Closed-loop Control Algorithm Research Articles

Epidural Spinal Cord Recordings (ESRs): sources of neural-appearing artifact in stimulation evoked compound action potentials.

Evoked compound action potentials (ECAPs) measured during epidural spinal cord stimulation (SCS) can help elucidate fundamental mechanisms for the treatment of pain and inform closed-loop control of SCS. Previous studies have used ECAPs to characterize neural responses to various neuromodulation therapies and have demonstrated that ECAPs are highly prone to multiple sources of artifact, including post-stimulus pulse capacitive artifact, electromyography (EMG) bleed-through, and motion artifact. However, a thorough characterization has yet to be performed for how these sources of artifact may contaminate recordings within the temporal window commonly used to determine activation of A-beta fibers in a large animal model.
We characterized sources of artifacts that can contaminate the recording of ECAPs in an epidural SCS swine model using the Abbott Octrode™ lead. Spinal ECAP recordings can be contaminated by capacitive artifact, short latency EMG from nearby muscles of the back, and motion artifact. The capacitive artifact can appear nearly identical in duration and waveshape to evoked A-beta responses. EMG bleed-through can have phase shifts across the electrode array, similar to the phase shift anticipated by propagation of an evoked A-beta fiber response. The short latency EMG is often evident at currents similar to those needed to activate A-beta fibers associated with the treatment of pain. Changes in CSF between the cord and dura, and motion induced during breathing created a cyclic oscillation in all evoked components of recorded ECAPs. 
Controls must be implemented to separate neural signal from sources of artifact in SCS ECAPs. We suggest experimental procedures and reporting requirements necessary to disambiguate underlying neural response from these confounds. These data are important to better understand the framework for recorded ESRs, with components such as ECAPs, EMG, and artifacts, and have important implications for closed-loop control algorithms to account for transient motion such as postural changes and cough.

Robust Control of Exo-Abs, a Wearable Platform for Ubiquitous Respiratory Assistance

Abstract Existing noninvasive breathing assist options compatible with out-of-hospital settings are limited and not appropriate to enable essential everyday activities, thereby deteriorating the quality of life. In our prior work, we developed the Exo-Abs, a novel wearable robotic platform for ubiquitous assistance of respiratory functions in patients with respiratory deficiency. This paper concerns the development of a model-based closed-loop control algorithm for the Exo-Abs to automate its breathing assistance. To facilitate model-based development of closed-loop control algorithms, we developed a control-oriented mathematical model of the Exo-Abs. Then, we developed a robust absolutely stabilizing gain-scheduled proportional-integral control algorithm for automating the breathing assistance with the Exo-Abs, by (i) solving a linear matrix inequality formulation of the Lyapunov stability condition against sector-bounded uncertainty and interindividual variability in the mechanics of the abdomen and the lungs and (ii) augmenting it with a heuristic yet effective gain scheduling algorithm. Using in silico evaluation based on realistic and plausible virtual patients, we demonstrated the efficacy and robustness of the automated breathing assistance of the Exo-Abs under a wide range of variability in spontaneous breathing and Exo-Abs efficiency: the absolutely stabilizing gain-scheduled proportional-integral control resulted in small exhalation trajectory tracking error (<30 ml) with smooth actuation, which was superior to (i) its proportional-integral control counterpart in tracking efficacy and to (ii) its proportional-integral-derivative control counterpart in chattering.

Solutions for the Implementation of Algorithms for Closed-Loop Control of the Frequency and Power of Large Power Plant Units Comprising Once-Through Boilers

Solutions for the Implementation of Algorithms for Closed-Loop Control of the Frequency and Power of Large Power Plant Units Comprising Once-Through Boilers

A GENERATIVE APPROACH TO TESTING THE PERFORMANCE OF PHYSIOLOGICAL CONTROL ALGORITHMS.

Physiological closed-loop control algorithms play an important role in the development of autonomous medical care systems, a promising area of research that has the potential to deliver healthcare therapies meeting each patient's specific needs. Computational approaches can support the evaluation of physiological closed-loop control algorithms considering various sources of patient variability that they may be presented with. In this paper, we present a generative approach to testing the performance of physiological closed-loop control algorithms. This approach exploits a generative physiological model (which consists of stochastic and dynamic components that represent diverse physiological behaviors across a patient population) to generate a select group of virtual subjects. By testing a physiological closed-loop control algorithm against this select group, the approach estimates the distribution of relevant performance metrics in the represented population. We illustrate the promise of this approach by applying it to a practical case study on testing a closed-loop fluid resuscitation control algorithm designed for hemodynamic management. In this context, we show that the proposed approach can test the algorithm against virtual subjects equipped with a wide range of plausible physiological characteristics and behavior, and that the test results can be used to estimate the distribution of relevant performance metrics in the represented population. In sum, the generative testing approach may offer a practical, efficient solution for conducting pre-clinical tests on physiological closed-loop control algorithms.

