PID control

In this paper we investigate the stability and the onset of chaotic oscillations around the pointing-up position for a simple inverted pendulum that is driven by a control torque and is harmonically excited in the vertical and horizontal directions. The driven control torque is defined as a proportional plus integral plus derivative (PID) control of the deviation angle with respect to the pointing-down equilibrium position. The parameters of the PID controller are tuned by using the Routh criterion to obtain a stable weak focus around the pointing-up position, whose stability is investigated by using the normal form theory. The normal form theory is also used to deduce a simplified mathematical model that can be resolved analytically and compared with the numerical simulation of the complete mathematical model. From the harmonic prescribed motions for the pendulum base, necessary conditions for chaotic motion are deduced by means of the Melnikov function. When the pendulum is close to the unstable pointing-up position, the PID parameters are changed and the chaotic motion is destroyed, which is achieved by employing very small control signals even in the presence of random noise. The results of the analytical calculations are verified by full numerical simulations.

Pump-charged water tanks are common in industrial utilities, yet the pressure and level inside them are seldom regulated in a continuous, closed-loop manner. This work develops and evaluates a microcontroller-resident controller for an open-top, pump-charged 1 m³ water tank in which both the control law and the measurement filter run entirely as firmware. A proportional-integral-derivative (PID) algorithm is recast in discrete time using a Type-A formulation, with the integral term approximated by the trapezoidal rule and the derivative term by a backward difference, so that it executes directly on an Arduino Uno. The manipulated variable is a self-made servo valve placed at the tank outlet, which throttles the outflow while the pump supplies a constant inflow. The process variable is the water pressure reported by an Endress+Hauser Cerabar M PMC-41 industrial transmitter (4-20 mA, spanned to 0-7 kPa) and converted to a 1-5 V Arduino input by an XY-ITOV module; through the hydrostatic relation P = ρgh this pressure maps directly onto a water level of 0-71.379 cmH₂O, so a single transmitter regulates both pressure and level. As the raw transmitter reading was heavily corrupted by noise, a first-order infinite-impulse-response (IIR) filter was derived from the discretised RC equation and tuned from a measured noise spectrum; the cutoff was placed at ωc ≈ 1 rad/s-about a decade above the process band (≈0.1 rad/s) so the level signal passes almost untouched, and about two decades below the dominant 105 rad/s noise. A frequency-response analysis confirms that this setting rejects the noise by roughly 40 dB (a factor of about 100) while adding only a few degrees of phase lag in the process band, so the fast closed-loop response is preserved. Initial gains were taken from the Ziegler-Nichols reaction-curve rule applied to an identified first-order-plus-dead-time model (L = 0.30 s, T = 9.94 s) and refined with standard rule-based steps. Multi-set-point simulations at 25, 50, 75 and 100 % of span show that, because the rise is limited by the fixed pump inflow (the outlet valve saturates fully closed while the tank fills), the time to reach the set point is essentially unchanged by tuning, whereas the final controller (Kp = 5000, Ti = 300000, Td = 0.15) removes the 33-37 % Ziegler-Nichols overshoot and shortens the settling time several-fold. At the 75 % set point the final loop produced a 9.25 s rise time, a 9.98 s settling time, zero overshoot and a 0.03 kPa (≈0.31 cmH₂O) steady-state error, and it held the set point under load disturbances. Because the chosen integral time is very large, the loop is effectively proportional-dominant; the small residual error follows from the high proportional gain and is of the order of the transmitter's own resolution. A damping-ratio analysis confirms that the tuning moves the loop from underdamped (ζ ≈ 0.30) towards over-damped, matching the observed overshoot. The study shows that a fully embedded discrete controller with in-software filtering is sufficient for accurate, robust water-pressure and level regulation on commodity hardware.

The Archimedes Wave Swing (AWS) is a a fullysubmerged Wave Energy Converter (WEC), that is to say, a device that converts the kinetic energy of sea waves into electricity. A first prototype of the AWS has already been built and tested. This paper presents simulation results of the performance of several control strategies applied to this device, including PID control, reactive control, phase and amplitude control, latching control, feedback linearisation control, internal model control, switching control, and combinations thereof. Linear, white-box nonlinear, and neural network models were employed. Significant (above threefold) increases in yearly energy production were found to be possible with properly designed control strategies.

