Active Control Experiments on a Smart Robotic Glass with End-Point Control for Parkinson ’ s Patients

This paper describes a robotic system that uses an actively controlled glass to help patients with tremors. End-point control is proposed for the upper part of a robotic device that becomes active in response to motion changes or vibrations of its holder. The device mechanisms, hardware, software, and sensory system are all integrated, presenting a novel robotic glass design. The control system consists of two degrees of freedom proportional – integral velocity regulators for direct current motors. These regulators are designed, implemented, and tuned to keep the robotic glass stable against changes in its position. In realizing direct current motor control, it is essential to take system constraints into consideration to develop regulators that can handle the nonlinear Coulomb friction and avoid operating in the saturation zone. This is crucial when designing, tuning, and implementing regulators for real-time applications. The computer simulations of the system, which involved developing and running all the control algorithms for real-time applications, are carried out in Matlab/Simulink. The proposed designs are validated by comparing system simulations to real-time physical experiments. The recorded results con ﬁ rmed the outstanding performance of the proposed experimental platform mechanisms and the accurate control tracking, which provides fast and precise control responses to meet the high requirements of a fast end-point control application.


Introduction
Tremors are a kind of neuromotor disorder characterized by involuntary vibrational movements in specific body parts, most notably the upper extremities. It is the most common movement disorder, interfering with daily living and physical activities and resulting in a lower quality of life [1]. Over 6 million people worldwide are affected by the disease [2]. It is suggested that end-point vibrations can be reduced when tremor patients manipulate a glass-shaped robotic device to drink the liquid. Because it uses control methods for stabilization, this smart glass is different from any other glass design. Active stabilizing technology [3], passive stabilizing technology [4], and wearable and balanced active systems [5,6] are examples of robotic applications for Parkinson's tremors. However, to the best of the knowledge of the authors, there is no design of glass with active control. In the work by Mo and Priefer [1], some medical approaches for tremor suppression are classified as electrical stimulation systems designs, wearable orthoses, assistive feeding devices, gyroscopic stabilization and haptic stimulation systems, and tremor suppression devices.
The Gyenno Spoon handheld is an assistive feeding device that consists of motors linked to a control unit. It senses adverse vibration effects and generates movements in two different directions opposite to the tremor direction [7]. Liftware Steady is another handheld device that employs a motion-generating platform equipped with accelerometers and is capable of controlling two direct current (DC) motors to move the utensil against tremors [8]. In addition to the aforementioned utensils, this work proposes a two degrees of freedom (2-DOF) actively controlled device designed for end-point control. The system consists of a holder part and an upper part, which is used as the drinking glass. It employs DC motors and an inertial measurement unit (IMU)-based sensory system. A simplified model of the DC motor dynamics is presented, and all model parameters are identified experimentally in order to design and effectively tune two proportional integral with velocity feedback (PI-V) motion regulators.
DC motors are used in various electromechanical applications, including process automation, industrial systems, robotics, etc. DC motor dynamics modeling and parameter identification are critical components of a model-based control design. The robustness, perturbation rejection, and trajectory tracking of both conventional and unconventional control methods continue to present ongoing scientific and engineering challenges [9,10]. Certain conditions must be met by position regulators in order to ensure high performance and ease the end-point steady position of the glass. In this regard, the static or Coulomb friction effects and saturation limits must be taken into account in the control design. The controller must be resistant to disturbances, changes in inertia caused by the different possible positions of the glass, the amount of liquid in the glass, and system uncertainties. The control system is required to achieve precise tracking of rapidly varying references without exhibiting any steady-state error or overshoot, as these factors contribute to increased system vibration. To enable this, a sensor system is incorporated so that it comprises signals from accelerometers and motor encoders, which can be acquired and processed as per the requirements of the system.
Previous studies suggest that tremors can be modeled as harmonic signals, with the first frequency mode being the most representative [11]. Due to the presence of noise in the signal, some control approaches utilize time-varying signal analysis to identify the tremor frequency from unknown and noisy harmonic signals and propose control methods to minimize vibration. In some cases, the tremor characteristics and previous assumptions have been leveraged to design control strategies using inverse vibrational dynamics as a forward term, in combination with proportional and derivative for an outer loop [12].
