Design and Control of a Multi-Axis Servo Motion Chair System Based on a Microcontroller

Abstract

In this study, we present a design and a control based on a microcontroller for a multi-axis servo motion chair. The main purpose was to provide the pilot with the tactile sensations required by the human body to increase the immersion of simulation training. With high system control reliability and multi-functionality, the proposed architecture was built with an effective split of the control tasks involved between a master controller and five slave drivers. To assess the effectiveness of the proposed control system, RS485 and RS232 communication transmission interfaces were provided for the control system to obtain related movement information. The performance of the motion chair was assessed through various experimental tests. The results confirmed that the proposed multi-core system-on-chip microcontroller (MCU) with independent communication and real-time control subsystems was feasible to control a multi-axis servo motion chair system.

1. Introduction

Due to the scarcity of energy, the increase in its cost and its wide range of applications, the use of other types of renewable resources for power generation is a primary concern. One of the renewable energy sources used for power generation is solar energy. A solar tracking system increases the efficiency of solar panels by converting them into a source of electricity [1]. The way sunlight is detected can be improved by using the system so that more electrical energy can be collected. Climate change causes changes in sunlight availability, leading to higher temperatures; this can affect the performance efficiency of PV modules. Sun-tracking technology has emerged to help photovoltaic systems capture maximum solar irradiance, thereby increasing the power output. To avoid human error, the concept of the Internet of Things (IoT) has been incorporated. The ability to transmit data over a network has no requirement of human–human or human–machine interactions. This is an effective competitive solution for an evolving technology using solar power [2]. It can also provide a power source for the simulators used for pilot training.

The training period for pilots around the world is usually lengthy. Hence, flight training simulators are in high demand and are an indispensable tool for flight training. As mentioned in [3], a motion simulation system with comprehensive high fidelity was first established in the 1950s. In 1954, the General Precision Equipment Corporation of the United States developed a motion simulation system that could perform three-degree pitch, roll and yaw. Through continuous improvement, the system achieved 10-degree pitch, roll and yaw [4]. Stewart proposed a six-axis parallel motion platform structure in 1965 [5]. Subsequently, a hydraulic drive has been used in civil aviation simulators with six degrees of freedom to control the movement of each axis. The basic framework design of a simulator is as shown in [6]. However, the sense of contact of the human body is different from the sense of space produced by a platform with six degrees of freedom. Several researchers have investigated and improved this framework, including a discussion identifying the relationship of six-axis motion with each actuator based on kinematics [7,8] and a discussion of how compensating for the perturbation rate of the load improves positioning accuracy [9].

The gravity pressure on human bodies can be simulated by contact with an exercise chair. In the study by Gum [10], a test of the research model showed that there was a time delay between the applied forces and the perceptions of various mechanisms. The results showed that pressure-sensing structures and intramuscular senses applied forces at a faster rate than the vestibular system. Cardullo et al. [11] engaged with this type of chair design, hoping to stimulate a haptic system with the chair. The objective was that the seat could independently produce the expected changes in skeletal posture, mimic the areas associated with the changes in skin contact and reflect the changes in muscle pressure gradients. In addition, the seat was designed to simulate the effects of acceleration variation. The chair included two airbags, which led to the seat and back cushions. Consequently, a control approach was utilized to independently actuate the airbags to manipulate the height, position and shape of the supporting surface. In the design, the tactile feel of bodies changed with the airbags. In [12], Berger et al. presented a study on perceptions and visual sensations. The results demonstrated that perception had qualitative matching in the magnitude of visual acceleration that could enhance the information transfer between them. The findings displayed that the use of the visual effect in building a motion notification of an early warning algorithm could increase the linear acceleration motion effect of the simulator. Bruschetta et al. [13] utilized a Stewart platform with the seat as a motion platform. Specifically, they produced the sensation of sustained acceleration with a low frequency by placing eight inflators on the chair. Four were equipped on the seatback, two were placed on the seat pan and one was placed on either side of the seatbelt. The sense of restraint exerted by the inflatable device through the seatbelt created a sense of sustained low frequency acceleration after the device was inflated. In [14], Toda et al. designed a single degree of freedom seat simulator to examine the fatigue that bodies perceive after a long period of driving. The simulator consisted of a single degree of freedom chair and a steering wheel as well as visual effects; tests for physical fatigue were performed by adjusting the impact axis on the back. In [15], Ishii et al. developed a dual DOF (roll and pitch axes) seat where they used the rotation in the seat roll and the shock axis to investigate whether self-driving cars could predict the position and behavior of other cars after few seconds. In [16], a vibration table was designed that consisted of a linear servo motor to test the perceived riding comfort of drivers. Berthoz et al. [17] investigated different motion scaling factors in a driving simulator. With motion feedback, the participants drove more carefully and had better control of the cars. As a result, they could better predict the dynamic behavior of the car and were not surprised when the car crashed. Greatly reduced or absent motion cues significantly reduced the drivability.

