Comparative Analysis of Control Strategies for Position Regulation in DC Servo Motors

Raihan Khan Akash

REVIEW 3 major objections 4 minor 17 references

Comparative Analysis of Control Strategies for Position Regulation in DC Servo Motors

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper claims that a state-feedback controller with integral action (SFCIA) outperforms P, PI, PID, and plain state feedback in simulated DC servo position regulation, achieving zero overshoot, zero steady-state error, and the shortest…

desk verdict A clean but unreproducible textbook comparison: SFCIA beats ZN-tuned PID, yet the missing pole placements and an overstated abstract keep it from being accepted as-is. read the letter →

arxiv 2501.11820 v1 pith:ZOAWQYR5 submitted 2025-01-21 eess.SY cs.SY

Raihan Khan Akash This is my paper · ORCID

classification eess.SYcs.SY

keywords DCservomotorpositioncontrolstatefeedbackcontrollerintegralactionZiegler-Nicholstuningpoleplacementovershootsettlingtime

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks which of five standard controllers—P, PI, PID, state feedback (SFC), and state feedback with integral action (SFCIA)—best regulates the angular position of a DC servo motor in simulation. It builds a third-order state-space model from the motor's electrical and mechanical dynamics, tunes the first three with the Ziegler-Nichols rule, places poles for the state-feedback designs, and compares step responses. The central claim is that SFCIA wins outright: zero overshoot, zero steady-state error, and the fastest settling time, with only a slightly slower rise and peak time than PID. A sympathetic reader would care because the paper offers a concrete, reproducible framework for choosing a controller when precision is the priority, and it isolates the value of integral action in a state-feedback design.

What carries the argument

The central object is the augmented state-space system built from the three physical states $\theta$, $\dot{\theta}$, and $i$ plus a fourth state $w = \int (y - r)\,dt$ representing the integral of the tracking error. The control input $u = -K_a x_a$ couples state feedback with integral action, and the combined gain $K_a$ is computed by a pole-placement routine. This mechanism removes steady-state error without introducing the overshoot typical of high-gain classical integral action. For P, PI, and PID, the mechanism is the Ziegler-Nichols rule producing $K_p$, $T_i$, and $T_d$ from the critical gain $K_{cr}$ and oscillation period $P_{cr}$.

What would settle it

Re-run the five-controller comparison with a common design constraint, such as forcing SFCIA's closed-loop poles to give a rise time equal to PID's 0.03 s; if SFCIA then shows nonzero overshoot or a settling time no faster than PID's 0.32 s, the paper's ranking is an artifact of pole placement rather than a property of integral action.

Watch

Extended reading notes

Core claim

The author's discovery is that augmenting the state-space model with an integral-of-error state—so the control law becomes $u = -K_c x - K_i w$, with $w = \int (y - r)\,dt$—lets a state-feedback controller eliminate steady-state error while keeping the closed-loop response essentially free of overshoot. In the reported simulations, SFCIA reaches the reference with 0% overshoot, zero steady-state error, and a settling time of 0.26 s, compared with 56.13% overshoot and 0.32 s for PID, 46.31% and 0.60 s for P, 85.41% and 1.11 s for PI, and 2.39% overshoot with 0.90 steady-state error for SFC. The slightly longer rise (0.15 s) and peak (0.34 s) times than PID are the trade-off the paper accepts in exchange for precision.

Load-bearing premise

The load-bearing premise is that the closed-loop pole locations chosen for SFC and SFCIA, which the paper does not report, were selected with tuning effort comparable to the Ziegler-Nichols settings used for P, PI, and PID.