The positioning and stabilization of glass objects are maintained by a single-phase DC motor that is regulated by a controller to adjust its angular position. The control strategy used for a DC motor is contingent upon the number of phases it possesses. For effective speed and position control of DC motors, algorithms must be developed that account for the motor's specific classification. Recent research has explored innovative DC/DC buck power converter topologies aimed at improving the performance of the converter's electronics, which include the reduction of current and torque ripples, as well as noise. Furthermore, sophisticated control schemes have been proposed to address nonlinearity and uncertainty in the motor speed and position, thereby enhancing the overall stability and accuracy of the controlled system [13].
Classical control techniques, which rely on model accuracy, precise parameter identification, and complicated tuning methods, are sometimes not feasible [14]. To address these requirements, modern control, and intelligent control methods have been developed to reduce steady-state errors, improve response times, and enhance sensitivity to controller gain tuning. Traditional Ziegler and Nichols techniques are inadequate for meeting the performance criteria using the classical proportional-integral-derivative (PID) approach. However, modifications to the system structure coupled with an effective tuning approach present a viable option for obtaining a good DC motor model and precise system identification. This paper presents a comprehensive method to address these challenges.
Recent advancements in DC motor controllers have led to the development of various control techniques. These include sliding mode control, robust control approaches, and adaptive and learning control systems [15,16]. To tackle control challenges, several robust controllers have been proposed. For instance, output-feedback control schemes with innovative methods for disturbance compensation have been introduced, where the static component of friction is estimated and compensated [17,18]. Accurate model construction, parameter estimation, and tuning approaches are employed to achieve desired robust control performance. Observer-based robust controllers have also been proposed, which are robust to friction disturbance and compensate for disturbance inputs that have an impact on the observed plant through dynamic output reconstruction and error injections [19]. In their paper, Jiyang et al. [19] proposed a reduced-order extended-state observer that can estimate the states and overall disturbances of a DC motor system. To ensure robustness and stability, they employed the Lyapunov stability theory to design a control algorithm that can eliminate the effects of parameter and load torque changes. Their approach demonstrated promising results in experiments and provided an effective solution for controlling DC motors under uncertain and time-varying conditions. High-level programing using active disturbance rejection control simplifies the control architecture, and specialized observers reconstruct different types of disturbances to compensate for them using powerful computing systems like field programmable gate arrays (FPGAs) [20,21]. Generalized proportional integral controllers are 2-DOF regulators that can more easily reject DC motor disturbances, are less sensitive to changes in friction, and do not require a precise friction model [22]. Finally, FPGA-based fractional order controllers offer an alternative for designing reliable DC motor regulators, where more parameters can be used to meet various requirements, thereby improving system performance and enhancing the system's resistance to plant disturbances and uncertainties. The design of fractional order PID controllers is typically based on frequency domain performance specifications.
The advancements in hardware and computing capabilities have made it possible to employ various artificial intelligence techniques for adaptive and learning methods in DC motor controls. One such technique is adaptive backstepping control, which is used for buck DC/DC converters [23], and fuzzy logic control is used to determine optimal control parameters. Speed control is achieved through the utilization of genetic algorithms, which are used to identify the best PID gains and overcome the limitations of traditional PID tuning [24]. Furthermore, particle swarm optimization (PSO) algorithms have been investigated for tuning PID parameters, including the fractional order ones, which are effectively utilized for position and attitude tracking control of unmanned aerial vehicles [25,26]. The PSO optimization approach has been shown to be superior to traditional tuning methods in terms of control performance [27]. A combination of artificial neural networks-fuzzy and fuzzy-swarm control methods, and also various tuning methods have been developed for DC motor controllers to improve the control performances [28].
The use of PI-V for motor positioning requires an accurate estimation of the angular motor speed. This controller has a derivative gain that increases noise signals and errors. This issue can be solved by using low-pass filters before the signal is processed. In this work, the use of the 2-DOF PI-V controllers is explained by means of comparing system simulation and real-time experiment results. This paper is organized as follows: following this section, the experimental platform, the mechanism, the software and hardware requirements, the sensory system, and a reduced dynamic model of the system are described in Section 2. Section 3 proposes two PI-V controllers for driving the robotic device quickly and precisely, while Section 4 compares the results of simulation and real-time control experiments. Finally, Section 5 draws the relevant conclusions of this work.