Most simulators are designed based on the Stewart platform with a 6 DOF structure [18,19,20], which simulates and presents the global motion of 6 DOF. However, the Stewart platform cannot offer the kinematic sensations pilots experience whilst flying. Therefore, the purpose of this work was to design a four DOF chair system for motion simulation, providing pilots with tactile sensations related to motion. The physical sensations experienced by the pilots during flight were converted into data. This enabled the pilots to experience relevant haptic sensations and ensure that the flight simulation was a more immersive experience. The design and control of the chair were based on mathematical modeling. A kinematic model was used to describe the relationship between the motion position of the simulator in space and the rotation angle of each joint via a structural analysis; the limitations of the motion space were then observed. The seat plate assembly was composed of a heave shaft and a roll shaft. The back pad assembly included a swing axis and a surge axis. The seat height structure had an adjustable vertical structure for the entire seat. As each component had a single DOF motion, we referred to the methods used in [21,22,23] to determine the kinematic model based on the geometric relationship between the links. In contrast, inverse kinematics involves obtaining displacements or angles of each joint based on the reverse engineering of the moving position of a simulator and its attitude in space.

It is challenging to train pilots using the Stewart platform as a simulator, especially for a sense of gravity with short distance movements. We designed a chair with four degrees of freedom as the gravitational motion required for flight. An electromechanical integrated control architecture combined with an MCU was proposed. Motion simulation helps to achieve the highly sensitive human perception of motion through platform motion and enhances the effect of virtual reality. The whole controlled system comprised a dual-core master controller combining a C2000 Texas Instruments (TI) MCU for real-time control tasks with an Arm Cortex-M3 processor for communication purposes. To the best of our knowledge, the above-mentioned ideas were original as they have not been presented in previously published papers [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24].

The rest of the article is organized as follows. Section 2 introduces the system architecture and the control strategy process is explained. Section 3 discusses the kinematics of the motion chair system. The implemented system and the experimental results are shown in Section 4 and Section 5, respectively, and Section 6 presents the conclusions.

2. System Architecture

2.1. System Overview

The mechanism of the motion chair system was divided into three layers: a monitor layer, a control layer and an execution layer. The overall structure is shown in Figure 1. The execution layer was the verification platform of the motion chair system, which mainly comprised the servo motors, a toggle joint mechanism, a slider-crank mechanism, a four-link mechanism and an adjustable height mechanism. The control layer was the hardware aspect of the control system and included a dual-core MCU, five drivers and an RS485 communication transmission interface. The monitor layer was part of a host monitoring system with the monitoring software written by C# in the Windows system as the control core. The monitor layer communicated with the control layer through the RS232. RS232 and RS485 serial communications remain in use at present because they are more immune to electromagnetic interference. Most of the older available devices/equipment only support one of the communication standards: the RS232 is used to program servo drivers and computerize numerical control equipment; the RS485 is used in many automation systems. The basic functions and the operating procedure of our motion chair system were as follows. The user operated the monitoring software to plan the trajectory, generate the trajectory of the discrete point data and then analyze the equivalent impulse control data of the servo motors, which was transmitted to the controller through the RS232. The controller generated five commands, directional signals and enabled signals based on the control data. The five drivers then received the signals to drive the servo motors according to the control requirements. The servo motor drove the chair for motion control. At the same time, the encoder fed back the angular displacement information of the servo motors to the drivers. The drivers then executed the position regulation according to the feedback signals. The motor angular displacements were uploaded to the monitoring software in the host computer through the RS485. Eventually, the real-time tracking control of the mechanism based on the angular displacement information was realized. During the process, the controller could also respond to relevant operation commands from the host computer.

