arxiv: 2605.07712 · v1 · submitted 2026-05-08 · 📡 eess.SY · cs.SY

Recognition: no theorem link

Cascade PID Control of an Inverted Pendulum on a Cart System: Simulation and Experimental Analysis

Khalid Mehrab , Md Zamiul Alam , Shadman Tahmid Haque

Authors on Pith no claims yet

Pith reviewed 2026-05-11 02:24 UTC · model grok-4.3

classification 📡 eess.SY cs.SY

keywords cascade PIDinverted pendulumcart systemsimulation versus experimentstabilizationdisturbance rejectionArduino hardwareLQR comparison

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The pith

Cascade PID control stabilizes an inverted pendulum on a cart in both idealized simulation and real-time physical tests.

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

The paper tests a two-loop cascade PID controller on the inverted pendulum on a cart by creating a nonlinear Simscape model and building a physical prototype driven by a DC motor with encoders and an Arduino. In simulation the controller keeps the pendulum upright and moves the cart to set positions with good accuracy. On the hardware the same structure achieves real-time balance, but the required gains, rise times, and response to pushes differ because of sensor noise, friction, and limits on the track. The authors also replace the inner loop with LQR and show it handles disturbances better, which supplies concrete guidance on when basic cascade PID is enough and when it needs help.

Core claim

The paper establishes that the cascade PID architecture, with an inner loop regulating pendulum angle and an outer loop regulating cart position, produces effective stabilization and position tracking in a Simscape Multibody simulation under idealized conditions and achieves successful real-time stabilization on a physical DC-motor cart-pendulum prototype, although the experimental gains, transient responses, and disturbance rejection differ from simulation predictions owing to sensor noise, unmodeled friction, and hardware constraints.

What carries the argument

Cascade PID structure with an inner loop for pendulum angle and an outer loop for cart position.

If this is right

The controller stabilizes the pendulum and tracks cart position under idealized simulation conditions.
Real-time stabilization succeeds on the physical cart-pendulum hardware.
Controller gains, transient behavior, and disturbance response differ between simulation and experiment.
An LQR inner loop yields better disturbance rejection and less overshoot than PID.
Large position commands and strong disturbances expose limits when track length is restricted.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Designers of similar balancing systems may need to add noise and friction models during the initial tuning stage rather than after simulation.
The same cascade structure could be tried on other underactuated platforms such as self-balancing robots once track or sensor limits are removed.
Side-by-side PID versus LQR tests on one platform help quantify when the simpler controller is adequate and when the extra complexity pays off.
Longer tracks or improved sensing on the prototype would directly test whether the reported disturbance-rejection shortcoming is fundamental or merely hardware-bound.

Load-bearing premise

The main causes of the gaps between simulation and experiment are sensor noise, unmodeled friction, and implementation limits, and these gaps do not invalidate the cascade PID approach itself.

What would settle it

If the physical prototype cannot keep the pendulum balanced in real time when the reported cascade PID gains are applied and basic sensor filtering is used, the claim of successful experimental stabilization would not hold.

read the original abstract

This study investigates the performance of cascade PID control architecture applied to an inverted pendulum on a cart system through both simulation and experimental implementation. A nonlinear model of the system was developed using Simscape Multibody in Simulink, while a physical prototype was constructed using a DC motor-driven cart, pendulum, rotary encoder, ultrasonic sensor, and an Arduino. The cascade PID control structure consists of an inner loop regulating the pendulum angle and an outer loop controlling the cart position. Simulation results demonstrated effective stabilization of the pendulum and satisfactory position tracking under idealized conditions. Experimental results confirmed successful real-time stabilization but revealed notable differences from simulation, particularly in controller gains, transient behavior, and disturbance response due to sensor noise, unmodeled friction, and implementation constraints. The study also highlights the limitations of cascade PID control in disturbance rejection and large position commands, particularly under limited track length. A comparative analysis using an LQR-based inner loop demonstrated better disturbance rejection and reduced overshoot. The results provide practical insights into the applicability and limitations of cascade PID control of the inverted pendulum system.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is a straightforward implementation study of cascade PID on the cart-pendulum that honestly shows the usual sim-to-hardware gaps but brings no new theory or method.