Adaptive Disturbance Suppression Method for Servo Systems Based on State Equalizer.

Disturbances in the aviation environment can compromise the stability of the aviation optoelectronic stabilization platform. Traditional methods, such as the proportional integral adaptive robust (PI + ARC) control algorithm, face a challenge: once high-frequency disturbances are introduced, their effectiveness is constrained by the control system's bandwidth, preventing further stability enhancement. A state equalizer speed closed-loop control algorithm is proposed, which combines proportional integral adaptive robustness with state equalizer (PI + ARC + State equalizer) control algorithm. This new control structure can suppress high-frequency disturbances caused by mechanical resonance, improve the bandwidth of the control system, and further achieve fast convergence and stability of the PI + ARC algorithm. Experimental results indicate that, in comparison to the control algorithm of PI + ARC, the inclusion of a state equalizer speed closed-loop compensation in the model significantly increases the closed-loop bandwidth by 47.6%, significantly enhances the control system's resistance to disturbances, and exhibits robustness in the face of variations in the model parameters and feedback sensors of the control object. In summary, integrating a state equalizer speed closed-loop with PI + ARC significantly enhances the suppression of high-frequency disturbances and the performance of control systems.

Dynamic feature-based deep reinforcement learning for flow control of circular cylinder with sparse surface pressure sensing

This study proposes a self-learning algorithm for closed-loop cylinder wake control targeting lower drag and lower lift fluctuations with the additional challenge of sparse sensor information, taking deep reinforcement learning (DRL) as the starting point. The DRL performance is significantly improved by lifting the sensor signals to dynamic features (DFs), which predict future flow states. The resulting DF-based DRL (DF-DRL) automatically learns a feedback control in the plant without a dynamic model. Results show that the drag coefficient of the DF-DRL model is 25 % less than the vanilla model based on direct sensor feedback. More importantly, using only one surface pressure sensor, DF-DRL can reduce the drag coefficient to a state-of-the-art performance of approximately 8 % at Reynolds number $(Re) = 100$ and significantly mitigates lift coefficient fluctuations. Hence, DF-DRL allows the deployment of sparse sensing of the flow without degrading the control performance. This method also exhibits strong robustness in flow control under more complex flow scenarios, reducing the drag coefficient by 32.2 % and 46.55 % at $Re =500$ and 1000, respectively. Additionally, the drag coefficient decreases by 28.6 % in a three-dimensional turbulent flow at $Re =10\,000$ . Since surface pressure information is more straightforward to measure in realistic scenarios than flow velocity information, this study provides a valuable reference for experimentally designing the active flow control of a circular cylinder based on wall pressure signals, which is an essential step toward further developing intelligent control in a realistic multi-input multi-output system.

Design of real time closed loop control in hybrid energy system using cascaded converters: a dynamic solution for high power applications

ABSTRACT This paper presents a Hybrid Renewable Energy system combining multiple sources of renewable energy, such as PV, Wind, and energy storage devices, to provide a reliable and sustainable power supply. Cascaded converters are used to efficiently transform and manage the energy from these sources. To achieve optimal performance and reliable operation, a real-time closed-loop control algorithm is designed and implemented for the cascaded converter. The control algorithm facilitates the smooth integration of energy from various renewable sources, optimizing the utilization of available resources and ensuring a consistent power supply. The algorithm maximizes the energy conversion efficiency of the cascaded converter, reducing energy losses and minimizing waste. It also optimizes the integration of renewable sources, regulates output parameters, and ensures efficient energy conversion.