2.2. Closed-Loop Control Strategy

In the $d-q$ axis synchronous frame, the differential equations of the $d-q$ axis voltage equations could be expressed as [25]:

$$v_d=r_s{i}_d+L_d\frac{d}{dt}{i}_d-{\omega }_{re}{L}_q{i}_q$$

(1)

and:

$$v_q=r_s{i}_q+L_q\frac{d}{dt}{i}_q+{\omega }_{re}{L}_d{i}_d+{\omega }_{re}{\lambda }_m$$

(2)

where $v_d$ and $v_q$ are the $d-q$ axis voltages, $r_s$ is the stator resistance, $i_d$ and $i_q$ are the $d-q$ axis currents, $L_d$ and $L_q$ are the $d-q$ axis inductances, ${\omega }_{re}$ is the electrical rotor speed and ${\lambda }_m$ is the flux linkage generated by the permanent magnet material, which was placed in the rotor. Through realizing $i_d$ = 0 by applying a field-oriented control, Equations (1) and (2) could be rewritten as:

$$v_d=-{\omega }_{re}{L}_q{i}_q$$

(3)

and:

$$v_q=r_s{i}_q+L_q\frac{d}{dt}{i}_q+{\omega }_{re}{\lambda }_m=u_q+{\omega }_{re}{\lambda }_m$$

(4)

The electromagnetic torque could then be given by:

$$T_e=\frac{3}{2}\frac{P}{2}{\lambda }_m{i}_q=K_T{i}_q$$

(5)

where $K_T$ represents the torque constant and $P$ is the number of poles of the motor. The dynamic mechanical equations of the rotor speed and rotor position were expressed as:

$$\frac{d}{dt}{\omega }_{rm}=\frac{1}{J_m}\left(T_e-T_L-B_m{\omega }_{rm}\right)$$

(6)

and:

$$\frac{d}{dt}{\theta }_{rm}={\omega }_{rm}$$

(7)

where $J_m$ is moment of inertia of the motor, $B_m$ is the viscous coefficient of the motor and $T_L$ is the external load. The electrical rotor position and speed were, respectively, expressed as follows:

$${\theta }_{re}=\frac{P}{2}{\theta }_{rm}$$

(8)

and:

$${\omega }_{re}=\frac{P}{2}{\omega }_{rm}$$

(9)

The PID control law was designed as:

$$u=K_{P}e\left(t\right)+K_I{\displaystyle \int e\left(t\right)dt}+K_D\frac{d}{dt}e\left(t\right)$$

(10)

where $K_P$, $K_I$, $K_D$ and $e\left(t\right)$ are the proportional, integral and differential coefficients and the control error, respectively. The closed-loop control system was designed and independently applied to each of the five actuators. In Figure 2, the control blocks $G_i$, $G_{\omega }$ and $G_{\theta }$ represent the PID controller for the current loop, speed loop and position loop functions, respectively.

3. Inverse Kinematics Solutions

The execution layer of the motion chair included the three components shown in Figure 1. The seat pan assembly consisted of the roll and heave structures. The back assembly of the chair consisted of the surge and sway structures. For the seat height, the whole chair was equipped with an adjustable height structure. The process used to discover the inverse kinematics solutions of the motion chair system is described below.

3.1. Kinematics of the Seat Pan

3.1.1. Roll Axis Design

The roll structure of the seating plate was a toggle joint structure and is shown in Figure 3. $L_2$, $L_3$, $L_4$, $L_5$ and $L_6$ represent the link lengths, where $L_4$ is the length of the driving link and $L_6$ is the seat length. In addition, $L$, $L_0$ and $L_1$ represent the distances between the rotation axes and $L_0$ and $L_1$ are known. The constraint equations were required to satisfy the geometric relationship in the following Equations (11)–(14).

$$L_2\left(\cos {\theta }_2\right)+L_3\left(\cos {\theta }_3\right)-L_4\left(\cos {\theta }_4\right)-W_1=0$$