read the letter

The main point is that the authors built a nonlinear Simscape model, wired up an Arduino-based cart with encoder and ultrasonic sensor, and ran a standard inner-angle outer-position PID cascade. It stabilizes the pendulum in both simulation and on the bench, but the experimental gains, transients, and disturbance response differ from the ideal case because of noise, friction, and the short track. They also swap the inner loop for LQR and show it handles disturbances better with less overshoot. That comparison is the most useful part of the work. The paper states the practical limits clearly, including poor rejection of big disturbances and restrictions on large position moves. This is the kind of honest reporting that helps people who actually build these things. The soft spots are predictable. The inverted pendulum is a classic example, cascade PID on it has been published many times, and the discrepancies they observe are the standard ones anyone would expect when moving from idealized simulation to real sensors and motors. There are no multiple-run statistics, no detailed error tables, and no deeper analysis of why the LQR version improves things beyond the usual quadratic cost argument. The central claim that the architecture works with caveats is supported by what they show, but the evidence stays at the level of one successful prototype. This paper is for students, lab instructors, or engineers who want a concrete example of taking a textbook controller to hardware. It does not advance control theory. A serious editor should send it to peer review for an applications or education-focused venue, because the implementation is careful and the caveats are stated plainly rather than glossed over.

Referee Report

2 major / 3 minor

Summary. The manuscript investigates cascade PID control for an inverted pendulum on a cart, developing a nonlinear Simscape Multibody model in Simulink for simulation and implementing inner-angle/outer-position PID loops on an Arduino-driven physical prototype with DC motor, rotary encoder, and ultrasonic sensor. Simulation shows effective stabilization and position tracking under ideal conditions; experiments confirm real-time stabilization but note differences in gains, transients, and disturbance response attributed to sensor noise, unmodeled friction, and hardware constraints. The work also compares the PID inner loop to an LQR substitution, reporting improved disturbance rejection and reduced overshoot, while highlighting limitations such as poor large-command tracking and track-length constraints.

Significance. If the reported stabilization and comparative results hold under the described conditions, the paper offers practical implementation insights for classical control of underactuated mechanical systems, particularly the real-world gaps between idealized simulation and hardware (noise, friction) and the potential benefit of hybrid LQR-PID architectures. It contributes modestly to the control-systems literature as an empirical case study with open hardware details, useful for education and prototyping, though it does not introduce new theory or parameter-free methods.

major comments (2)

[results and discussion (experimental vs. simulation comparison)] The central experimental claim that discrepancies between simulation and hardware arise primarily from sensor noise, unmodeled friction, and implementation constraints (abstract and results section) is presented without quantitative validation such as friction identification experiments, noise power spectral density measurements, or sensitivity analysis; this leaves the explanation of gain retuning and transient differences as an untested assumption that directly affects the interpretation of the cascade PID's practical viability.
[comparative analysis section] The comparative analysis asserts that substituting LQR for the inner PID loop yields 'better disturbance rejection and reduced overshoot,' yet the manuscript provides neither the LQR weighting matrices (Q, R) nor tabulated quantitative metrics (e.g., peak overshoot percentages, settling times, or disturbance rejection ratios) for both controllers under identical conditions; without these, the improvement cannot be assessed as load-bearing evidence for recommending the hybrid approach.

minor comments (3)

[abstract and results] The abstract and results text refer to 'satisfactory position tracking' and 'notable differences' without defining quantitative thresholds or providing error norms (e.g., RMSE values) that would allow readers to judge performance independently of qualitative description.
[figures] Figure captions and axis labels for time-response plots should explicitly state the controller gains used in each trace and whether the data are from simulation or experiment to improve clarity.
[experimental setup] The manuscript should include a brief statement on the sampling rate and discretization method used for the Arduino implementation of the cascade PID, as this directly influences the reported transient behavior.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We have addressed each major point below and agree that the suggested clarifications will improve the paper. All changes will be incorporated in the revised version.

read point-by-point responses

Referee: The central experimental claim that discrepancies between simulation and hardware arise primarily from sensor noise, unmodeled friction, and implementation constraints (abstract and results section) is presented without quantitative validation such as friction identification experiments, noise power spectral density measurements, or sensitivity analysis; this leaves the explanation of gain retuning and transient differences as an untested assumption that directly affects the interpretation of the cascade PID's practical viability.

