Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 9, No. 3, 2024 

 

274 

Research	on	the	Driving	and	Control	of	an	Intelligent	
Book	Robot	
Xingyu Wang 

College of Electrical Engineering, Southwest Minzu University, Chengdu, Sichuan 610225, China 

 

Abstract: Based on the theoretical foundation provided by kinematic simulations under various parameter conditions using 
Adams for robots' control, this paper designs a dual-closed-loop drive control system for the robot. It constructs the drive speed 
control hardware circuit and simulates the step response of positional PID, incremental PID, and fuzzy PID in Simulink. 
Positional PID is selected as the velocity control algorithm due to its fast response characteristics and ease of implementation. 
The drive circuit and control algorithm are jointly simulated using Proteus to verify the speed control effect of the robot's drive. 

Keywords: Robot, PID, Driving and Control, Simulink Simulation. 
 

1. Introduction 
In China, the construction process of smart libraries has 

already been initiated. In 2016, the National Development and 
Reform Commission issued the notice 'On Organizing and 
Promoting the Practical Evaluation of New Smart City 
Development to Facilitate Healthy and Rapid Development 
of New Smart Cities' [1]. The 'Thirteenth Five-Year Plan for 
Education Informatization' formulated by the Ministry of 
Education in 2017 sets the goal for higher education 
institutions to achieve basic completion of smart campus 
construction by the end of 2020 [2]. 

As of 2023, the total number of universities and public 
libraries in China has exceeded 6,000. According to 
incomplete statistics, each library holds from several hundred 
thousand to over a million physical books, and these 
collections are continuously expanding [3-4]. Therefore, the 
imperative for intelligent and informatized development of 
libraries is evident. The trend of using robots to replace library 
personnel for the tedious tasks of book organization is 
emerging as a future direction for library development. This 
paper investigates the driving and control of an intelligent 
book robot, which holds practical significance for the 
intelligent construction of libraries. 

The paper designs a dual-closed-loop drive control system 
for the robot, constructs a drive speed regulation hardware 
circuit, and conducts simulation analyses on traditional digital 
PID and fuzzy PID using the Simulink module in MATLAB. 
Positional PID, characterized by favorable response 
characteristics and ease of implementation, is selected as the 
speed control algorithm. The results indicate that the 
overshoot of speed adjustment is 7%, the adjustment time is 
2.5 ms, and the steady-state error is 0, meeting the 
requirements for intelligent control of motor speed. 

2. Research on the Driving and Control 
of Robot 

2.1. Transfer Function of the DC Motor 
System 

When an electric motor is used within a rapidly changing 
operational range, its dynamic performance can be assessed 
using a transfer function. The term 'transfer function' refers to 
the ratio of the Laplace transforms of the output and input 

signals of the electric motor. 
 

 
Figure 1. Laplace Transform of the Electric Motor 

 

Based on Fig. 1, it can be observed that by applying a 
Laplace transform to the signal, i.e., transforming the function 
of time 't' into a function with 's' as a variable, the transfer 
function of the electric motor is defined as follows: 

 

             (1) 

 

 
Figure 2. Equivalent Circuit of the Armature Winding 

 

The principles of the armature winding equivalent circuit 
in the above Fig. 2 lead to the following formula. 

(1) Voltage balance equation (i.e., describing the electrical 
portion of the model): 

 



 

275 

    (2) 

 

In Eq. (2),   represents the armature voltage,   is 

the armature resistance,   is the armature current,   is 

the armature inductance, and   is the back electromotive 

force. 
(2) Torque balance equation (i.e., describing the 

mechanical portion of the model): 
 

         (3) 

 
In Eq. (3), represents the motor output torque, is the 

angular displacement of the motor shaft,  is the 

equivalent moment of inertia, and  is the equivalent 

friction coefficient. 
(3) Coupling relationship: 
The coupling between the mechanical and electrical 

components involves two aspects: the electrical influence on 
the mechanical part, manifested in the linear variation of 
torque on the motor shaft with the armature current; and the 
mechanical influence on the electrical part, manifested in the 
proportionality between the back electromotive force of the 
motor and its angular velocity. 