(11)

$$L_2\left(\sin {\theta }_2\right)+L_3\left(\sin {\theta }_3\right)-L_4\left(\sin {\theta }_4\right)-H_1=0$$

(12)

$$-L_3\left(\cos {\theta }_3\right)+L_4\left(\cos {\theta }_4\right)+L_5\left(\cos {\theta }_5\right)+L_6\left(\cos {\theta }_6\right)-W_0+W_1=0$$

(13)

$$-L_3\sin {\theta }_3+L_4\sin {\theta }_4+L_5\sin {\theta }_5-L_6\sin {\theta }_6-H_0+H_1=0$$

(14)

For the inverse kinematics of the roll axis, the angles of each link and the turning angle of the seating plate were obtained starting from ${\theta }_6$. First, we determined ${\theta }_2$ and then solved $L$ in terms of ${\theta }_0$ and $L_0$ as:

$${\theta }_0={\tan }^{-1}\left(\frac{H_0}{W_0}\right)$$

(15)

$$L_0=\sqrt{{\left(H_0\right)}^2+{\left(W_0\right)}^2}$$

(16)

$$L=\sqrt{{\left(L_0\right)}^2+{\left(L_6\right)}^2-2L_0^2{L}_6^2\cos \left({\theta }_0+{\theta }_6\right)}$$

(17)

${\theta }_A$ could then be obtained from $L,L_0$ and $L_6$. In addition, the following equation was satisfied:

$$L·\left(\sin {\theta }_A\right)=L_6·\left(\sin \left({\theta }_0+{\theta }_6\right)\right)$$

(18)

According to (18), we obtained:

$${\theta }_A=\frac{L_6}{L}{\sin }^{-1}\left(\sin \left({\theta }_0+{\theta }_6\right)\right)$$

(19)

Based on $L$, $L_2$ and $L_5$, ${\theta }_B$ could be expressed as follows:

$${\theta }_B={\cos }^{-1}\left(\frac{L_{}^2+L_2^2-L_5^2}{2L·L_2^{}}\right)$$

(20)

${\theta }_2$ could then be calculated and given as:

$${\theta }_2={\theta }_0+{\theta }_A-{\theta }_B$$

(21)

${\theta }_3$ and ${\theta }_4$ were then solved. As shown in Figure 4a,b, there were two solutions for ${\theta }_3$ and ${\theta }_4$.

Based on Figure 3 and Figure 4a, ${\theta }_3$ could be obtained from solution 1. $L_{34}$ was solved first and expressed as:

$${\theta }_1={\tan }^{-1}\left(\frac{H_1}{W_1}\right)$$

(22)

$$L_1=\sqrt{{\left(H_1\right)}^2+{\left(W_1\right)}^2}$$

(23)

$$L_{34}=\sqrt{{\left(L_1\right)}^2+{\left(L_2\right)}^2-2L_1^2{L}_2^2\cos \left({\theta }_2-{\theta }_1\right)}$$

(24)

${\theta }_F$ could be obtained from $L_3$, $L_4$ and $L_{34}$:

$${\theta }_F={\cos }^{-1}\left(\frac{L_3^2+L_{34}^2-L_4^2}{2L_{34}^{}{L}_3^{}}\right)$$

(25)

As shown in Figure 3, ${\theta }_E$ could be expressed as:

$${\theta }_E={\tan }^{-1}\left(\frac{L_2\left(\sin {\theta }_2\right)-H_1}{W_1-L_2\left(\cos {\theta }_2\right)}\right)$$

(26)

From Equations (25) and (26), ${\theta }_3$ could be obtained:

$${\theta }_3=\left({\theta }_F-{\theta }_E\right)$$

(27)

Similarly, ${\theta }_D$ could be obtained from $L_3$, $L_4$ and $L_{34}$; ${\theta }_4$ could then be calculated as:

$${\theta }_D={\cos }^{-1}\left(\frac{L_4^2+L_{34}^2-L_3^2}{2L_4^{}{L}_{34}^{}}\right)$$

(28)

$${\theta }_4=180-\left({\theta }_D+{\theta }_E\right)$$

(29)

