Senol Gulgonul

Senol Gulgonul

This paper presents a PID tuning method based on step response curve fitting (PID-SRCF) that utilizes L2-norm minimization for precise reference tracking and explicit transient response shaping. The algorithm optimizes controller parameters by minimizing the root-mean-square error between desired and actual step responses. The proposed approach determines optimal PID parameters by matching any closed-loop response to a desired system step response. Practically a first-order plus time delay model or a second-order system with defined settling time and overshoot requirements are preferred. The method has open-source implementation using constrained nonlinear optimization in MATLAB. Comparative evaluations demonstrate that PID-SRCF can replace known analytical methods like Ziegler Nichols, Lambda Tuning, Pole Placement, Dominant Pole and MATLAB proprietary PID tuning applications.

Senol Gulgonul

A unified, closed-form analytical PI/PID tuning method is presented for all-pole plants up to third order that yields a strictly monotonic (zero-overshoot) step response with minimum settling time. The design target is the binomial closed loop p^n/(s+p)^n, which is monotonic with robustness depending only on the order n. Because adding a left-half-plane zero to a fixed pole pattern only slows the response, the minimum-settling solution requires the controller zeros to be cancelled, which forces the controller numerator to divide the plant denominator. Carrying this principle through shows that an exact, real-gained solution exists for any stable plant precisely up to second order with a PI controller and third order with a PID controller; the residual binomial factor acquires a complex pair beyond that, which a generic plant does not contain. Explicit gains are derived for first-order plants (PI), second-order plants with real and complex poles (PI and PID), and third-order plants with three real poles and with one real pole plus a complex pair (PID). The second-order PI case is treated in full as the lowest-order instance. Monotonicity guarantees Mt = 1, hence Ms less then 2, phase margin above 60 degree, and gain margin above 6 dB, tightening to universal constants for the binomial family. Numerical verification confirms the results.

Senol Gulgonul

Background: Tuning proportional-integral (PI) controllers for second-order plants to achieve monotonic step response with minimum settling time is an important problem in analytical control design. Existing methods address these objectives only partially or require numerical optimization. Methods: A closed-form analytical solution is derived through pole placement in the framework of Astrom and Hagglund. The key insight is that designing the closed-loop poles slower than the fast plant pole forces pole-zero cancellation of the slow plant pole as a consequence, not an assumption. The critically damped condition is then applied to minimize settling time. Results: The optimal PI parameters are K=T1/(4KpT2), Ti=T1, where T1 and T2 are the plant time constants and Kp is the plant gain. No free parameter remains. The resulting closed-loop system possesses universal robustness properties independent of plant parameters: maximum complementary sensitivity Mt = 1, maximum sensitivity Ms = 1.155, and phase margin PM = 76.35 degree. Conclusions: The proposed tuning formulas are explicit, analytically proven, and apply directly to any stable second-order plant with two real poles. Simulation results across six plant configurations confirm the analytical predictions exactly. The notation follows Astrom and Hagglund [5] throughout. Keywords: PI controller; second-order plant; pole placement; critically damped; monotonic response; settling time; robustness

Senol Gulgonul

HeceTokenizer is a syllable-based tokenizer for Turkish that exploits the deterministic six-pattern phonological structure of the language to construct a closed, out-of-vocabulary (OOV)-free vocabulary of approximately 8,000 unique syllable types. A BERT-tiny encoder (1.5M parameters) is trained from scratch on a subset of Turkish Wikipedia using a masked language modeling objective and evaluated on the TQuAD retrieval benchmark using Recall@5. Combined with a fine-grained chunk-based retrieval strategy, HeceTokenizer achieves 50.3% Recall@5, surpassing the 46.92% reported by a morphology-driven baseline that uses a 200 times larger model. These results suggest that the phonological regularity of Turkish syllables provides a strong and resource-light inductive bias for retrieval tasks.