 

              (4) 

 

             (5) 

 

In Eq. (4), Eq. (5),  represents the motor current-torque 

constant, and  is the back electromotive force coefficient. 

By simultaneously applying a Laplace transform to both 
sides of Eq. (3) to Eq. (5) and combining them, the transfer 
function from armature voltage to motor shaft angular 
displacement is obtained as: 

 

 (6) 

 
Similarly, it can be derived that the transfer function of 

motor speed relative to input voltage is: 
 

      (7) 

 

In Eq. (7),   is the mechanical time constant,   is 

the electrical time constant, and   is the motor 

electromotive force coefficient. 
Based on the derived mathematical model and referencing 

engineering empirical formulas [5-6], the transfer function of 
the DC motor can be estimated. Furthermore, the motor 
parameters for the DC geared motor MG513 are provided in 
Table 1. It is noteworthy that the motor model 'MG' represents 
the DC brushed motor series, '513' is the motor model, and 
'P30' indicates a gear ratio of 1:30. 

 

Table 1. DC Geared Motor MG513 Specifications 
Motor type Rated 

voltage (V) 
Rated 

current (A) 
Lock-rotor 
current (A) 

No-load 
speed (rpm) 

Rated speed 
(rpm) 

Rated 
torque 

(kg.cm) 

No-load 
torque 

(kg.cm) 
MG513P10 12 0.36 3.2 1100±132 850±102 0.5 1.9 
MG513P20 12 0.36 3.2 549±40 439±32 0.66 3.8 
MG513P30 12 0.36 3.2 366±26 293±21 1 4.5 
MG513P60 12 0.36 3.2 183±13 146±10 2 9 

 
Therefore, by substituting the parameter values of the 

selected motor MG513P30, an approximate transfer function 
for motor speed relative to input voltage can be obtained as: 

 

(8) 

 

2.2. PID control algorithm 
2.2.1. PID control principles 

The PID control, from its establishment to development, 
has become highly mature and is characterized by its 
simplicity, ease of understanding, independence from the 
need for mathematical modeling, and strong robustness [7]. 
As a result, it has found widespread applications, and the 
classic control structure is illustrated in the following figure. 

 

 
Figure 3. Typical Structure of PID Control 

 
As indicated in the above Fig. 3, the differential equation 

representation of the analog signal PID is: 
 

(9) 

 

In Eq. (9),   represents the difference between the 

setpoint and the actual value,  is the setpoint,  is 



 

276 

the actual value,  is the control signal directly affecting 

the controlled object,  is the proportional gain,  
represents the ratio of the integral gain to the integral time, 

defined as the integral gain  ,   represents the 

product of the proportional gain and the derivative time, 

defined as the derivative time . 

The main functions of each component are as follows: the 
proportional component provides a rapid response to the 

current error value. In general, a larger value of  leads to 

steeper control, but it should not be excessively large, as it 
may cause the controlled object to oscillate above and below 
the setpoint. It should also not be too small, as it may result in 
the controlled object never reaching the setpoint and 
stabilizing. The integral component considers the influence of 
historical errors on the controlled object, aiming to eliminate 
steady-state errors between the setpoint and the actual value. 
However, it may counteract the control effectiveness of the 
proportional component and slow down the response speed of 
the controlled object. The derivative component takes into 
account the future trend of error changes, with a stronger 
effect when the error change is larger. It helps eliminate 
oscillations in the controlled object but is susceptible to 
interference from noise signals. 

The adjustment effects of the above three components are 
conflicting, and therefore, it is necessary to rationally tune the 
parameters of PID based on the actual application to achieve 
control with rapid response, low steady-state error, and 
minimal overshoot. With the advent of computers, the 
principles of analog PID control have gradually gained 
widespread application. Based on the computer's continuous 
sampling mechanism, various digital PID control methods 
have evolved. The following sections introduce the control 
principles of traditional digital PID and fuzzy PID, 
respectively. 