The geometric relationship in Figure 4b was another solution for ${\theta }_3$ and ${\theta }_4$:

$${\theta }_3=-\left({\theta }_F+{\theta }_E\right)$$

(30)

$${\theta }_4=180-\left({\theta }_E-{\theta }_D\right)$$

(31)

The next step was to solve ${\theta }_5$. Given that $L_3+L_4<W_1$, ${\theta }_2$ and ${\theta }_5$ had only one solution. ${\theta }_C$ could be obtained according to $L$, $L_2$ and $L_5$ whereas ${\theta }_5$ could be obtained according to ${\theta }_C$ and ${\theta }_2$:

$${\theta }_C={\cos }^{-1}\left(\frac{L_2^2+L_5^2-L_{}^2}{2L_2^{}{L}_5^{}}\right)$$

(32)

$${\theta }_5=180-\left({\theta }_C-{\theta }_2\right)$$

(33)

From Equations (21), (27), (30), (31) and (33), the link angles could be obtained as control commands to realize the seating plate control in the roll region.

3.1.2. Heave Axis Design

In the heave axis, the seating plate structure was designed as a slider-crank mechanism, as shown in Figure 5, which was similar to the press machine in [19,20]. In Figure 5, $L_8$ represents the driving link, $L_7$ represents the initial height of the seating plate and z is the displacement of the seating plate. The displacement and the angles of each link were required to satisfy the constraints of Equations (34) and (35).

$$L_7-z=L_8\left(\sin {\theta }_8\right)+L_9\left(\sin {\theta }_9\right)$$

(34)

$$L_8\left(\cos {\theta }_8\right)+L_9\left(\cos {\theta }_9\right)=0$$

(35)

The inverse kinematics of the heave axis and the angles of each link from the z-axis displacement of the seating plate were first obtained. There were two solutions for this relationship, these are represented in Figure 6a,b.

As seen in Figure 6a, solution 1 obtained ${\theta }_G$ and ${\theta }_H$ from z. $L_8$ and $L_9$ were then solved and expressed as:

$${\theta }_G={\cos }^{-1}\left(\frac{L_8^2+L_9^2-{\left(L_7-z\right)}^2}{2L_8{L}_9}\right)$$

(36)

$${\theta }_H={\cos }^{-1}\left(\frac{{\left(L_7-z\right)}^2+L_8^2-L_9^2}{2L_8\left(L_7-z\right)}\right)$$

(37)

${\theta }_8$ and ${\theta }_9$ could then be obtained as:

$${\theta }_8=90-{\theta }_H$$

(38)

$${\theta }_9=180-\left({\theta }_G-{\theta }_8\right)$$

(39)

Figure 6b is another solution for ${\theta }_8$ and ${\theta }_9$:

$${\theta }_8=90+{\theta }_H$$

(40)

$${\theta }_9=-180+\left({\theta }_G+{\theta }_8\right)$$

(41)

By combining (40) and (41), we obtained:

$${\theta }_9=-90+\left({\theta }_G+{\theta }_H\right)$$

(42)

Through this observation, the connecting rod angles in Equations (40) and (42) could be acquired as control commands and further realized the control of the seating plate of the heave region.

3.2. Kinematics of the Back Pad

3.2.1. Surge Axis Design

As shown in Figure 7, the surge axis structure of the back of the chair adopted a four-bar linkage mechanism. In Figure 7, $L_{11}$ represents the driving link and $L_{13}$ is the back of the chair. The angles of each link were required to satisfy Equations (43) and (44).

$$L_{11}\left(\cos {\theta }_{11}\right)+L_{12}\left(\cos {\theta }_{12}\right)-L_{13}\left(\cos {\theta }_{13}\right)-L_{10}=0$$

(43)

$$L_{11}\left(\cos {\theta }_{11}\right)+L_{12}\left(\sin {\theta }_{12}\right)-L_{13}\left(\sin {\theta }_{13}\right)=0$$

(44)

The inverse kinematics in the surge axis involved obtaining ${\theta }_{11}$ and ${\theta }_{12}$ from the turning angle and ${\theta }_{13}$ from the rear panel. As shown in Figure 8a,b, there were two solutions with the collinear boundaries of links $L_{11}$ and $L_{12}$.