Experimental Platform
The smart glass is a robotic device that operates in 2-DOF and moves in both azimuthal and elevation directions, creating a spherical workspace. The proposed device mechanism comprises an upper part that acts as a glass and a lower part that is used as a holder. Two sets of DC motors with reductions and incremental encoders control and move the upper part. The system's end-point position is determined using spherical coordinates, ψ and ϕ, for the azimuthal and elevation movements, respectively. The sampling time for all processes is selected as T s = 0.005 s. The sensory system uses two MPU9250 IMU sensors, four safety switches, and two encoders. The safety switches prevent unexpected events that can damage the device, stopping the overall control system. IMU sensors have a 3-axis gyroscope, an accelerometer, and a magnetometer.

DC Motor Dynamics.
A reduced DC motor dynamic model with only the motor's mechanics is used to design the 2-DOF control system. In order to obtain the DC motor's model, the system dynamics must be determined by a parameter identification method.

Generalized DC Motor Dynamic
Model. The 2-DOF control system uses reduced DC motor dynamics that can be generalized as follows: where Γ m is the motor torque, k m stands for the torque constant, and V i is the input voltage. J represents the rotor inertia, and ν is the viscous friction coefficient. Γ coul stands for the Coulomb friction [29]. The second order DC motor transfer function G s ð Þ is obtained by using Laplace transforms of both sides of (1), where A ¼ k m =J, B ¼ ν=J, G s ð Þ is simply found to be as follows: This research assumes a simple Coulomb friction model to be considered in the control design. The model includes the static friction Γ c as an estimated parameter, and the Coulomb friction Γ coul can then be represented as follows: 2.2.2. Motor Identification Method. The method of identifying a system, known as frequency sweep or chirp, is developed to accurately determine the dynamic behavior of a system through experiments [30]. This study employs the method by using quasi-sinusoidal DC motor control inputs with increasing input frequencies. The spectral range of interest is swept by chirp inputs, which provide uniform excitation by means of frequency (speed) test data. The chirp identification method is robust to uncertainties, changes in the system dynamics, and temperature conditions but requires prior knowledge of the system dynamics. A critical aspect of designing a chirp frequency identification is basically determining the minimum and maximum frequencies required, denoted as ω min and ω max , respectively.
In this research, the frequency range of sinusoidal input signals used for motor identification is determined by the bandwidth frequency of ω. A frequency sweep is performed with a lower limit of 0.1 Hz and an upper limit of 4 Hz. The motor response is measured as the angular velocity in rad/s and is proportional to the duty cycle input (0-255), as depicted in Figure 2.
The data obtained from the identification test, as depicted in Figure 2, is utilized to develop a Hammerstein-Wiener model [31]. The dynamic response of the system is characterized by a linear and a nonlinear component, which can be represented by a combination of a linear transfer function and a nonlinear function. The Hammerstein-Wiener model implements this approach by cascading static nonlinear blocks with dynamic linear blocks. The linear block may be either continuous or discrete transfer function.  Applied Bionics and Biomechanics The system model of a Hammerstein-Wiener model is shown in Figure 3, where u, ω denote the pulse-width modulation (PWM) inputs and angular speed respectively under the without nonlinear assumption ðH t; ð u; ωÞ ¼ 1). The model consists of three distinct blocks: (1) the initial block represents a nonlinear input model that corresponds to the motor's static Coulomb friction; (2) a linear component that can be represented by a transfer function with a V i input; and (3) an output nonlinear component that is assumed to be unity, as the system is not expected to exceed the saturation region. The motor model is represented by a first-order continuous-time transfer function.
To identify the Hammerstein model, the System Identification Toolbox in Matlab is employed, with sequential quadratic programing serving as the optimization search algorithm. The Coulomb friction Γ coul is modeled as a dead zone in this study, as defined in Equation (3). The static friction parameter Γ c serves as a threshold value that prevents motor motion upon the application of control effort, as illustrated in Figure 4. The threshold Γ c for identifying the static friction is determined experimentally by: (1) detecting nonzero change points in the speed response data; (2) determining the corresponding control input values at each change point; and finally; and (3) calculating the mean value of each control input. The Hammerstein-Wiener model obtained through this experimental process is utilized for simulation and controller design purposes.