Fault-tolerant control for satellite autonomous rendezvous with quality characteristics and actuator uncertainties

An autonomous fault detection and fault-tolerant control solution combining Model Predictive Control (MPC) and Label Distributed Learning (LDL) is developed for the position tracking and attitude synchronization problems in autonomous satellite rendezvous and docking. The proposed algorithm can deal with center of mass (CM) variations and time-varying mass characteristics due to satellite fuel consumption, actuator saturation and fault, and external disturbances. Firstly, a six-degree-of-freedom (6-DOF) satellite translation-rotation coupling model was established to express the relative motion between the satellite and the target, taking the above factors into account. Subsequently, an on-board autonomous closed-loop fault-tolerant control algorithm using MPC is proposed, in which an LDL-based fault detection mechanism is embedded. The scheme specifies that propulsion faults are estimated by calculating the difference between the MPC's prediction of the satellite's future state and the measured change in the actual state. And the mapping matrix between the commanded force/torque and the actual force of the propulsion system is updated in real time to achieve autonomous fault detection and compensation on board the satellite. Among them, the LDL-based fault detection scheme is trained offline. It requires only simple matrix operations for on-orbit use, which is low-cost and suitable for resource-limited space environments. The additional creation of a time-varying disturbance observer allows the estimation and compensation of unmodelled errors and external disturbances. The stability of the proposed fault-tolerant control algorithm is rigorously demonstrated using Lyapunov analysis. Finally, numerical simulations show that the proposed method can successfully achieve autonomous satellite docking under different combinations of thruster faults.

Organ Neuroprosthetics: Connecting Transplanted and Artificial Organs with the Nervous System.

Implantable neural interfaces with the central and peripheral nervous systems are currently used to restore sensory, motor, and cognitive functions in disabled people with very promising results. They have also been used to modulate autonomic activities to treat diseases such as diabetes or hypertension. Here, this study proposes to extend the use of these technologies to (re-)establish the connection between new (transplanted or artificial) organs and the nervous system in order to increase the long-term efficacy and the effective biointegration of these solutions. In this perspective paper, some clinically relevant applications of this approach are briefly described. Then, the choices that neural engineers must implement about the type, implantation location, and closed-loop control algorithms to successfully realize this approach are highlighted. It is believed that these new "organ neuroprostheses" are going to become more and more valuable and very effective solutions in the years to come.

Firmware development for the fibre-optic seismometer based on FOG

The main goal of the article is to present the concept of using a simulation environment when designing an advanced fibre-optic seismometer (FOS) using a field-programmable gate array (FPGA) computing system. The first part of the article presents the advanced requirements regarding the FOS principle of operation, as well as the measurement method using a closed-loop operation. The closed-loop control algorithm is developed using the high-level language C++ and then it is synthesised into an FPGA. The following part of the article describes the simulation environment developed to test the operation of the control algorithm. The environment includes a model of components of the measurement system, delays, and distortions in the signal processing path, and some of the measurement system surroundings. The article ends with a comparison of simulation data with measurements. The obtained results are consistent and prove correctness of the methodology adopted by the authors.

Fuzzy Neural Network PID-Based Constant Deceleration Control for Automated Mine Electric Vehicles Using EMB System.

It is urgent for automated electric transportation vehicles in coal mines to have the ability of self-adaptive tracking target constant deceleration to ensure stable and safe braking effects in long underground roadways. However, the current braking control system of underground electric trackless rubber-tired vehicles (UETRVs) still adopts multi-level constant braking torque control, which cannot achieve target deceleration closed-loop control. To overcome the disadvantages of lower safety and comfort, and the non-precise stopping distance, this article describes the architecture and working principle of constant deceleration braking systems with an electro-mechanical braking actuator. Then, a deceleration closed-loop control algorithm based on fuzzy neural network PID is proposed and simulated in Matlab/Simulink. Finally, an actual brake control unit (BCU) is built and tested in a real industrial field setting. The test illustrates the feasibility of this constant deceleration control algorithm, which can achieve constant decelerations within a very short time and maintain a constant value of -2.5 m/s2 within a deviation of ±0.1 m/s2, compared with the deviation of 0.11 m/s2 of fuzzy PID and the deviation of 0.13 m/s2 of classic PID. This BCU can provide electric and automated mine vehicles with active and smooth deceleration performance, which improves the level of electrification and automation for mine transport machinery.