Based on Figure 8a, solution 1 was obtained from $L_{11\_12}$, $L_{10}$, $L_{13}$ and ${\theta }_{13}$ where $L_{11\_12}$ was first solved and represented as:

$$L_{11\_12}=L_{10}^2+L_{13}^2+2L_{10}^{}{L}_{13}^{}\left({\theta }_{13}\right)$$

(45)

${\theta }_I$, ${\theta }_J$, ${\theta }_K$, ${\theta }_{11}$ and ${\theta }_{12}$ could then be obtained as follows:

$${\theta }_I={\cos }^{-1}\left(\frac{L_{10}^2+L_{11\_12}^2-L_{13}^2}{2L_{10}^{}{L}_{11\_12}^{}}\right)$$

(46)

$${\theta }_J={\cos }^{-1}\left(\frac{L_{11}^2+L_{11\_12}^2-L_{12}^2}{2L_{11}^{}{L}_{11\_12}^{}}\right)$$

(47)

$${\theta }_K={\cos }^{-1}\left(\frac{L_{11}^2+L_{12}^2-L_{11\_12}^2}{2L_{11}^{}{L}_{12}^{}}\right)$$

(48)

$${\theta }_{11}={\theta }_I+{\theta }_J$$

(49)

$${\theta }_{12}=-180+\left({\theta }_K+{\theta }_{11}\right)$$

(50)

The geometric relationship for Figure 8b was another solution. ${\theta }_I$, ${\theta }_J$ and ${\theta }_K$ could be solved by the same method. ${\theta }_{11}$ and ${\theta }_{12}$ could then be found as follows:

$${\theta }_{11}={\theta }_I-{\theta }_J$$

(51)

$${\theta }_{12}=180-\left({\theta }_K-{\theta }_{11}\right)$$

(52)

From Equations (49)–(52), the angles of each link could be obtained as the control commands. In this way, the real-time panel control of the surge region was achieved.

3.2.2. Sway Axis Design

The sway axis structure design of the back pad was the same as that of the heave axis. Both were designed as the slider-crank mechanism shown in Figure 5. Hence, Equations (30) and (32) could be acquired according to the same derivation.

3.3. Kinematics of the Seat Height

The seat height design involved a ball screw that was employed as the adjustable height structure of the whole chair. Assuming that the lead of the ball screw was $L_B$ (m/rev), the relationship between the displacement $D$ and rotating angle ${\theta }_{14}$ was:

$$D=\left(\frac{L_B}{2\pi }\right){\theta }_{14}$$

(53)

4. Implementation

In this research, the main power was three-phase 220 volts used as the power supply source for the control box. The implemented circuit of the control box is shown in Figure 9a. The hardware circuit included a control board, a host computer, an AC to DC power supply, five sets of servo drivers, a set of relays, a connecting terminal and related components. The output of the AC to DC power supply was 24 V, which was used as the power supply of the control board. As shown in Figure 9b, the control board adopted a dual-core control processing chip (F28M35) produced by Texas Instruments for the implementation of the proposed control system. The F28M35 had an embedded Cortex-M3-based ARM processor as well as a C28 DSP core. The frequency of the ARM Cortex-M3 could reach 100 MHz, with 5 groups of UART and 74 individually programmable GPIOs. This research used five UART channels to perform the control mode release, command and servo status return to five sets of servo drivers. The frequency of the DSP 32-bit CPU was 150 MHz. It was integrated by digital input and digital output channels, including five servo motor signals, upper and lower limit signals and external button signals. The RS232 communication interface communicated with a host computer that was used to design the user interface.