DC Motor Parameters. This section presents the results of parameter identification experiments. G s
ð Þ is a first-order transfer function that includes the unknown model parameters of A and B. The system identification toolbox of Matlab is used to obtain these parameters. The toolbox gives the best-fitting values of A and B after an optimization process. A close loop controller for position tracking must be robust to parameter uncertainties and changes in the system inertia. However, a close estimation of these parameters is essential to carry out an accurate control tuning. Table 1 presents the estimated parameters for both motor joints, ψ and ϕ. The table also includes the estimated static friction Γ c and the saturation limits.
The typical magnetization curve of a motor is a graph that illustrates the relationship between the magnetic field strength and the magnetic flux. However, in this work, a reduced magnetization curve of the motor is obtained using the available input-output pairs of the setup we constructed. PWM vs. speed can be used to characterize the DC motor. This nonlinear characteristic relationship can be approximated to a linear curve that includes friction effects when PWM values are close to zero, a linear zone with the allowed   Applied Bionics and Biomechanics values of control signal, and finally, a saturation zone. The saturation starting point corresponds to the hardware computation limitations of the experimental platform in which PWM = 255 is the maximum value. The position controller must operate in the available linear zone, compensating for initial friction as much as possible, which can be accomplished by using an extra friction compensation term or managed by designing high-gain closed-loop controllers robust to this nonlinearity. The controller must not exceed the stated saturation limits. Furthermore, the system must be resistant to friction effects as the motor's angular speed approaches zero.

Motor Positioning: PI-V Control
The difference between PID and PI-V control is that PID control is based on position error, while PI-V control is based on both position and also velocity errors. In servo systems, disturbances are unexpected forces that cannot be modeled in advance. Hence, getting feedback both from position and also velocity proves to be more effective. Figure 5 shows a block diagram with the reduced model of the motor that has a friction term or disturbance Γ coul =k m , and a closed-loop PI-V regulator for each degree of freedom. The regulator gains are K p , K v , and K i known as the proportional, derivative, and integral coefficients, respectively. Regulators are tuned using pole placement and considering the system constraints such as saturation and the sampling time requirements. The control system is of order three; therefore, each control makes use of three real multiple poles s 1;2;3 ¼ −P to obtain critically damped responses, which means the faster response without any overshoot. The poles are placed considering the sampling rate T s ; and Nyquist rate that assumes P max ¼ pi=T s ð Þ rad=s. The best poles were selected by performing multiple experiments looking for the best control performance [30]. The corresponding control parameters, poles, and constraints used in simulations and real-time experiments are depicted in Table 2. The control design makes use of a feedforward term F c s ð Þ, which prefilters the system input to cancel the closed loop zeros in the system, as follows: Γ coul =k m , The final closed loop transfer function can be found to be as follows: The desired closed loop G DCL s ð Þ transfer function and controller gains are as follows: The classical PID regulators often experience the windup problem, where the integral term accumulates the error beyond a controllable range. This leads to output overshooting, control signal saturation, and increased settling time until the control signal stabilizes the system. This is particularly critical when the system is subjected to sustained disturbances or operating at the limits of the system. To avoid Motor dynamics + -  Applied Bionics and Biomechanics the wind-up phenomena, various methods can be employed, including limiting the integral term or using anti-windup mechanisms that dynamically adjust the control signal. The clamping method limits the output of the controller to a clamp value, which is the maximum control signal that the actuator can stand. If the regulator output exceeds the clamp value, the value is kept constant until the motor moves within its limits. However, the clamping method can cause the controller to become "stuck" at the clamp value, which results in slower time responses and hence reduced performances. On the other hand, back-calculation involves estimating the amount of windup and adjusting the controller output accordingly, providing better performance than the clamping method, but it is more complicated to implement. The clamping method for anti-windup is sometimes called a batch unit and can be regarded as a type of conditional integration.
In this study, we implemented the clamping method as an anti-windup mechanism, along with PI-V position regulators and a feedforward term. A diagram of this implementation is shown in Figure 6 [32].