2.2.2. Traditional digital PID control 
Due to the inability of digital signals to provide continuous 

output like analog signals, it is necessary to make an 
approximation for the integral and derivative components for 
their utilization. Typically, the following discretization 
process is employed. 

With a computer sampling period of  and the sequence 

value of the acquired signal as , the discrete relationships 

for the various physical quantities in the analog PID are: 
 

(10) 

 
The final expression for the discrete digital PID is: 
 

 (11) 

 

In Eq. (11),   represents the sequence value of the 

acquired signal (k=0,1,2…),  denotes the output value of 

the control signal at the k times sampling,  is the deviation 

value at the k times sampling,  represents the initial value 

of the control signal at the beginning of control. 
In principle, as long as the sampling period is small enough, 

the control effect obtained should closely match that of analog 
PID, resulting in sufficiently accurate control outcomes. The 
control methods mentioned above are based on positional PID, 
meaning the control is applied directly to the numerical values 
of physical quantities that induce changes in the controlled 
object. However, if this control method fails, there is an 
immediate risk of system imbalance, potentially leading to 
engineering accidents. Therefore, there is also the control 
method of incremental PID, which controls the increment of 
the numerical values of physical quantities that directly cause 
changes in the controlled object. 

By recursively applying Eq. (11) and combining, we can 
obtain: 

 

(12) 
 

In Eq. (12), , . 

Since incremental PID controls only the increment of 
relevant quantities, it reduces the impact scope in case of 
system control failure. Additionally, as  is only related 

to the deviations from the most recent three samplings, less 
data is required, leading to relatively lower hardware 
requirements. 

2.3. Fuzzy PID control algorithm 
2.3.1. Fuzzy PID control principles 

 

 
Figure 4. Fuzzy PID Control Structure 

 

As shown in Fig. 4, the structure of the fuzzy PID control 

involves , representing the real-time deviation between 

the setpoint and the actual value, and , the real-time 

rate of change of the deviation. The fuzzy controller takes 
these two signals as inputs and, through a series of internal 
fuzzy rules, outputs three increments for the parameters of the 
traditional PID controller. This enables real-time corrections, 
leading to enhanced system stability. 

2.3.2. Fuzzy controller 
 



 

277 

 
Figure 5. Internal Structure of the Fuzzy Controller 

 

In Fig. 5, the internal structure of the fuzzy controller is 
depicted. Typically, the input consists of one or more explicit 

physical quantities. In this design, the inputs are  and 

. When utilizing a fuzzy controller, the first step is to 

perform fuzzy quantization on the inputs, obtaining the 
corresponding fuzzy vectors. Subsequently, based on an 
extensive set of human knowledge rules, fuzzy reasoning is 
applied to derive the fuzzy set for the output. Finally, a 
defuzzification process is employed to obtain the actual 
output value of the fuzzy control [8]. 

2.3.3. Fuzzifications Process 
Fuzzification is the process of transforming precise 

physical quantities with actual meanings into fuzzy vectors 
with membership degrees between 0 and 1 on a certain fuzzy 
set. The choice of the membership function will determine the 
resulting vector in which fuzzy space. Commonly used 
membership functions include triangular membership 
function (trimf), trapezoidal membership function (trapmf), 
Gaussian membership function (gaussmf), generalized bell-
shaped membership function (gbellmf), etc. In this paper, the 
gaussmf-type membership function is chosen for precise 
fuzzy quantization. As shown in Fig. 6, it illustrates the 

membership function corresponding to   used in this 

study. 
 

 

Figure 6. Membership Function Graph of  

 

2.3.4. Fuzzy Inference 
Fuzzy inference relies on a set of fuzzy control rules, where 

the rules essentially take the form of numerous 'IF-THEN' 
statements, expressing statements based on human 
knowledge and expert experience. An example rule from the 
ruleset in this paper is: 

 

The corresponding physical interpretation is that if the error 
is significantly negative and the rate of change of the error is 
significantly positive, the three adjustment quantities 
correspondingly are zero, zero, and significantly positive. It 
is important to note that before performing inference, the 
determined physical quantities must be normalized to a 
predefined domain. 