A user interface for the PC was established by C# software with a stroke control mode, as shown in Figure 10. The stroke mode adjusted the desired commands to be executed by sliding according to the selected number of servo axes. The commands were transmitted to the DSP through the digital communication interface to execute the kinematics and calculate the control commands sent to the drivers through the ARM to the selected number of servo axes. In this way, it realized multi-axis distance stroke control and achieved a closed-loop control. The block diagram of the control system is shown in Figure 11. It consisted of four parts. Part A was the control box, which provided a dual-core control processing chip and a host computer to communicate with five sets of servo motors through the serial communication RS485 interface. Part B was the back pan that could control the surge axis and the sway axis. Part C was the seat pan that could control the roll axis and the heave axis. Part D was the seat height that could adjust the height of the chair by servo motors. On the PC side, the RS232-to-USB device used a standard RS232 protocol with baud rates of up to 921,600 bit/s. The device could be controlled and configured over a serial interface by a set of control commands. According to the data processing on the PC side, a stable sampling rate above 100 Hz could be achieved in practice.

The control flowchart of the motion chair is shown in Figure 12. After starting the power supply, it performed an automatic zero-point procedure for each axis to obtain the correct initial position of the servo motors. After reading the parameters of the chair mechanism, executing the kinematics and selecting the COM port of the host computer to connect to, the user interface then generated the commands and monitored the operation status of each axis. The DSP used (TI F28M35; 150 MHz) worked with a control frequency of 100 Hz on the computational limit. The actual computation time required was 80 μs with an additional 10 μs for safety checks. The experimental motion chair is shown in Figure 13a. The dimensions of the chair are listed in

Table 1. Dimensions of the chair.

$L_2$	10 mm
$L_3$	180 mm
$L_4$	3 mm
$L_5$	10 mm
$L_6$	22.5 mm
$L_{8,\mathrm{sway}}$, $L_{8,\mathrm{heave}}$	15 mm, 3 mm
$L_{9,\mathrm{sway}}$, $L_{9,\mathrm{heave}}$	75 mm, 70 mm
$L_{10}$	388.5 mm
$L_{11}$	52.5 mm
$L_{12}$	192.2 mm
$L_{13}$	224 mm
$H_0$	16 mm
$H_1$	4.5 mm
$W_0$	22.5 mm
$W_1$	122.5 mm

. The chair was connected to the control box by five power lines, encoder lines and signal lines, as shown in Figure 13b. The layout in the control box is shown in Figure 9a. According to the proposed control scheme, user interface and software-embedded program, the dual-core control processing chip achieved the purpose of the system integration of the multi-axis servo motion chair. The servo motor parameters are listed in

Table 2. Parameters of the motor.

	DOF	Surge	Sway	Roll/Heave	Adjustable Height
Item
Power dissipation		0.75 kW	1.3 kW	3.0 kW	2.0 kW
Rated voltage		220 V	220 V	220 V	220 V
Rated current		4.3 A	11.4 A	14 A	9 A
Rotor inertia		1.03 kg-cm2	20.77 kg-cm2	18.62 kg-cm2	12.84 kg-cm2
Rated speed		3000 r/min	1500 r/min	2000 r/min	2000 r/min
Maximum speed		5000 r/min	3000 r/min	2500 r/min	2500 r/min
Rated torque		2.39 N.m	8.34 N.m	14.327 N.m	9.55 N.m
Maximum torque		7.16 N.m	23.3 N.m	42.96 N.m	28.65 N.m

.

5. Experimental Results

The measured steps for the components and the development of a four-axis chair motion system are described next. In terms of displacement measurements, we measured the total maximum displacement. The used tools were a vernier caliper, a metal ruler and a height gauge. The measurements for the four DOFs and the adjustable height conditions were as follows. The ball screw was FSIW-R25-5T4-172-265 with a lead of 5 mm. The total displacement of the adjustable height structure was 55 mm and the movable displacement was 50 mm. The total displacement of the surge axis was 42 mm. The total displacement of the sway axis was 30 mm. The total displacement of the heave axis was 6 mm. The total displacement of the roll axis was 100 mm. In addition, the used sensor was an MTi-680G inertial navigation system (INS), produced by Xsens Co; the INS uses an accelerometer and a gyroscope to measure the acceleration and angular velocity of objects. The transmission time was 10 ms. The output channel was an RS232 interface and the data were transmitted to the PC device through the RS232 to a USB. The characteristics of the sensor are shown in

Table 3. Specifications of gyroscope and accelerometer of Xsens MTi enclosure [26].

