Metaheuristics-Based Optimization of a Robust GAPID Adaptive Control Applied to a DC Motor-Driven Rotating Beam with Variable Load
<p>(<b>a</b>) Upwards; (<b>b</b>) downwards Gaussian function shapes; (<b>c</b>) Adjustable concavity.</p> "> Figure 2
<p>Flowcharts of GA strategies: (<b>a</b>) traditional strategy; (<b>b</b>) modified strategy.</p> "> Figure 3
<p>Flowchart of PSO.</p> "> Figure 4
<p>Fitness behavior of IAE, ISE, and ITSE as function of <math display="inline"><semantics> <mi>ζ</mi> </semantics></math>.</p> "> Figure 5
<p>Simulink model of the motor system.</p> "> Figure 6
<p>Six PSO strategies.</p> "> Figure 7
<p>Schematic of the control system.</p> "> Figure 8
<p>(<b>a</b>) Motor system with beam; (<b>b</b>) motor with encoder.</p> "> Figure 9
<p>Test beams: light slim aluminum, carbon steel, and thick heavy aluminum.</p> "> Figure 10
<p>DC motor driver hardware.</p> "> Figure 11
<p>Evolution of GA strategies.</p> "> Figure 12
<p>Boxplot of the six GA strategies.</p> "> Figure 13
<p>Boxplot of the six PSO strategies.</p> "> Figure 14
<p>Evolution of PSO strategies.</p> "> Figure 15
<p>Transient responses of the system with PID and GAPID controllers subjected to variation of the moment of inertia <span class="html-italic">J</span> from 0.002 to 0.015.</p> "> Figure 16
<p>DC motor angular speed with PID control for different loads, to set point of 5 rad/s.</p> "> Figure 17
<p>DC motor angular speed with GAPID control for different loads, to set point of 5 rad/s.</p> ">
Abstract
:1. Introduction
2. Theoretical Foundation
2.1. GAPID Controller
2.1.1. Free Parameters Case
2.1.2. Linked Parameters Case
2.2. Bio-Inspired Optimization
2.2.1. Genetic Algorithm
2.2.2. Particle Swarm Optimization
2.2.3. Fitness Function
3. Test Plant Model
4. Methodology
4.1. Methodology for Simulation Analysis
4.1.1. GA Variations
- GA1: The first GA follows the classic version initially proposed, except considering the mutation, which always occurs at a low rate. The roulette wheel is used to select the individuals that will participate in the crossover. The same individual may be selected more than once. The one-point crossover occurs with 70% probability, and 5% of the genes considering the entire population are randomly chosen and pass thought the mutation. In this case, it is addressed as a perturbation considering a Gaussian distribution;
- GA2: The second GA is almost identical, but the crossover probability is 100%. It means that all selected individuals will generate offspring;
- GA3: This version uses the binary tournament instead of a roulette wheel. However, if an agent loses the game, it returns to the previous population and can be selected again;
- GA4: This version differs from the last because the “death tournament” is used. It means that if an agent loses the tournament, it is suppressed from the population;
- GA5: This proposal is more different from the others. The order of the operations is changed so that the crossover happens first, then the mutation, and finally the selection. With this idea, note that an intermediate subpopulation is created with the double individuals (see Section 2.2.1: Ultimately, the selection procedure (roulette wheel) is responsible for choosing the remaining agents, leaving the population with the original size. In this approach, all parents are chosen once at random to perform crossover;
- GA6: The last GA is similar to the previous one, but a tournament replaces the roulette wheel as a selection procedure.
4.1.2. PSO Variations
- PSO2: It also uses the global topology but includes the inertial weight as a constant value between 0 and 1 [47]. Large values for the inertia are effective for global searching, while small values are better for local searching.
- PSO3: Another global topology, with a variable inertial weight, decreasing linearly from an initial value to a final one during the iterations, according to Equation (12), where
- PSO4: The same as PSO1, but using the ring topology [41].
- PSO5: The same as PSO2 with the ring topology.