Active vibration control of rotating smart bidirectional FGPTC subjected to internal mechanical shock

This study considers the active vibration control of a sandwich truncated cone, whose intermediate layer is made of bidirectional functionally graded (FG) porous material bonded with integrated piezoelectric actuator and sensor layers on its outer and inner surfaces. The material properties of the bidirectional functionally graded porous truncated cone (FGPTC), with even and uneven porosity distributions along the length and thickness directions, are changed using a power law function. The governing motion equations utilize the two-dimensional (2D) axisymmetric theory of elasticity rather than simple shell theories. The solving of the governing motion equations is accomplished through the utilization of graded finite element and Newmark methods. The study investigates the impact of dimensions, parameters, and porosity types on transient response behavior, including the semi-vertex angle and the ratio of truncated cone length to outer radius. Furthermore, the effects of power index, porosity volume fractions, rotational velocities, and boundary conditions are examined. Active vibration control (AVC) of the piezoelectric FGPTC is achieved by employing a closed-loop control algorithm based on velocity feedback. Several numerical simulations are conducted to evaluate the effectiveness of the proposed active vibration control system in reducing structural vibrations. The results demonstrate significant reductions in vibration amplitudes and improved structural stability achieved through the active control approach.

High-precision servo control design and optimization for dicing semiconductor wafer

The dicing of semiconductor wafers is an essential component for fabricating electronic circuits. A servo control approach with high-precision and stability was designed to enhance the positioning accuracy and stability for dicing semiconductor wafers. The principal control and dicing processes were studied. The High Definition closed-loop control algorithm was designed, and the control parameters were optimized. The control performance was enhanced using the PID + Feedforward + NOTCH filter control algorithm. The error detection of linear and rotation axes was designed to compensate servo axis errors by using the laser interferometer and control card. After error compensation, the positioning accuracy and repeatability of the Y-axis were 2.031 μm and 1.889 μm. That of the C-axis were 0.00423°, and 0.00347°. The dicing experiment revealed the maximum chipping width was <10 μm and the dicing channel width was <42 μm. The designed servo control system ensured the high-precision and stable dicing of semiconductor chips.

Sensors Based Optimized Closed Loop Control Algorithm to Minimize Hypoglycemia/Hyperglycemia using 4-Variate Time Series Data

Sensors Based Optimized Closed Loop Control Algorithm to Minimize Hypoglycemia/Hyperglycemia using 4-Variate Time Series Data

Soft modularized robotic arm for safe human–robot interaction based on visual and proprioceptive feedback

This study proposes a modularized soft robotic arm with integrated sensing of human touches for physical human–robot interactions. The proposed robotic arm is constructed by connecting multiple soft manipulator modules, each of which consists of three bellow-type soft actuators, pneumatic valves, and an on-board sensing and control circuit. By employing stereolithography three-dimensional (3D) printing technique, the bellow actuator is capable of incorporating embedded organogel channels in the thin wall of its body that are used for detecting human touches. The organogel thus serves as a soft interface for recognizing the intentions of the human operators, enabling the robot to interact with them while generating desired motions of the manipulator. In addition to the touch sensors, each manipulator module has compact, soft string sensors for detecting the displacements of the bellow actuators. When combined with an inertial measurement unit (IMU), the manipulator module has a capability of estimating its own pose or orientation internally. We also propose a localization method that allows us to estimate the location of the manipulator module and to acquire the 3D information of the target point in an uncontrolled environment. The proposed method uses only a single depth camera combined with a deep learning model and is thus much simpler than those of conventional motion capture systems that usually require multiple cameras in a controlled environment. Using the feedback information from the internal sensors and camera, we implemented closed-loop control algorithms to carry out tasks of reaching and grasping objects. The manipulator module shows structural robustness and the performance reliability over 5,000 cycles of repeated actuation. It shows a steady-state error and a standard deviation of 0.8 mm and 0.3 mm, respectively, using the proposed localization method and the string sensor data. We demonstrate an application example of human–robot interaction that uses human touches as triggers to pick up and manipulate target objects. The proposed soft robotic arm can be easily installed in a variety of human workspaces, since it has the ability to interact safely with humans, eliminating the need for strict control of the environments for visual perception. We believe that the proposed system has the potential to integrate soft robots into our daily lives.