Editorial extensions

If this is right

For high-precision position regulation of a DC servo motor in this simulated setting, SFCIA is the recommended choice: it is the only controller achieving both zero overshoot and zero steady-state error.
PID remains the best compromise when speed of response matters most, since it has the fastest rise (0.03 s) and peak (0.09 s) times while still reaching zero steady-state error.
Plain state feedback without integral action cannot reach the reference (steady-state error 0.90), so any precision application needs either integral action or a different compensation scheme.
P and PI controllers, as tuned here, are poorly suited to precision tasks because their overshoot (46.31% and 85.41%) and long settling times (0.60 s and 1.11 s) violate stability-critical requirements.
Because all states ($\theta$, $\dot{\theta}$, $i$, and $w$) are assumed directly measurable, the SFCIA design needs no observer, simplifying implementation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's ranking is contingent on the unstated pole-placement choices for SFC and SFCIA; a fairer comparison would fix a common design target, such as equal rise time or equal phase margin, across all five controllers.
If the physical system's parameters vary or sensor noise is present, the zero-overshoot and zero-steady-state-error claims likely degrade; the paper itself lists experimental validation as future work.
A direct extension would apply the same five controllers to a two-mass or flexible-load servo system, where the extra integral state may interact with resonance modes differently than in the rigid third-order model.
The transfer function used, $\theta/V = K/[s((Ls+R)(Js+b)+K^2)]$, assumes $K_t = K_e = K$; if that equality is dropped, the SFCIA pole-placement calculation changes and the quantitative rankings could shift.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague, here's my read of Akash's DC servo motor controller comparison. The headline: it's a clean, ordinary simulation study that confirms a well-known result—integral state feedback beats ZN-tuned PID on overshoot and settling time—but the paper cannot be fully checked because the SFC/SFCIA pole locations and gains are never reported.

What it does well: the DC motor model in Eq. (5)-(6) is algebraically consistent with the parameters in Table I. The state-space matrices check out. The performance table is laid out clearly, and the Ziegler-Nichols tuning for P/PI/PID is reproducible. The paper is readable and the comparison methodology (same plant, same step input, five controllers, five standard metrics) is sound in spirit.

The soft spots, in order of importance. First, Section II-F4 and F5 say the SFC and SFCIA poles were 'carefully chosen' and MATLAB's place was used, but no poles or gain matrices are given. That means an independent reader cannot rerun Table III or verify that the SFCIA advantage is a property of the control structure rather than of chosen pole locations. This is the load-bearing gap. Second, the abstract claims SFCIA achieves 'optimized rise and peak times,' but Table III shows PID has faster rise (0.03 vs 0.15 s) and peak (0.09 vs 0.34 s). The Section III text actually concedes this; the abstract overstates. Third, the conclusion confusingly calls SFC 'Sliding Mode Control' when the paper is about State Feedback Control. That's a terminology slip that should be fixed. Fourth, as the paper's own references [16] and [17] show, the central comparison is not new; this is a parameter-specific replication. Nothing wrong with that if positioned as a tutorial or verification, but the paper should say so.

Net: the central claim—SFCIA gives zero overshoot, zero steady-state error, and fastest settling for this plant—is plausible and likely true. But the missing design details mean the result is not yet verifiable. I'd send it to review with a request for the full controller gains and a rewritten abstract. There is enough there for a useful referee exchange, and the paper is honest in its limitations except for those two overstatements.

Referee Report

3 major / 4 minor

Summary. The paper develops a third-order linear model of a DC servo motor from electrical and mechanical dynamics, then designs and simulates five controllers for position regulation: P, PI, and PID tuned via the Ziegler-Nichols method, plus state-feedback control (SFC) and state-feedback control with integral action (SFCIA) designed by pole placement. Based on MATLAB step responses, it reports performance metrics in Table III and concludes that SFCIA achieves zero overshoot, zero steady-state error, and the shortest settling time, while the abstract further claims 'optimized rise and peak times.' The central comparison rests on the simulation results; however, the SFC/SFCIA design details (pole locations, gain matrices, and design criteria) are not reported, and the rise/peak time claim is contradicted by the paper's own Table III.

Significance. If the missing design information were supplied, the paper could serve as a reproducible comparative case study for teaching position control of DC servo motors. The motor model in Equations (5)-(8) is algebraically consistent with the stated parameters, and the general conclusion that adding integral action to state feedback eliminates steady-state error is standard and plausible. The paper's strength is its explicit system parameters and a full transfer function, which allow independent verification given the omitted controller gains. The contribution is modest in novelty—the comparison is simulation-only and prior work already compares integral state feedback with PID—but a fully documented comparison would still be useful as an educational benchmark. The current significance is limited by the failure to report the SFC and SFCIA pole placements, which makes the headline comparison unverifiable.

major comments (3)

