In the MATLAB simulations, the performance of the proposed control technique was thoroughly evaluated using various performance metrics. The tracking error, rise time, settling time, overshoot and control effort were computed based on the output trajectories and system responses. These metrics provided valuable insights into trajectory tracking accuracy, response time, stability and the control effort required for maintaining trajectory accuracy. The simulation results provided a convincing validation of the control system’s behavior, demonstrating the effectiveness and reliability of the proposed approach.
Simulation and Results
The proposed control technique for the spherical motor (SM) system underwent a comprehensive evaluation using MATLAB and was employed as the simulation platform due to its versatile computational capabilities and user-friendly interface. The control algorithms were coded and integrated into the simulation environment, enabling real-time interaction with the spherical motor system. The parameters of NLFC, ANFIS and LSTM were meticulously calibrated to optimize their performance for the specific system. The parameter-tuning process involved iterative experimentation and validation against predefined performance metrics, such as rise time, settling time, tracking error and control effort. The selection of parameters was guided by a combination of expert knowledge, system identification techniques and extensive simulation trials.
The system’s step response without a control system was analyzed (
Figure 11), revealing typical open-loop behavior with slow settling time and unwanted behavior. This underscored the necessity of a control system to enhance performance.
To evaluate the effectiveness of the proposed control technique, a comprehensive comparison was conducted with a classical proportional derivative (PD) feedback controller across various scenarios. In the absence of a load, the proposed controller exhibited a smooth response with no oscillations, rapidly reaching stability without any overshoot (
Figure 12). On the other hand, both the proposed controller and the Nonlinear Feedback Controller (NLFC) demonstrated similar responses, showing close resemblance in their step responses under no-load conditions (
Figure 13).
However, as the reference speed increased, the advantages of the proposed controller became evident. The proposed controller exhibited a quicker rise time and maintained a steady response with no oscillations, outperforming the NLFC, which showed significant oscillations (
Figure 14). Moreover, in the presence of noise and disturbances, the proposed controller demonstrated superior performance with a faster recovery time and reduced oscillations compared to the NLFC, which exhibited substantial oscillatory behavior under the same conditions (
Figure 15).
Table 3 provides a thorough performance evaluation of the proposed control technique in different scenarios, labeled “Condition 1”, “Condition 2” and “Condition 3”. The evaluation metrics, including Mean Squared Error (MSE), Root-Mean-Squared Error (RMSE) and Mean Absolute Error (MAE), quantitatively measure the predictive accuracy of the LSTM model compared to the actual system responses.
Remarkably, “Condition 1” demonstrates an exceptional predictive accuracy with remarkably low values for MSE (0.002), RMSE (0.045) and MAE (0.034), indicating a precise control performance under this condition. These favorable trends are consistently observed in “Condition 2” and “Condition 3”, reaffirming the robustness and adaptability of our proposed control technique across diverse environmental scenarios (
Figure 16).
Additionally,
Table 4 illustrates the control system’s performance in various operational scenarios: “Normal (Controlled)”, “Harsh Environment 1”, “Harsh Environment 2” and “Harsh Environment 3”. Under normal operating conditions, the control system achieves a tracking error of 1.5 degrees, a rise time of 50 ms, a settling time of 200 ms, an overshoot of 5% and a control effort of 85%. The system’s ability to achieve precise trajectory tracking, rapid response and efficient control effort is evident.
Even in the face of challenging environmental conditions in the “Harsh Environment” scenarios, the control system maintains remarkable performance. The slightly increased tracking errors of 2.0 degrees, 2.2 degrees and 2.5 degrees, respectively, are mitigated by the system’s fast response times, limited overshoot and robust control effort. This exceptional performance highlights the adaptability and reliability of our proposed control technique, making it a promising solution for controlling complex systems under varying conditions (
Figure 17).
In addition to evaluating the proposed control approach under various scenarios, harsh environments with symmetric disturbances are evaluated (see
Table 4,
Figure 18).
Figure 19 depicts overlaid plots showcasing the system’s response to symmetric disturbances, with the red line representing the applied symmetric disturbance and the blue line representing the system’s response with the modified control strategy that compensates for disturbances. Remarkably, the introduced compensation effectively mitigated the impact of symmetric disturbances, leading to an enhanced performance and stability under harsh environmental conditions. The modified control strategy demonstrated its capability to handle symmetric challenges, exhibiting more robust control and precise trajectory tracking, even in the presence of symmetric disturbances.
Furthermore, the incorporation of symmetric trajectories for task frame motion during the testing phase provided valuable insights into the system’s response to symmetric challenges.
Figure 20 and
Figure 21, consisting of overlaid plots for symmetric joint and task frame trajectories, facilitated a comprehensive analysis of the control strategy’s behavior under symmetric conditions. By observing the trajectories of symmetric components, it was evident that the control approach maintained stability and accuracy, showcasing its potential for successful real-world implementation, particularly when facing symmetric disturbances. The emphasis on symmetry in the visualizations effectively showcased the control strategy’s improved performance and robustness in the face of symmetric perturbations.
To quantify the environmental impact,
emissions resulting from power consumption were evaluated. The proposed control technique significantly reduced energy consumption and
emissions compared to the classical PID control method. The reduction in
emissions was calculated using the following equation:
where
QdCO2em is the reduction in
emissions (in kg
). The
R1
CO2em,
R2
CO2em are the
emissions in kg
/kWh for electrical source 1, which is the replaced source and the used renewable one, kWhgn is the consumed electrical energy in kWh and the results are shown in
Table 5, demonstrating the potential benefits of the proposed control technique in improving both system performance and environmental sustainability.