Double closed-loop feedback control strategy for enhanced external counterpulsation to regulate hemodynamic response of human common carotid artery

Enhanced external counterpulsation (EECP) is a mechanical therapy for the clinical management of ischemic cardio-cerebrovascular diseases. Applying different EECP modes to different patients would be based on the experience of physicians. Existing hemodynamic models could describe the quantitative relationship between different EECP modes and hemodynamic parameters of specific parts of human blood circulatory system. However, currently there is no closed-loop control system available for precisely, personally, and intelligently performing the EECP. Therefore, to significantly improve the clinical benefits of rehabilitation treatment of ischemic cardio-cerebrovascular diseases with the EECP, this study developed a double closed-loop physiological control algorithm for the EECP device. Firstly, a detailed lumped parameter model describing the hemodynamics of human blood circulatory system was updated based on the available models; then the EECP device was coupled to it and the updated model was tested with the clinical data; finally, a double closed-loop feedback control strategy for precise regulation of the carotid hemodynamic response by the EECP was proposed. The control objectives were to maintain the mean arterial pressure and EECP pressure amplitude of patients with two gain-scheduled proportional-integral (PI) controllers. In-silico results showed that the clinical data can prove the accuracy of the updated model, and the appropriate EECP pressure amplitude could provide patients with the best benefits. The proposed control system could generate satisfied hemodynamic effects even with noise, demonstrating its feasibility and robustness. It is also easy to apply with high accuracy, and may be the effective solutions for developing intelligent and personalized EECP devices.

A compact fractional-order model for hypnosis in general anesthesia

The research field of clinical practice has witnessed a notable increase in the integration of information technology and control systems engineering tools and the paradigm of drug dosing management for general anesthesia is no exception. Progressing from adequate to optimal drug dosing requires suitable models for closed loop control algorithms. High order, complex parameterized models for hypnosis are available but as one cannot measure real drug concentrations, accurate modelling is not possible. Moreover, ethical limitations impose serious restrictions as to the type of excitatory signals acceptable to patient effect response evaluations. This paper proposes an innovative approach to determine fractional order models to compactly represent the dynamics inherent to the hypnosis response. A simplifying assumption is being made: instead of multi-compartmental models, a single transfer model is proposed consisting of a fractional-order dynamic that directly connects Propofol, the administered drug, and the Bispectral (BIS) index, the measure of hypnosis. The proposed model is validated against clinical data and compared to integer order models to prove its suitability. Results suggest the model may be well used with control algorithms for computerized drug dosing management.

NClSilico: A Closed-Loop neuromodulation platform in silico

The closed-loop electrophysiology is gradually applied to targeted stimulation of nervous system. According to desired neural biomarkers acquired by biological signal measurement, the stimulus pattern can be automatically adjusted with the suitable closed-loop control algorithms. Moreover, the neural computing uses the numerical computing models to simulate the structures, functions and relations of the neurons and the neural networks, as the substitute of biological brain. As the prevalence of the hardware-in-loop (HIL), the HIL closed-loop electrophysiology not only bypasses the problem of biological experiments but also makes up for the insufficient efficiency and real-time performance of software digital simulation. This paper proposes a hardware experiment platform mainly made up of TMS320F28377D digital signal processor (DSP) and AMD Ryzen 5 5600X 6-Core Processor (CPU) for closed-loop electrophysiological research. The hardware platform is programable, portable, real-time and supports the repeated experiments. Closed-loop electrophysiological experiments with different kinds of control algorithms, stimulation waveforms, feedback variables or neuron models can be implemented on the platform, it may promote the development of researches in the field of closed-loop neuroscience and biomedical engineering.

Automated oxygen delivery for preterm infants with respiratory dysfunction.