Shape Memory Alloy (SMA) actuators are attractive for wearable hand rehabilitation due to their high power-toweight ratio, silent operation, and muscle-like contraction behavior; however, their limited stroke and slow thermal recovery restrict multi-finger actuation in compact gloves. Differential mechanisms that enable one actuator to drive multiple fingers are common in motor-driven hands but remain rare in SMA-based wearable gloves due to force sharing, thermal, and spatial constraints. This study presents a Wearable Dual-Finger Actuation System (W-DFAS) integrating DFAM_6X stroke amplification, a double U-shaped parallel SMA layout, and a hybrid recovery approach combining elastic elements, a passive spring, and PWM-controlled forced-air cooling. Under PWM control at 2.2 A for 1 s, the glove achieved maximum flexion with coordinated MCP-PIP-DIP bending across all four fingers, and total bending angles exceeded 200 • for the index/middle and 190 • for the ring/little. DFAM transmission analysis showed a fixed experimental gain of 3.19X, reducing required actuator stroke by 68.7% and enabling full-range postures with short SMA strokes (e.g., 12.0 mm at 100% PWM), while reducing required SMA length from ~ 958 mm (no DFAM) to 300 mm (with DFAM). Forced convection reduced extension recovery to ~ 7 s, enabling ~ 7 cycles/min for repetitive rehabilitation tasks. Grasping trials across cylindrical, spherical, box-shaped, and irregular objects demonstrated stable manipulation of ~ 20-400 g items, supporting ADL-oriented rehabilitation.

This Paper presents a comparative study of Genetic Algorithm method (GA) and Particle swarm optimization (PSO) method to determine the optimal proportional-integral (PI) and proportional-integral-derivative (PID) controller parameters, for speed control of a Field Oriented Control (FOC) induction motor. The FOC induction motor has been modeled in MATLAB (SIMULINK); the GA and PSO algorithm has been programmed and implemented in MATLAB. Comparing with traditional Ziegler-Nicholson method and the evolutionary algorithms (EA), it has been observed that during optimizing the controller parameters of a FOC IM drive with PSO the performance of the controller is improved for the step input in speed control as well as for speed tracking problem more efficiently, than Ziegler – Nicholson method and EAs.

This paper considers the synthesis of linear parameter-varying controllers based on dilated linear matrix inequalities (LMIs). It is an extension of robust output feedback dynamic controller synthesis based on dilated LMIs. The parameters are assumed to vary inside a convex polytope. Introducing a slack variable allows the separation between system matrices and a Lyapunov matrix and enables the use of a parameter-dependent Lyapunov function. The linear parameter-varying controller obtained by the proposed method does not require a bound on the rate of change of variation of the scheduling parameters in real time, which make the linear parameter-varying controller synthesis approach more practical. The main idea is to have a simple less conservative method based on a parameter-dependent Lyapunov function so that to apply it experimentally. The efficiency of the method is illustrated with experimental results on an Arm-Driven Inverted Pendulum.

Abstract— Most control engineering problems are character-ized by several, often contradicting, objectives, which have to be satisfied simultaneously. Two widely used methods for finding the optimal solution to such problems are aggregating to a single criterion, and ...

In modern vehicles, Autonomous Driving Systems (ADSs) are designed to operate partially or fully without human intervention. The ADS pipeline comprises multiple layers, including sensors, perception, localization, mapping, path planning, and control. The Robot Operating System (ROS) is a widely adopted framework that supports the modular development and integration of these layers. Among them, the path-planning and control layers remain particularly challenging due to several limitations. Classical path planners often struggle with non-smooth trajectories and high computational demands. Meta-heuristic optimization algorithms have demonstrated strong theoretical potential in path planning; however, they are rarely implemented in real-time ROS-based systems due to integration challenges. Similarly, traditional PID controllers require manual tuning and are unable to adapt to system disturbances. This paper proposes a ROS-based ADS architecture composed of eight integrated nodes, designed to address these limitations. The path-planning node leverages a meta-heuristic optimization framework with a cost function that evaluates path feasibility using occupancy grids from the Hector SLAM and obstacle clusters detected through the DBSCAN algorithm. A dynamic goal-allocation strategy is introduced based on the LiDAR range and spatial boundaries to enhance planning flexibility. In the control layer, a modified Pure Pursuit algorithm is employed to translate target positions into velocity commands based on the drift angle. Additionally, an adaptive PID controller is tuned in real time using the Differential Evolution (DE) algorithm, ensuring robust speed regulation in the presence of external disturbances. The proposed system is practically validated on a four-wheel differential drive robot across six scenarios. Experimental results demonstrate that the proposed planner significantly outperforms state-of-the-art methods, ranking first in the Friedman test with a significance level less than 0.05, confirming the effectiveness of the proposed architecture.