[II-F4, II-F5, Table III] The closed-loop pole locations chosen for SFC and SFCIA are not reported, and the resulting gain matrices Kc and Ka are not given. The text only says the poles were 'carefully chosen' and that MATLAB's 'place' command was used. Without a stated performance criterion (e.g., desired damping ratio, dominant pole time constant, or LQR weights) and the actual pole locations and gains, an independent reader cannot reproduce Table III or judge whether the comparison is fair relative to the fixed Ziegler-Nichols tuning of P, PI, and PID. This is load-bearing for the central claim that SFCIA outperforms the classical controllers.
[Abstract, Section III, Table III] The abstract states that SFCIA achieves 'optimized rise and peak times,' but Table III reports a rise time of 0.15 s and a peak time of 0.34 s for SFCIA, while PID achieves 0.03 s and 0.09 s, respectively. The text itself acknowledges in Section III that SFCIA is 'marginally slower' than PID on these metrics. The abstract should be corrected to claim zero overshoot, zero steady-state error, and the shortest settling time, but not optimized rise and peak times.
[II-F5, Eq. (16)-(17)] The augmented state-space model for SFCIA is incompletely specified. The integral state w is defined as w = ∫(y−r)dt, so wdot = y − r = θ − r, but the matrix Aa as printed has row4 = [1 0 0 0], which gives wdot = θ, not θ − r. The reference-input matrix Br that would supply the −r term is never given. The author should provide Br explicitly or define wdot directly in terms of the error in the augmented state equation.

minor comments (4)

[Section IV and Section III, concluding paragraph] The text refers to 'Sliding Mode Control (SFC)' in the concluding paragraph of Section III and in Section IV; the abbreviation SFC has been used throughout as 'State Feedback Controller.' This typo should be corrected.
[Section II-C] There is a typographical error in 'euation' that should read 'equation.'
[Table II and Section II-F] The computed Ziegler-Nichols parameters are not reported. The values of Kcr and Pcr, and hence the final Kp, Ti, and Td used for P, PI, and PID, should be listed to make the classical-controller comparison reproducible.
[Eq. (5)] The denominator term 'K 2' in Equation (5) should be typeset as K^2 to avoid confusion with a variable K2.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the comparison is a simulation study whose metrics follow from the stated model and controller structures, with no load-bearing self-citation or definitional reduction.

full rationale

The paper is a numerical comparison study, not a derivation from first principles. The controllers are defined by standard laws (Eqs. 9-11, 12-14, 16-19) and evaluated by simulating the DSM transfer function (Eq. 6) with parameters in Table I. The SFCIA conclusion is computed from the resulting step responses (Table III), not obtained by substituting the conclusion into the premises. There are no self-citations by the author, no imported uniqueness theorem, and no fitted parameter renamed as a prediction. The only methodological weakness is that the SFC/SFCIA closed-loop poles are described only as "carefully chosen" (Section II-F4) without reporting the pole locations or gain matrices, which impairs reproducibility and the fairness of the tuning comparison, but this omission does not make any result equivalent to its inputs by construction. Accordingly, no circular step can be quoted, and the score is 0.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central comparison rests on the assumed linear model, the assumed measurability of all states, and the tuning choices. The only hand-selected free parameter is the pole placement for SFC and SFCIA, which is unreported and could bias the comparison. No new entities are introduced.

free parameters (1)

Closed-loop pole locations for SFC and SFCIA = not reported
Chosen 'carefully' in MATLAB place command (Section II-F4); without values or design criteria, the comparison may be tuned to favor these controllers.

assumptions (5)

domain assumption The DC servo motor is accurately described by the linear third-order model in Eq. (5).
Used throughout to derive transfer function and state-space model; nonlinearities, saturation, and disturbances are ignored.
domain assumption All states (position, velocity, current) are directly measurable by sensors, enabling full-state feedback without an observer.
Stated in Section II-F4; if current or velocity measurement is noisy or unavailable, observer dynamics would alter the comparison.
domain assumption Ziegler-Nichols tuning rules from Table II are appropriate for P, PI, and PID on this plant.
Used without justification; ZN is heuristic and can give large overshoot, which shapes the comparison.
domain assumption The reference input is a unit step with no noise or load disturbance.
Not stated explicitly, but the step response metrics imply a step reference; performance under other inputs is untested.
domain assumption The plant parameters in Table I are correct and constant.
Values are taken from the literature or assumed; no sensitivity analysis is provided.