According to engineering experience [8-9], employing 
empirical induction to obtain fuzzy control rules, the 
correction rules for the three PID parameters correspond to 
the following table of fuzzy control rules. 

 

Table 2. Fuzzy Control Rule for  

EC 
E 

NB NM NS Z0 PS PM PB 

NB PB PB PM PM PS Z0 Z0 

NM PB PB PM PS PS Z0 NS 

NS PM PM PM PS Z0 NS NS 

Z0 PM PM PS Z0 NS NM NM 

PS PS PS Z0 NS NS NM NM 

PM PS Z0 NM NM NM NM NB 

PB Z0 Z0 NM NM NM NB NB 

 

Table 3. Fuzzy Control Rule for  

EC 
E 

NB NM NS Z0 PS PM PB 

NB NB NB NM NM NS Z0 Z0 

NM NB NB NM NS NS Z0 Z0 

NS NB NM NS NS Z0 PS PS 

Z0 NM NM NS Z0 PS PM PM 

PS NM NS Z0 PS PS PM PB 

PM Z0 Z0 PS PS PM PB PB 

PB Z0 Z0 PS PM PM PB PB 



 

278 

Table 4. Fuzzy Control Rule for  

EC 
E 

NB NM NS Z0 PS PM PB 

NB PS NS PM NB NB NM PS 

NM PS NS NB NM NM NS Z0 

NS Z0 NS NM NM NS NS Z0 

Z0 Z0 NS NS NS NS NS Z0 

PS Z0 Z0 Z0 Z0 Z0 Z0 Z0 

PM PB NS PS PS PS PS PB 

PB PB PM PM PS PS PS PB 

 

From Table 2 to Table 3, it is evident that for any input pair 
of E and EC, a 7x7 membership matrix will be generated. 
Therefore, we only need 49 fuzzy statements to fully describe 
the fuzzy control rules for the three tables. Corresponding 
memberships and fuzzy meanings together constitute the final 
fuzzy set. Summing the memberships with the same fuzzy 
meaning yields the final fuzzy vector. 

2.3.5. Defuzzification 
After fuzzy inference, the result is still a fuzzy vector, and 

therefore, a conversion is required to obtain a precise value 
that can directly affect the controlled object. This process is 
called defuzzification and can be understood as the inverse 
process of fuzzification. To achieve this, it is necessary to 
define basic domains and fuzzy sets for the output variable. 
In this paper, the centroid method is used for defuzzification, 
and its calculation formula can be expressed as: 

 

              (13) 

 

In Eq. (13),   represents the precise value after 

defuzzification,  denotes the values corresponding to the 

seven fuzzy meanings in the control variable domain (i.e., the 
values corresponding to the seven meanings in the output 

variable),  is the membership degree of . 

3. Simulation Analysis of Motor 
Response using Simulink 

3.1. Traditional digital PID model construction 
 

 
Figure 7. Simulink Models of Position and Incremental PID Control 

 

Based on the principles of traditional digital PID, a 
simulation model was constructed in the Simulink module of 
MATLAB, as shown in the simulation model depicted in Fig. 
7. Various modules, including Gain, Step Signal, Delay, 
Transfer Function, and Oscilloscope, were utilized in the 
construction. 

3.2. Fuzzy PID model construction 
Firstly, it is necessary to define the fuzzy controller based 

on the workflow of fuzzy PID. In MATLAB, the fuzzy logic 
designer can be opened by using the 'fuzzy' command. The 
design of the fuzzy controller mainly includes two parts: the 
selection of membership functions for input and output 
variables, determination of the domain values, and the 
addition of fuzzy rules. 

The first step involves establishing a two-dimensional 
fuzzy control structure as shown in Fig. 8. Then, define the 
domain values for both input and output variables as {-1, -2/3, 



 

279 

-1/3, 0, 1/3, 2/3, 1}. For two input variables, use the gaussmf 
Gaussian membership function, and for three output variables, 
use the trimf triangular membership function. In the second 
step, add corresponding fuzzy relationships according to the 
control rule tables provided in Table 2 to Table 4. A total of 

49 rules needs to be added, as shown in the fuzzy rule 
inference result in Fig. 9. Subsequently, export and generate 
the fuzzy control structure file with the .fis suffix. Finally, 
observe the geometric shapes corresponding to each rule in 
the observer, as illustrated in the following figure. 