Pill control loops are becoming quite common in the commercial, institutional, and industrial HVAC industry. Proper application and tuning of this control algoritlun can bring many efficiency and performance benefits with it. However, improper applications, lack of understanding and poor tuning of these loops are often the root cause behind many commissioning problems. This paper will discuss the background and theory behind Pill and why it offers certain advantages from a precision and energy conservation standpoint. It will also look at when the algoritlun should and should not be applied. Finally, it would look at how to set up, verify and address control loop tuning issues based on field experience and the work of David W. St. Gair.

An inverted pendulum is a pendulum - a free body hung from a fix point and can swing freely in all directions – that has its center of mass above its pivot point. Unlike regular pendulum which is inherently stable, an inverted pendulum is inherently unstable and must be actively balanced in order to remain upright by applying some force at the pivot point, thus moving the pivot point horizontally as a feedback system. The pivot point is moved using a simple vehicle consisting of two wheels that moves freely in one direction. The feedback control to move the pivot point horizontally is a sensor system consisting of solid state accelerometer and gyroscope. The accelerometer will detect the angle of the inverted pendulum device and the gyroscope will detect the rate of rate of change of angle and therefore measure the angular velocity. The vehicle robot is a two-wheel vehicle which is controlled independently using two independent DC motor. The DC motors are controlled by a microproces...

We present the first application of spiking neural networks (SNNs) to tokamak plasma position control and provide a rigorous head-to-head benchmark of four controller architectures-classical proportional-integral-derivative (PID), Riccatibased H∞ robust control, nonlinear model predictive control (NMPC) with JAX auto-differentiation, and a Nengo-based SNN with leaky integrate-and-fire (LIF) neurons-evaluated on an identical nonlinear tokamak flight simulator with stochastic perturbations. Over a 400-episode stress-test campaign (100 episodes per controller, 3,000 timesteps each), the SNN achieves a 0% disruption rate with energy efficiency of 0.994 and median per-step latency of 17.1 ms on a CPU-hosted Nengo simulatormatching PID stability while offering a direct pathway to sub-microsecond inference on neuromorphic hardware (Intel Loihi 2, FPGA). The H∞ controller, synthesised for a linearised two-state vertical stability model, achieves 100% disruption rate under nonlinear conditions, quantifying the robustness gap that motivates neural approaches. The hardware-in-the-loop control pipeline achieves 25.2 μs median total-loop latency, 40× below the ITER Plasma Control System design target of 1 ms. All code, data, and benchmark scripts are released as open-source software (GNU AGPL v3) with a persistent DOI.

This article presents a feedback linearization control of a distributed solar collector field, which main purpose is to heat a fluid using the energy provided by the solar irradiation. The control objective is to track an outlet temperature reference manipulating the fluid flow trying to attenuate the effect of disturbances (mainly radiation and inlet temperature). A feedback linearization technique has been developed and implemented to control this nonlinear plant by merging both feedforward and feedback control. The design of the feedback controller is performed based on a linear simplified version of the system. Experiments in the real plant are shown.

A structure based on a smart material and a PID control loop is presented in this paper. A glass fiber reinforced plastic material is instrumented with Fiber Bragg Gratings (FBG) and Shape Memory Alloy (SMA) actuators. The smart material and the smart structure are both successfully checked by being subjected to different operational conditions at the laboratory. Very good responses are obtained under both slow and quicker varying conditions.

The paper presents a digital control application, in which a tuning method is proposed for DC motors, using DSP from Texas Instruments (TI). Experimental application for the DC motor illustrates the effectiveness and the simplicity of the proposed method for controller design. The control algorithm for the drive application runs on a TMS320F2812 DSP. Once the desired functionality has been captured and simulated, using MATLAB/Simulink/Embedded Target for TI C2000 DSP environment can be generated code for the DSP. All task assignments to processor are automatically made by the software. The DC Motor is driven by pulse width modulated (PWM) signals generated by the DSP.