Motor Positioning: Comparing System Simulations and Real Time Results
The presented figures depict significant outcomes of the proposed control system, which is assessed through computer simulation and real experimental results to determine the system's modeling and control performances and the integrated mechanisms of the robotic system. By comparing the real-time experiment and computer simulation results, the control design assumptions are validated, which leads to the development of a robust, safe, accurate, and fast motion responses capable of meeting the high expectations of the presented smart robotic device. Multiple control experiments were conducted while considering the system constraints, in particular, control signal sampling time and control signal maximum allowed values. Two experimental tests were performed to showcase the tracking performance of the PI-V regulators for both azimuthal and elevation movements simultaneously. Figures 7 and 8 illustrate the motor responses for the azimuthal and elevation movements, ψ and ϕ, respectively. Both PI-V control responses compare simulation and real-time tracking for a given reference. In these examples, the reference moves from 0°to 10°in 0.5s, which are realistic reference characteristics for a fast system response. Each of the figures depicts the remarkable position tracking, tracking error, and control effort of each degree of freedom. Figures 9  and 10 show motor responses for simultaneous azimuthal and elevation movements. In this case, a long reference with multiple movements is provided to validate system performance. The provided references go from 0°to 20°several times in a total time of 4 s. Once again, PI-V real-time control responses are compared to those of the equivalent simulations. In addition, real-time responses are found to be very similar to those of simulations, which also validates the remarkable efforts when obtaining the robotic system models, control designs, and the right use of simulation tools.
The results of the experiments show that the controllers can track references with little error and without exceeding the saturation constraints. We refer to making  Applied Bionics and Biomechanics control regulators robust to static Coulomb friction Γ c and never exceeding DC motor saturation limits, also known as maximum control signal effort (PWM AE 255), as shown in Table 1. Figures 7 and 8 reveal control efforts for ψ and ϕ movements, in which the control efforts never reached at levels more than PWM = 120 and PWM = 150, respectively. The position regulators follow fast, sharp references with no steady-state error or overshoot. Table 3 shows the calculated performance metrics with error values for 10°a nd 20°, as well as the settling time for each response. For performance metrics analysis, the integral square error (ISE) and the integral absolute error (IAE) are used. T s−t is used to remember the settling time of each response. The designed regulators compensate for the effects of nonlinear friction and provide very fast responses with settling times of less than 0.15 s.

Conclusions
A novel robotic platform that incorporates essential hardware and software was introduced, which represents smart glass technology. The robotic device comprises a 2-DOF system with a spherical workspace that employs active control to maintain the end-point position of a drinking glass. The study presents the potential application of this robotic system as a utensil for patients with tremors.
In this paper, a simple dynamic model is proposed along with parameter identification to perform model-based controls. The method employs PI-V regulators to drive DC motors, ensuring that all motion positioning and endpoint control requirements are satisfied. System simulations and experimental results are compared to validate the dynamic models, control designs, and general design assumptions.
The PI-V control experiments exhibit remarkable performance in tracking system references, producing critically damped results with very fast settling times and almost zero static error. Several control performance metric analysis figures are also provided. The control system is Applied Bionics and Biomechanics found to be robust to the effect of Coulomb friction even when working with very small angles and at low speeds. The designs take into account other system constraints, such as saturation, while keeping the control effort within control limits.
The designed experimental platform will be used in future work to develop closed-loop control techniques to reduce system vibration. However, it is presumed that a more robust and redundant sensory system must be incorporated to perform multiple control strategies.

Data Availability
All data generated during this work are available in the manuscript; additional data are available upon reasonable request from the corresponding author.