 

 
Figure 8. Two-Dimensional Fuzzy Control Structure 

 

 
Figure 9. Inference Results of Fuzzy Rules 

 

 
Figure 10. Fuzzy Relationships between Input Variables and  

 



 

280 

 
Figure 11. Fuzzy Relationships between Input Variables and  

 

 
Figure 12. Fuzzy Relationships between Input Variables and  

 

Similar to the traditional digital PID model, a fuzzy PID 
simulation model was constructed in Simulink by invoking 
modules such as Fuzzy Logic Controller, Zero-Order Holder, 

Numeric Compute, Constant, Integrator, and Derivative, 
according to the corresponding principles. The resulting 
simulation model is shown in Fig. 13. 

 

 
Figure 13. Simulink Model of Fuzzy PID Control 

 

3.3. PID tuning and simulation 
With a step value set to 1 and a simulation time of 0.02s, 

 ,  ,  , the simulation 

curves for the position-based PID are as shown in Fig. 14. 
Performance metrics were measured in the Scope module, 
resulting in an adjustment time of 2.5ms, a steady-state error 
of 0, and an overshoot of 7%. 

 



 

281 

 
Figure 14. Simulation Results of Position PID 

 

Similarly, with the simulation parameters set , 

 ,  , the simulation results for the 

incremental PID are shown in Fig. 15. The overshoot is 18%, 
the adjustment time is 12.5ms, and the steady-state error is 0. 

 

 
Figure 15. Simulation Results of Incremental PID 

 
The fuzzy PID performs real-time corrections on the 

traditional PID through fuzzy control rules. To accelerate the 
simulation speed, a zero-order holder is added before the 

fuzzy controller,  ,  ,   are set to -4, 0.1, 

and 0.05, respectively. The response curve is obtained as 
shown in Fig. 16. 

 

 
Figure 16. Simulation Results of Fuzzy PID 

 
From the simulation curve of the fuzzy PID in Fig. 16, it 

can be observed that the overshoot is 8%, the adjustment time 
is 2.3ms, and the steady-state error is 0. 

In order to compare the advantages and disadvantages 
between traditional PID and fuzzy PID control under the same 

conditions, parameters  ,  , 

 are set to the same values for both controllers. 

They are then placed in the same scope for observation, and 
the output response curves are shown in Fig. 17. The 
simulation performance parameters are summarized in Table 
5. 

 

 
Figure 17. Simulation Results of Traditional PID and Fuzzy 

PID 
 

Table 5. Performance Metrics for Traditional PID and 
Fuzzy PID 

Controller Overshoot 
(%) 

Stabilization 
Time (ms) 

Steady-state 
Error 

Traditional 
PID 

7.8 2.5 0 

Fuzzy PID 2.3 3.0 0 

 

From Fig. 17 and Table 5, it can be observed that fuzzy PID, 
while ensuring response speed, reduces the overshoot of the 
motor response, shortens the system's stabilization time, and 
provides a smoother output response curve, demonstrating 
more stable control characteristics. 

4. Conclusion 
This paper mainly introduces the drive and control of a 

robot omnidirectional mobile platform. Through the analysis 
of the motor's equivalent circuit, the system transfer function 
of the DC motor is derived in detail. After substituting the 
motor parameters, the mathematical model of the motor's 
speed relative to the armature voltage is obtained, laying the 
groundwork for later MATLAB simulation. Then, based on 
the principles of traditional PID and fuzzy PID, 
corresponding controllers are designed. Simulations are 
conducted using Simulink for various PID controllers, and 
comparative analysis reveals that fuzzy PID exhibits superior 
control characteristics compared to traditional PID. 

Acknowledgment 
This project is supported by the Graduate Innovative 

Research Project of Southwest Minzu University (Project No. 
ZY2022650). 



 

282 

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