The adaptability of the proposed control strategy to changing environmental conditions was rigorously examined through robustness testing under harsh scenarios (
Table 6). The performance of the control system was extensively evaluated, and the efficacy of the LSTM algorithm in predicting and mitigating the impact of temperature and humidity variations was demonstrated (
Figure 22 and
Figure 23). The results reaffirmed the stability and reliability of the proposed control strategy, showcasing its ability to maintain a reduced energy consumption and
emissions even in challenging environmental settings.
In the context of the proposed spherical motor control strategy outlined in the paper, the concept of environmental sustainability assumes a pivotal role. The seamless integration of advanced control algorithms, including Nonlinear Feedback Control (NLFC), Adaptive Neuro-Fuzzy Inference System (ANFIS) and Long Short-Term Memory (LSTM), not only amplifies the motor system’s operational prowess, but also resonates with the fundamental tenets of environmental sustainability.
The energy consumption comparison chart illuminates a compelling shift from the original control strategy to an intricate sequential approach, showcasing the potential of the proposed strategy to revolutionize energy consumption optimization within the SM system. In the ‘Normal (Controlled)’ scenario, the original control consistently consumes around 1.908 kWh of energy. However, the introduction of the proposed strategy, integrating Nonlinear Feedback Control (NLFC), Adaptive Neuro-Fuzzy Inference System (ANFIS) and Long Short-Term Memory (LSTM), presents a transformative departure. The proposed strategy consistently achieves energy consumption ranging between approximately 1.6 kWh and 2.8 kWh across diverse operational scenarios, underscoring its adaptability and significant energy savings potential. Sequentially deploying NLFC, ANFIS and LSTM effectively leverages the strengths of each element, culminating in an energy-efficient control solution. Particularly notable is the pattern of reduced energy consumption in challenging ‘Harsh Environment’ scenarios—‘Harsh Environment 1’, ‘Harsh Environment 2’ and ‘Harsh Environment 3’—highlighting the strategy’s capacity to adapt and optimize energy utilization amid adversity. These findings firmly establish the viability of advanced control techniques in augmenting energy efficiency and ushering in an era of environmentally conscious, economically viable operations within the SM system (
Figure 24).
Within the context of the spherical motor control framework, environmental sustainability involves optimizing energy consumption, reducing emissions and mitigating the overall environmental impact. This is achieved through several vital mechanisms:
(1) Enhanced Energy Efficiency: The meticulous calibration and fusion of NLFC, ANFIS and LSTM algorithms result in an energy-efficient control strategy. This precision in energy utilization minimizes wastage and optimizes power consumption, thus reducing the carbon footprint.
(2) Emission Reduction: A notable aspect of environmental sustainability, the paper quantifies the reduction in emissions attributed to the proposed control strategy. By significantly lowering energy consumption compared to traditional methods, the strategy contributes to decreasing emissions, a potent greenhouse gas.
(3) Resource Conservation: The strategy’s ability to ensure precise trajectory tracking and robust disturbance rejection reduces wear and tear on the motor system. This extended operational lifespan conserves natural resources by reducing the need for frequent component replacements.
(4) Resilience in Challenging Environments: Robustness testing showcases the control strategy’s ability to maintain low energy consumption and emissions even in demanding conditions. This resilience ensures a consistent and efficient performance across diverse scenarios.
(5) Technological Advancement: The incorporation of advanced control algorithms underscores the role of cutting-edge technology in advancing environmental sustainability. The integration of NLFC, ANFIS and LSTM lays the foundation for energy-efficient and eco-friendly control solutions.
To rigorously assess the effectiveness of the proposed strategy, a comparative analysis was conducted, juxtaposing the performance of the “NLFC+ANFIS+LSTM” control strategy against alternative “Neural Networks” and “Reinforcement Learning” approaches. “Neural Networks” and “Reinforcement Learning” were chosen for comparison due to their prominence as widely recognized and utilized control techniques in the field of automation and control systems. Neural networks are known for their ability to model complex nonlinear relationships, making them suitable for various control applications. Reinforcement learning, on the other hand, offers a dynamic approach to optimizing control strategies through learning from interactions with the environment.
By comparing the “NLFC+ANFIS+LSTM” strategy against these established approaches, the study aims to highlight the innovative and advantageous features of the proposed strategy. The results clearly demonstrate the superiority of the “NLFC+ANFIS+LSTM” control strategy in achieving both environmental sustainability and predictive accuracy. With a substantial
emission reduction of 21.64%, this strategy outperforms “Neural Networks” and “Reinforcement Learning” approaches. Moreover, the lower MSE, RMSE and MAE values further underscore its effectiveness in optimizing energy consumption and enhancing control system performance (
Figure 25).
Following these results, several intriguing avenues for future research and development emerge. The pursuit of advanced control algorithms and optimization techniques offers the promise of further elevating the overall efficiency and performance of the control strategy. Additionally, extending the assessment to gauge the scalability and applicability of the proposed approach across various motor systems and industrial applications presents an exciting direction for future investigation.
In conclusion, the comprehensive evaluation of the proposed control technique has underscored its effectiveness in achieving precise trajectory tracking, robust disturbance rejection and energy efficiency. The integration of LSTM has enabled a more sustainable and reliable control strategy for the spherical motor system, even in harsh environmental conditions.