- PSO6: The same as PSO 3 with the ring topology.
4.2. Methodology for Experimental Analysis
5. Results
5.1. Simulation Results
5.2. Comparison of GA Strategies
5.3. Comparison of PSO Strategies
5.4. Experimental Results
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Parameter | Value |
---|---|
0.0032 H | |
4.57 Ω | |
B | 0.001405 |
J | depends on the beam |
0.25 | |
0.02508 | |
0.23309 | |
0.23309 |
Parameter | Value [kg·m2] |
---|---|
0.00026 | |
0.00250 | |
0.00400 | |
0.00550 | |
0.00700 | |
0.00850 |
Beam (Load) | Inertia Value (J) [kg·m2] |
---|---|
Light slim aluminum | 0.0035 |
Carbon steel beam | 0.0077 |
Heavy thick aluminum beam | 0.0080 |
Parameter | GA1 | GA2 | GA3 | GA4 | GA5 | GA6 |
---|---|---|---|---|---|---|
Sequence 1 | S+C+M | S+C+M | S+C+M | S+C+M | C+M+S | C+M+S |
Selection 2 | RW | RW | BT | DT | RW | BT |
Crossover probability | 70% | 100% | 70% | 70% | 100% | 100% |
Mutation | 5% | |||||
Population | 30 | |||||
Repetitions | 10 |
GA model | Fitness | Rank |
---|---|---|
GA1 | 0.993574 | 5 |
GA2 | 0.993661 | 4 |
GA3 | 0.993898 | 2 |
GA4 | 0.993680 | 3 |
GA5 | 0.993432 | 6 |
GA6 | 0.993999 | 1 |
Parameter | PSO1 | PSO2 | PSO3 | PSO4 | PSO5 | PSO6 |
---|---|---|---|---|---|---|
Topology | Global | Ring | ||||
1 | 0.5 | 0.9→0.4 | 1 | 0.5 | 0.9→0.4 | |
Search space | 100 | |||||
Population | 30 | |||||
Dimensions | 6 | |||||
Maximum iterations | 50 | |||||
and | 2.05 | |||||
Repetitions | 10 |
PSO Model | Best Fitness | Rank |
---|---|---|
PSO1 | 0.992541 | 3 |
PSO2 | 0.992565 | 2 |
PSO3 | 0.992588 | 1 |
PSO4 | 0.992280 | 4 |
PSO5 | 0.990775 | 5 |
PSO6 | 0.990427 | 6 |
Gain type | Gaussian Parameters | ||
---|---|---|---|
Proportional | |||
Integral | |||
Derivative |
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Borges, F.G.; Guerreiro, M.; Sampaio Monteiro, P.E.; Janzen, F.C.; Corrêa, F.C.; Stevan, S.L., Jr.; Siqueira, H.V.; Kaster, M.d.S. Metaheuristics-Based Optimization of a Robust GAPID Adaptive Control Applied to a DC Motor-Driven Rotating Beam with Variable Load. Sensors 2022, 22, 6094. https://doi.org/10.3390/s22166094
Borges FG, Guerreiro M, Sampaio Monteiro PE, Janzen FC, Corrêa FC, Stevan SL Jr., Siqueira HV, Kaster MdS. Metaheuristics-Based Optimization of a Robust GAPID Adaptive Control Applied to a DC Motor-Driven Rotating Beam with Variable Load. Sensors. 2022; 22(16):6094. https://doi.org/10.3390/s22166094
Chicago/Turabian StyleBorges, Fábio Galvão, Márcio Guerreiro, Paulo Eduardo Sampaio Monteiro, Frederic Conrad Janzen, Fernanda Cristina Corrêa, Sergio Luiz Stevan, Jr., Hugo Valadares Siqueira, and Mauricio dos Santos Kaster. 2022. "Metaheuristics-Based Optimization of a Robust GAPID Adaptive Control Applied to a DC Motor-Driven Rotating Beam with Variable Load" Sensors 22, no. 16: 6094. https://doi.org/10.3390/s22166094