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Control energy and peaks for different controllers_
| Controller | Control energy [J] | Peak value |
|---|---|---|
| PI | 41.178 | 1.6136 |
| PID | 50 | 1.5405 |
| FOPI | 28.954 | 1.2464 |
| MRAC-PID | 27.678 | 1.231 |
| MRAC (Proposed) | 20.832 | 1.002 |
Comparative analysis of different controllers_
| Controllers | Peak overshoot [%] | Settling time [s] | Rise time [s] | ISE | IAE |
|---|---|---|---|---|---|
| PI | 18.17 | 402 | 109 | 47.73 | 2681 |
| PID | 21.32 | 421 | 114 | 51.03 | 2968 |
| FOPI | 12.74 | 408 | 157 | 43.09 | 2902 |
| MRAC-PID | 7.19 | 391 | 174 | 41.35 | 2863 |
| MRAC (Proposed) | 0.8 | 200 | 103 | 38.25 | 2167 |
Literature review_
| Author | Method | Outcome | Advantages | Drawbacks |
|---|---|---|---|---|
| Arun and Sahaya Aarti [21] | MPC | Rise time is 262 s, overshoot is 9.3 % | Lower peak and settling time | Overshoot is higher in the second tank |
| Kumar et al. [22] | IMC-PID | ITAE is 0.0661, overshoot is 7.611·10-4 | It can be applied to the conical transfer function | Poor robustness |
| Rajiv Ranjan [23] | MRAC | Settling time is 30 s | System performance is stable under unmodelled dynamic | Longer settling time |
| Espitia-Cuchango et al. [24] | NFAC | Desired response is obtained under varying system conditions | Suitable for multi-input and multi-output systems | More settling time |
| Aguila-Camacho et al. [25] | FOPI | ITAE is 1.4465·106 | Lower variance | More time to settle |
| Balaska et al. [29] | FO-MRAC | Sampling period is 0.1 s | Lowest error cost | Increases the noise |
| Patil and Agashe [30] | DRL | Desired response is obtained under varying system conditions | Reduces the complexity and non-linearity | Higher rise time |
| Ramanathan et al. [31] | Reinforcement learning algorithm | Settling time for trial 1 is 452 s | Reduces the non-linearity issues and settling time | Learning process slow |
Comparative analysis of PID controller with different optimization techniques_
| Controllers | Peak overshoot [%] | Settling time [s] | Rise time [s] | ISE | IAE |
|---|---|---|---|---|---|
| PID | 21.32 | 421 | 114 | 51.03 | 2968 |
| PID with GA | 10.52 | 376 | 131 | 44.17 | 2888 |
| PID with PSO | 5.44 | 305 | 122 | 40.93 | 2652 |
| MRAC (Proposed) | 0.8 | 200 | 103 | 38.25 | 2167 |