Model Free Speed Control of Spark Ignition Engines

An alternative to proportional-integral and proportional-integral-derivative regulators: Intelligent proportional-derivative regulators

“…The application of the Routh-Hurwitz [20], [21], [44] criterion to Equation (8) shows that the tuning of K P and K I alone does not permit to get arbitrary roots. It yields Fact 1.…”

“…See, e.g., the recent appraisal in [4]: "MFC is computationally efficient, easily deployable even on small embedded devices, and can be implemented in real time." Several conclusive concrete comparisons with PIs and PIDs have been published (see, e.g., [2], [3], [8], [13], [22], [27], [29], [35], [39], [41], [43], [46], [54], [55]). 1 Here we suggest a single universal feedback loop, i.e., the intelligent Proportional-Derivative controller, or iPD,…”

“…• The constants K P and K D are the gains. Successful implementation of iPDs have already been achieved a number of times (see, e.g., [8], [10], [23], [26], [38], [52], [53]):…”

An alternative to proportional‐integral and proportional‐integral‐derivative regulators: Intelligent proportional‐derivative regulators

“…The numerous successful concrete applications (see, e.g., References 7‐9, and the corresponding bibliographies for references until the beginning of 2020) demonstrate that those aims have been fulfilled to a great extent. See, for example, the recent appraisal in Reference 10: “MFC is computationally efficient, easily deployable even on small embedded devices, and can be implemented in real time.” Several conclusive concrete comparisons with PIs and PIDs have been published (see, e.g., References 11‐24). Here we suggest a single universal feedback loop, that is, the intelligent Proportional‐Derivative controller, or iPD , which is derived from the ultra‐local model of order 2 in the sense of Reference 7 u and y are the input and output variables. The time‐varying quantity F corresponds to the poorly known plant and to the disturbances; is an estimate of F . The constant is chosen such that the three terms of Equation (2) are of the same magnitude. is the reference trajectory. is the tracking error. The constants and are the gains.…”

“…Successful implementation of iPDs have already been achieved a number of times (see, e.g., References 13,26,34‐38): The gain tuning is straightforward. Recent algebraic parameter identification techniques (References 39,40) and Riachy's trick (Reference 41) permit to avoid tedious numerical derivations of the output signal y . Good robustness with respect to corrupting noises is ensured via a new noise understanding 42 …”