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Cite this review

Pith. "Pith review of Comparative Analysis of Control Strategies for Position Regulation in DC Servo Motors." pith.science (2026). https://pith.science/paper/ZOAWQYR5

@misc{pith2026250111820,
  author       = {Pith},
  title        = {Pith review of: Comparative Analysis of Control Strategies for Position Regulation in DC Servo Motors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZOAWQYR5}},
  note         = {Machine review of arXiv:2501.11820}
}

read the original abstract

A servomotor is a closed-loop system designed for precise movement control, utilizing position feedback to achieve accurate final positions. Due to the ability to deliver higher power output and operate at enhanced speeds, DC servo motors are considered ideal for applications requiring precision and performance. This research aims to design, simulate, and compare various control strategies for precise position control in DC servo motors (DSM). The controllers evaluated in this study include proportional (P), proportional-integral (PI), proportional-integral-derivative (PID), state-feedback controllers (SFC), and state-feedback controllers augmented with integral action (SFCIA). The performance of these controllers was evaluated using MATLAB simulations, characterized by overshoot, settling time, steady-state error, rise time, and peak time. The results indicate that the state-feedback controller with integral action (SFCIA) surpasses other control strategies by achieving zero steady-state error, minimal overshoot, the shortest settling time, and optimized rise and peak times. These findings highlight the effectiveness of SFCIA for tasks requiring high levels of stability, precision, and dynamic performance.

Figures

Figures reproduced from arXiv: 2501.11820 by the authors.

**Figure 2.** Block Diagram Representing the State Feedback Controller (SFC). [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Block Diagram Representing the State Feedback Controller with [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 5.** Figure 5: Although the rise time is 0.04 seconds and the peak [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]

**Figure 5.** Figure 5: Position Control Step Response of the DSM with PI Controller. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: Position Control Step Response of the DSM with PID Controller. [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

**Figure 8.** Figure 8: Position Control Step Response of the DSM with SFCIA Controller. [PITH_FULL_IMAGE:figures/full_fig_p005_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

17 extracted references · 16 canonical work pages

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [16]

Ma’ari and N

A. Ma’ari and N. R. Setiawan, ”Control of DC Motor Using Integral State Feedback and Comparison with PID: Simulation and Arduino Implementation,” J. Robot. Control (JRC) , vol. 2, no. 5, 2021. [Online]. Available: https://doi.org/10.18196/jrc.25122

work page doi:10.18196/jrc.25122 2021

[2] [17]

Debnath, P

D. Debnath, P. Malla, and S. Roy, ”Position control of a DC servo motor using various controllers: A comparative study,” Mater . Today: Proc., vol. 58, pp. 484–488, 2022

work page 2022

[3] [1]

A. A. Kadhum and M. M. Abdulhussein, ”Implementation of DC motor as servomotor by using arduino and optical ro- tary encoder,” Mater . Today: Proc. , 2019. [Online]. Available: https://doi.org/10.1016/j.matpr.2021.03.576

work page doi:10.1016/j.matpr.2021.03.576 2019

[4] [2]

H. H. Tesfamikael, A. Fray, I. Mengsteab, A. Semere, and Z. Amanuel, ”Construction of Mathematical Model of DC Servo Motor Mechanism with PID controller for Electric Wheel Chair Arrangement,” J. Electron. Informat., vol. 3, no. 1, pp. 49–60, 2021

work page 2021

[5] [3]

M. S. Qureshi, P. Swarnkar, and S. Gupta, ”Assessment of DC Servo Motor with Sliding Mode Control Approach,” in 2016 IEEE First International Conference on Control, Measurement and Instrumentation (CMI), 2016, pp. 351–355

work page 2016

[6] [4]

J. Liu, P. Zhang, and F. Wang, ”Real-Time DC Servo Motor Position Control by PID Controllers Using Labview,” in Int. Conf. Intell. Human- Mach. Syst. Cybernet. , 2009, pp. 206–209

work page 2009

[7] [5]

Chotai and K

J. Chotai and K. Narwekar, ”Modelling and Position control of Brushed DC motor,” in 2017 International Conference on Advances in Comput- ing, Communication and Control (ICAC3) , 2017. [Online]. Available: https://doi.org/10.1109/ICAC3.2017.8318792

work page arXiv 2017

[8] [6]

Shrivastava, V

S. Shrivastava, V . P. Singh, R. K. Dohare, S. P. Singh, and D. P. S. Chauhan, ”PID tuning for position control of DC servo-motor using TLBO,” Int. J. Adv. Technol. Eng. Exploration, vol. 4, no. 27, pp. 23–27, 2016

work page 2016