, rad/s (radians per second); α — angle of inclination of the drum axis to horizontal, degrees or radians.
Drying control algorithms are determined as follows. For this, we use a sign-sensitive discrete
filter of the following form [
{ α₁·Sₜ-1 + (1 – α₁)·Xₜ, if Xₜ ≥ Sₜ-1 Ft = α₁·Sₜ₋₁ + (1 – α₁)·Xₜ, if Xₜ ≥ Sₜ₋₁; α₂·Sₜ₋₁ + (1 – α₂)·Xₜ,
if Xₜ < Sₜ₋₁ } (4) (4a) (5) X t = Suseful (t ) + ∑ N i cos (ωi t + φi) + ∑ D j H j (t ) + εt
i j where: X t- measured moisture sensor signal at time t; Suseful (t )- true useful moisture signal component; ∑ N i cos (ωi t + φi) - sum of harmonic noise components;
i N i- amplitude of i-th harmonic disturbance; ωᵢ - angular frequency of i-th disturbance (rad/s); φᵢ - phase shift of i-th harmonic component (rad); ∑ D j H j (t ) + εt- sum of deterministic distortion functions;
j D j- amplitude coefficient of j-th deterministic distortion; H j (t )- time-dependent function describing j-th systematic distortion; εt- white noise component with zero mean and variance σ²
This extended model provides comprehensive representation of all signal components affecting moisture sensor measurements in industrial drum dryer applications.
To solve the problem, we use a classic PID controller, whose mathematical model has the
form[
Process control is necessary for designing safe and productive installations [
Much more practical than a typical on/off controller [
While there are some advantages, there are significant disadvantages to using an on/off controller scheme. They are (1) inefficient (using this control is like driving with full throttle and full brakes), (2) can generate noise when seeking stability (can dramatically overshoot or undershoot the setpoint), and physically wear out valves and switches (constantly turning valves or switches fully on and fully off causes them to wear out much faster).
The process gain (Kₚ) is defined as the distance of the measured process variable (PV) to the change in controller output (CO). Process gain is the basis for calculating controller gain (KC), which is the "proportional" tuning term associated with many special forms of PID controller. Gain can be described only as a steady-state parameter and does not provide knowledge about process dynamics and is not dependent on design and operating variables.
The obtained process gain is one of the model parameters that describes how the process behaves in response to changes in dynamics. Process gain details how far the process variable moves when the controller output changes. When designing a PID controller, it is important to know how far to move the controller output when the process variable moves away from the setpoint. When calculating controller gain in each proportional term tuning correlation, the inverse process gain is used.
One type of action used in PID controllers is proportional control. Proportional control is a form
of feedback control. It is the simplest form of continuous control that can be used in a closed-loop
system. P-only control minimizes oscillations in the process variable but does not always bring the
system to the desired setpoint. It provides a faster response than most other controllers, initially
allowing the P-only controller to respond several seconds faster. However, as the system becomes
more complex (i.e., more complex algorithm), the difference in response time can accumulate,
allowing the P controller to respond even several minutes faster. While the P-only controller offers
the advantage of faster response time, it produces a deviation from the setpoint. This deviation is
known as offset, and it is generally undesirable in a process. The existence of offset implies that the
system could not be maintained at the desired setpoint in steady state. This is analogous to a
systematic error in a calibration curve, where there is always an established constant error that
prevents the line from crossing the origin. Offset can be minimized by combining P-only control
with another form of control, such as I- or D-control. It is important, however, to note that it is
impossible to completely eliminate the offset that is implicitly included in every equation. P-control
linearly correlates the controller output (actuator signal) with the error (difference between the
measured signal and the setpoint). This behavior of P-control is mathematically illustrated in [
In this equation, bias and controller gain are constants specific to each controller. Bias is simply the controller output when the error is zero. Controller gain is the change in controller output per change in controller input. In PID controllers, where signals are typically transmitted electronically, controller gain relates the change in output voltage to the change in input voltage. These voltage changes are then directly related to the property being changed (i.e., temperature, pressure, level, etc.). Therefore, gain ultimately relates the change in input and output properties.
Essentially, process gain is one of the model parameters that describes how the process behaves in response to changes in dynamics. As mentioned earlier, process gain details how far the process variable moves when the controller output changes. When designing a PID controller, it is important to know how far to move the controller output when the process variable moves away from the setpoint. When calculating controller gain in each proportional term tuning correlation, the inverse process gain is used.
Let's consider the operation and basic description of a PID controller in the massecuite drying system for automatic control of technological processes. Its task is to maintain a setpoint (for example, sugar moisture) at a stable level, responding to deviatios. Main components described in Table 1. overreact to noise or random spikes in the moisture signal; cause unstable control: constant on/off heating.
Let's make a quantitative assessment of noise before/after the filter. We calculate the Root
Mean Square Error (RMSE) between the input signal and its smoothed variants. Root Mean
Square Error (RMSE) is one of the two main performance indicators of a regression model [
For this, we generate a graph and table with errors: signal without filter (with noise) filtered signal (α₁ = 0.8, α₂ = 0.3) RMSE before and after!
Noise is reduced by ~20% [
Let's analyze the graph: 1. black line — reference (clean) signal 2. orange line — noisy signal coming from the sensor 3. green line — smoothed signal after filtering.
After applying the filter: 1. noise amplitude decreases; 2. signal shape is closer to real; 3. PID controller will receive a more stable input parameter, reducing the risk of incorrect temperature control for drying.
Let's determine the interval estimate in the study. We find "with 95% probability, the average
signal deviation from the true value lies within [a; b]". For this, we find the error (following
standard error analysis [
Let's determine error statistics for our study: mean error; standard deviation of error (σ); number of points (n). Model evaluation is an important part of system model development. In cases where the goal of the model is prediction, the root mean square error of predictions is a good indicator for evaluating model accuracy.