Many preterm infants require respiratory support to maintain an optimal level of oxygenation, as oxygen levels both below and above the optimal range are associated with adverse outcomes. Optimal titration of oxygen therapy for these infants presents a major challenge, especially in neonatal intensive care units (NICUs) with suboptimal staffing. Devices that offer automated oxygen delivery during respiratory support of neonates have been developed since the 1970s, and individual trials have evaluated their effectiveness. To assess the benefits and harms of automated oxygen delivery systems, embedded within a ventilator or oxygen delivery device, for preterm infants with respiratory dysfunction who require respiratory support or supplemental oxygen therapy. We searched CENTRAL, MEDLINE, CINAHL, and clinical trials databases without language or publication date restrictions on 23 January 2023. We also checked the reference lists of retrieved articles for other potentially eligible trials. We included randomised controlled trials and randomised cross-over trials that compared automated oxygen delivery versus manual oxygen delivery, or that compared different automated oxygen delivery systems head-to-head, in preterm infants (born before 37 weeks' gestation). We used standard Cochrane methods. Our main outcomes were time (%) in desired oxygen saturation (SpO2) range, all-cause in-hospital mortality by 36 weeks' postmenstrual age, severe retinopathy of prematurity (ROP), and neurodevelopmental outcomes at approximately two years' corrected age. We expressed our results using mean difference (MD), standardised mean difference (SMD), and risk ratio (RR) with 95% confidence intervals (CIs). We used GRADE to assess the certainty of evidence. We included 18 studies (27 reports, 457 infants), of which 13 (339 infants) contributed data to meta-analyses. We identified 13 ongoing studies. We evaluated three comparisons: automated oxygen delivery versus routine manual oxygen delivery (16 studies), automated oxygen delivery versus enhanced manual oxygen delivery with increased staffing (three studies), and one automated system versus another (two studies). Most studies were at low risk of bias for blinding of personnel and outcome assessment, incomplete outcome data, and selective outcome reporting; and half of studies were at low risk of bias for random sequence generation and allocation concealment. However, most were at high risk of bias in an important domain specific to cross-over trials, as only two of 16 cross-over trials provided separate outcome data for each period of the intervention (before and after cross-over). Automated oxygen delivery versus routine manual oxygen delivery Automated delivery compared with routine manual oxygen delivery probably increases time (%) in the desired SpO2 range (MD 13.54%, 95% CI 11.69 to 15.39; I2 = 80%; 11 studies, 284 infants; moderate-certainty evidence). No studies assessed in-hospital mortality. Automated oxygen delivery compared to routine manual oxygen delivery may have little or no effect on risk of severe ROP (RR 0.24, 95% CI 0.03 to 1.94; 1 study, 39 infants; low-certainty evidence). No studies assessed neurodevelopmental outcomes. Automated oxygen delivery versus enhanced manual oxygen delivery There may be no clear difference in time (%) in the desired SpO2 range between infants who receive automated oxygen delivery and infants who receive manual oxygen delivery (MD 7.28%, 95% CI -1.63 to 16.19; I2 = 0%; 2 studies, 19 infants; low-certainty evidence). No studies assessed in-hospital mortality, severe ROP, or neurodevelopmental outcomes. Revised closed-loop automatic control algorithm (CLACfast) versus original closed-loop automatic control algorithm (CLACslow) CLACfast allowed up to 120 automated adjustments per hour, whereas CLACslow allowed up to 20 automated adjustments per hour. CLACfast may result in little or no difference in time (%) in the desired SpO2 range compared to CLACslow (MD 3.00%, 95% CI -3.99 to 9.99; 1 study, 19 infants; low-certainty evidence). No studies assessed in-hospital mortality, severe ROP, or neurodevelopmental outcomes. OxyGenie compared to CLiO2 Data from a single small study were presented as medians and interquartile ranges and were not suitable for meta-analysis. Automated oxygen delivery compared to routine manual oxygen delivery probably increases time in desired SpO2 ranges in preterm infants on respiratory support. However, it is unclear whether this translates into important clinical benefits. The evidence on clinical outcomes such as severe retinopathy of prematurity are of low certainty, with little or no differences between groups. There is insufficient evidence to reach any firm conclusions on the effectiveness of automated oxygen delivery compared to enhanced manual oxygen delivery or CLACfast compared to CLACslow. Future studies should include important short- and long-term clinical outcomes such as mortality, severe ROP, bronchopulmonary dysplasia/chronic lung disease, intraventricular haemorrhage, periventricular leukomalacia, patent ductus arteriosus, necrotising enterocolitis, and long-term neurodevelopmental outcomes. The ideal study design for this evaluation is a parallel-group randomised controlled trial. Studies should clearly describe staffing levels, especially in the manual arm, to enable an assessment of reproducibility according to resources in various settings. The data of the 13 ongoing studies, when made available, may change our conclusions, including the implications for practice and research.

Three link flexible arm robust regulation via proportional retarded control scheme

In this paper, a delayed distributed proportional control is developed for a class of multiple-input-multiple-output systems in order to reduce the effects of external disturbances and uncertain dynamics. The system under consideration is a three degrees-of-freedom planar robot, consisting of an active joint driving the first link and passive flexible joints for the second and third links. The control challenge for this system is to drive the flexible arm around the desired setpoint or trajectory by controlling the first link. Actually, by using a specific Lyapunov-Krasovskii storage functional associated with a constrained optimization problem, the robustness of the proposed proportional retarded control action is achieved. This analysis, together with the attractive ellipsoid concept allows to conclude with Ultimately-Uniformly-Bounded stability. The closed-loop control algorithm is tested in numerical simulation and a comparative study with some existing recent control schemes based on the performance error is presented.