	Gyroscope	Acceleration
Range	±2000 degree/s	±10 g
In-run bias stability	4 degree/h	15 μg
Bandwidth (−3 dB)	500 Hz	500 Hz
Operating Temperature	−40 to 85 °C
Input voltage	4.5 to 24 V
Power consumption	<1 W

. The sampling rate of the sensor was selected as 100 Hz. The angles of the roll axis and pitch axis were in the range of ±90 degrees. The angle of the yaw axis was in the range of ±180 degrees; the angular velocity could reach ±2000 degree/s. The measurement reference point is shown in Figure 14a–f. Figure 15a shows that the measured displacement of the surge axis motor moved between 0 and 360 degrees, with a total displacement of about 42 mm. Figure 15b shows that the error between the two in Figure 15a was about 0.9 mm. Figure 16a–c show the tuning angle ${\theta }_{12}$, relative angular velocity and acceleration responses measured using the INS. Figure 16a shows the surge axis from the zero point to the highest point. The corresponding tuning angle was about −9 degrees at this stroke. Figure 16b shows that the angular velocity of the surge axis was about ±10 degrees at this stroke. Figure 16c shows the x-axis acceleration of the surge axis, which ranged from −0.6 m/s²~0.4 m/s². Figure 17a shows that the measured displacement of the sway axis motor was between 0 and 360 degrees and the total displacement in the observation figure was ±15 mm. Figure 17b shows that the error response was about 0.3 mm. Figure 17c shows the movement of the sway axis from the center point to the left and right limits. The speed of this stroke was about ±0.01 m/s with a maximum value around zero. In addition, Figure 17d exhibits the y-axis acceleration of the sway axis. Figure 18a shows that the measured displacement of the heave axis motor was between 0 and 360 degrees and the total displacement was about ±3 mm. Figure 18b shows that the error of the heave axis was about ±0.1 mm. Figure 18c shows that the heave axis moved from the center point to the upper and lower limits. The velocity was about ±0.004 m/s at this stroke. Figure 18d shows the z-axis acceleration of the heave axis. Figure 19a shows the measured displacement responses of between 0 and 360 degrees for the roll axis motor with displacements of about +35 mm and −65 mm; Figure 19b shows the error response. The roll structure of the seating plate was the toggle joint structure. As can be seen from the figure, the seat plate assembly tolerance error was about 0.7 mm. Figure 20a shows the response of the electrical angle of the roll axis motor. As the servo motors of the chair were 8-pole, the electrical angle of the roll axis for 4 revolutions corresponded with a mechanical angle of 360 degrees. Figure 20b shows that the stroke of the roll axis was from −6 to +11 degrees. Figure 20c shows that angular velocity of the roll axis was about ±70 degrees. Figure 21a shows that the displacement of the adjustable height motor was between 0 and 360 degrees with a total displacement of about 50 mm. Figure 21b shows that the error response was about 0.02 mm. Figure 21c shows the adjustable height from the lowest point to the highest point. The velocity was about ±0.014 m/s. It can be seen from the figure that the speed transient and steady state were relatively smooth; the reason was that the height adjustment of the seat was driven by the servo motor directly connected to the screw. Figure 21d shows the measured acceleration was close to 0.6 m/s².

6. Conclusions

In this paper, the design, control and implementation of a digital control system for a four DOF adjustable-height chair were discussed. The architecture proposed consisted of a dual-core master controller and five slave drivers communicating together with RS485 and RS232 communication transmission interfaces. The first was used for the host computer and the digital control of the whole chair as well. The second one performed each axis drive of the motion chair mechanism such as the seat pan, back pad and seat height. The digital control systems of today have revolutionized the industrial world to virtually eliminate the typical drawbacks of analog systems and allow the diffusion of sophisticated control techniques that are not applicable without them. In order to achieve the predetermined motion path, the design and control of the chair structure as well as the mathematical model establishment, simulation and multi-axis servo drive technology were undertaken. The aim of the study was to develop a verification platform with a mathematical derivation, four DOFs, an adjustable height, software/hardware integration and relative control methods. An analysis of each component was conducted to gain an understanding of the structure assembly and further complete its production. The experimental results showed that the proposed multi-axis servo motion chair could bear a weight of about 90 kg.