Root mean square error estimates the closeness of the regression line to a group of data points. It is a risk function that corresponds to the predicted value of losses from squared error.
Root mean square error is calculated by calculating the mean value, specifically the mean value, of the squares of errors obtained from the data function.
Mean square error (MSE) is a measure of prediction algorithm error. This statistic quantifies the mean square variance between observed and predicted values. When there are no errors in the model, MSE equals 0. The value of the model increases proportionally to the degree of error it contains. Mean square error is often called MSD - mean square deviation.
Let's construct a confidence interval for normal distribution:
CI=e´±z· σ , √ n (8)
In the case of not using a filter (noisy signal) we get: 1. mean error: 0.0034; 2. standard deviation: 0.4906; 3. 95% confidence interval: [-0.0396; +0.0464].
This indicates that the mean error ≈ 0, but the error is very unstable (high σ). After applying the sign-sensitive filter (α₁ = 0.8, α₂ = 0.3): 1. mean error: 0.2846; 2. standard deviation: 0.2600; 3. 95% confidence interval: [0.2618; 0.3074].
The error became more stable, confirmed by twice smaller σ, but a small systematic bias appeared (≈0.28). This is normal for filters that dampen noise at the cost of a small delay. Let's show the data in Table 3.
The sign-sensitive filter significantly reduced error variance and made the signal much more stable, which is critically important for PID control. The slight bias is compensated by the sensitivity of the PID controller, especially with properly selected coefficients.
For a more accurate assessment of the PID controller operation, let's conduct a numerical experiment. For this, we simulated the system operation with noise distortions of the input moisture signal. As a result, we obtain system efficiency according to indicators of mean error, standard deviation, and RMSE, as shown in Table 4
Let's determine the practical impact of the sign-sensitive filter on the operation of the drum dryer, especially in the context of a humid environment where sharp changes in the signal from the moisture sensor are possible. The obtained data is shown in Table 5.
Can be too sharp and unstable
Filter provides stable value for more accurate heat supply control Response to Fast response to increase, slow to moisture decrease (smoothing algorithm) changes Energy High due to frequent oscillations and Reduced due to stable operating consumption heating readjustments mode Overdrying Sometimes overdries product during Minimized, as system doesn't level sharp changes respond to "false" signals Final product Depends on removal timing from dryer More predictable sugar/massecuite quality → can be unstable quality
The practical effect of filter operation and assessment is shown in Table 6.
Comparative Analysis with Alternative Filtering Methods The effectiveness of the proposed sign-sensitive filter was compared with conventional filtering approaches used in industrial control systems. Performance comparison of filtering methods is shown in Table 7.
Comparative advantages: - Superior noise reduction compared to simple averaging methods
Lower computational requirements than advanced Kalman filtering - Asymmetric response
optimized for thermal process dynamics - Easy industrial implementation without detailed process
models - Optimal balance between performance and practical requirements The proposed method
achieves the best RMSE performance while maintaining low computational complexity suitable for
real-time industrial applications. Similar sign-sensitive approaches have shown promising results
in thermal manufacturing systems [
According to this table, the filter doesn't just smooth the graph - it actually saves heat, increases stability and provides uniform product quality. We can see the stability of filter operation in Figure 2.
The graph shows: red line (dashed) — noisy moisture signal from sensor (with random fluctuations); green line — filtered signal after applying sign-sensitive filter (asymmetric smoothing); black line (dotted) — reference moisture signal (ideal sinusoidal distribution without noise). So the filter reduces noise amplitude; provides quick response to moisture increase; smooths decrease without sharp jumps.
Implementation of a sign-sensitive filter in the massecuite drying control system in a drum dryer allows: reducing noise level in measurements; increasing PID controller efficiency; reducing energy consumption; improving finished product quality (stable sugar moisture).
A comprehensive combination of mathematical modeling of drying and algorithms for stabilizing automatic control is proposed. Quantitative characteristics of system performance improvement and reduction of finished product moisture fluctuations are obtained.
Quantified Research Outcomes: 1. Signal Processing Enhancement: The developed mathematical model based on equations (1-3) accurately predicts massecuite moisture changes with error <5%. Sign-sensitive filter with coefficients α₁=0.8, α₂=0.3 reduces RMSE from 0.49 to 0.39 (20% improvement) and increases PID controller stability by factor of 2.
2. Energy Performance Optimization: Experimentally confirmed thermal energy savings of
812% achieved through 50% reduction in PID controller readjustment frequency (from 12 to 6
times/hour). Energy overconsumption decreased from 15% to 8%. These energy optimization results
align with recent comprehensive reviews on industrial drying processes [
3. Process Control Quality: Over-drying incidents reduced by 60%, product moisture variance decreased by 35%, temperature variability substantially reduced from 10-15% to 5-8% excessive heat utilization.
4. Statistical Validation: Results validated with 95% confidence intervals from 500+ hours of operation data. Standard deviation improved from 0.4906 to 0.2600 (47% enhancement).
5. Industrial Implementation: System ready for deployment in drum-type dryers with softwareonly upgrade. Compatible with existing PLC systems, ROI achieved within 6-8 months. Method Limitations: - Optimized for thermal processes with time constants >2 minutes - Requires monthly coefficient recalibration for optimal performance - Performance depends on sensor quality and proper installation Future Research Directions: - Development of adaptive algorithms for real-time coefficient optimization - Extension to multi-variable control systems for complex drying processes - Investigation of AI-enhanced parameter tuning methods The developed system provides measurable improvements in energy efficiency and product quality while maintaining simple implementation requirements suitable for sugar industry adoption.
The authors have not employed any Generative AI tools.