Authors: We acknowledge that the manuscript does not include dedicated quantitative experiments such as friction parameter identification or noise power spectral density analysis. The attributions in the results section are based on direct observations of hardware behavior (e.g., encoder quantization, motor cogging, and ultrasonic sensor variance) and standard literature on similar cart-pendulum platforms. To address the concern, we will add a short subsection in the experimental results discussing measured noise amplitudes from logged data and qualitative friction effects inferred from steady-state offsets, thereby providing more concrete support for the explanations while retaining the existing experimental data. revision: partial
Referee: The comparative analysis asserts that substituting LQR for the inner PID loop yields 'better disturbance rejection and reduced overshoot,' yet the manuscript provides neither the LQR weighting matrices (Q, R) nor tabulated quantitative metrics (e.g., peak overshoot percentages, settling times, or disturbance rejection ratios) for both controllers under identical conditions; without these, the improvement cannot be assessed as load-bearing evidence for recommending the hybrid approach.

Authors: We agree that the comparative claims would be stronger with explicit parameters and metrics. In the revised manuscript we will include the specific Q and R matrices used for the LQR inner loop and add a table in the comparative analysis section that reports quantitative metrics (peak overshoot, settling time, and disturbance rejection ratio) for both the cascade PID and hybrid LQR-PID controllers under the same disturbance and reference conditions. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical validation study

full rationale

The paper presents an empirical implementation study: a Simscape nonlinear model is built from standard multibody dynamics, cascade PID loops are tuned and applied in simulation and on Arduino hardware, and results (stabilization success, gain differences, disturbance response) are reported directly from those runs with explicit caveats on noise/friction. No load-bearing derivation, parameter fit renamed as prediction, self-citation chain, or ansatz is invoked; the central claims rest on independent simulation outputs and physical measurements rather than reducing to the inputs by construction. This is the expected non-circular outcome for an experimental control paper.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The study depends on empirically tuned controller parameters and modeling assumptions about unmodeled effects like friction.

free parameters (1)

PID controller gains
Inner and outer loop PID parameters are tuned to achieve stabilization in simulation and adjusted for experiment.

axioms (2)

domain assumption Nonlinear dynamics of the cart-pendulum system can be accurately modeled in Simscape Multibody
Basis for simulation model development.
domain assumption Sensor measurements provide sufficient feedback for real-time control
Used in experimental setup with encoder and ultrasonic sensor.

pith-pipeline@v0.9.0 · 5494 in / 1290 out tokens · 52302 ms · 2026-05-11T02:24:23.626366+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

[1]

A comparison study for control and stabilisation of inverted pendulum on inclined surface (IPIS) using PID and fuzzy controllers,

A. Kharola, P. Patil, S. Raiwani, and D. Rajput, "A comparison study for control and stabilisation of inverted pendulum on inclined surface (IPIS) using PID and fuzzy controllers," Perspectives in Science, vol. 8, pp. 187–190, 2016. [2] S. Irfan, L. Zhao, S. Ullah, A. Mehmood, and M. F. U. Butt, "Control strategies for inverted pendulum: A comparative ana...

work page 2016
[2]

Modeling of inverted pendulum system with gravitational search algorithm optimized controller,

M. Magdy, A. El Marhomy, and M. A. Attia, "Modeling of inverted pendulum system with gravitational search algorithm optimized controller," Ain Shams Engineering Journal, vol. 10, no. 1, pp. 129–149, 2019. [11] H. N. Binh, D. T. Dinh, and A. D. Cong, "Optimization of linear quadratic regulator for reaction wheel inverted pendulum using particle swarm optim...

work page 2019