Bronchopulmonary dysplasia (BPD) is a form of chronic lung disease that develops in neonates as a consequence of preterm birth, arrested fetal lung development, and inflammation. The incidence of BPD remains on the rise as a result of increasing survival of extremely preterm infants. Severe BPD contributes to significant health care costs and is associated with prolonged hospitalizations, respiratory infections, and neurodevelopmental deficits. In this study, we aimed to detect novel biomarkers of BPD severity. We collected tracheal aspirates (TAs) from preterm babies with mild/moderate (n = 8) and severe (n = 17) BPD, and we profiled the expression of 1048 miRNAs using a PCR array. Associations with biological pathways were determined with the Ingenuity Pathway Analysis (IPA) software. We found 31 miRNAs differentially expressed between the two disease groups (2-fold change, false discovery rate (FDR) < 0.05). Of these, 4 miRNAs displayed significantly higher expression levels, and 27 miRNAs had significantly lower expression levels in the severe BPD group when compared to the mild/moderate BPD group. IPA identified cell signaling and inflammation pathways associated with miRNA signatures. We conclude that TAs of extremely premature infants contain miRNA signatures associated with severe BPD. These may serve as potential biomarkers of disease severity in infants with BPD.

This work deals with the partial synchronization problem of two different chaotic oscillators considering model uncertainties in the slave system via control approach. The slave system is forced to follow the master signal via a linearizing controller based on model uncertainty reconstructor which leads to proportional-integral-derivative (PID) control structure. This reconstructor is related with a proportional-derivative (PD) reduced-order observer, it would be considered as a sub-slave system for the original slave of the synchronization procedure. The asymptotic performance of the synchronization methodology is proven via the dynamic of the synchronization error. Numerical experiment illustrates the closed-loop behavior of the proposed methodology.

In this study, a chattering free sliding mode controller (SMC) is designed for the control of MEM comb drives. Due to the highly nonlinear structure of the electrostatic comb drive, a robust nonlinear control approach is demonstrated to be more suitable for the control of such systems over linear control methods, particularly when considering issues of durability and reliability. The obtained simulation results are compared with those of a PID controller and it has been concluded that the reliability of comb drive can be improved using the developed SMC.

In this work we focus on the study of limit cycles that appear in a control scheme which is based on the use of a PI controller with an event-based send-on-delta sampling (SOD), which can be used to sample either the process variable or the control variable. We use an algorithm to calculate the limit cycles properties and then we compare the results obtained in simulations with experiments performed on a real plant, a distributed solar collector field at the Solar Platform of Almería (PSA, Spain). The process is identified as a first order plus time delay (FOPTD). Practical issues, such as the implementation of an anti-windup mechanism and a bumpless transfer between the manual and automatic mode are also addressed.

this paper introduces a method to design a robust adaptive predictive control based on Fuzzy model. The plant to be used as predictive model is simulated by Takagi-Sugeno Fuzzy Model, and the optimization problem is solved by a Genetic Algorithms or Branch and Bound. The method to tune parameters of the model predictive controller based on Lyapunov stability theorem is presented in this paper to bring higher control performance and guaranty Global Asymptotical Stable (GAS) for the closedloop system. This method is used for nonlinear systems with non-minimum phase (CSTR), uncertain dynamical systems and nonlinear DC motor. The simulation results for the Continuous Stirrer Tank Reactor (CSTR), nonlinear uncertain dynamical system and nolinear DC motor are used for verifying the proposal method.

Recently, Kikuuwe and Fujimoto have introduced Proxy-Based Sliding Mode Control. It combines responsive and accurate tracking during normal operation with smooth, slow recovery from large position errors that can sometimes occur after abnormal events. The method can be seen as an extension to both conventional PID control and sliding mode control. In this paper, Proxy-Based Sliding Mode Control is used to control a 2-DOF planar manipulator actuated by Pleated Pneumatic Artificial Muscles (PPAMs). The principal advantage of this control method is increased safety for people interacting with the manipulator. Two different forms of Proxy-Based Sliding Mode Control were implemented on the system, and their performance was experimentally evaluated. Both forms performed very well with respect to safety. Good tracking was also obtained, especially with the second form.

Estimating the force exerted by a pneumatic muscle actuator by measuring its gauge pressure is challenging since hysteresis is almost always present. This paper investigates the hysteresis phenomenon in Pleated Pneumatic Artificial Muscles, which is found to be largely independent of gauge pressure. A Preisach based hysteresis model that can cope with the specific shape of the force-contraction characteristic of pneumatic muscles is proposed, and its results are presented.