=Paper=
{{Paper
|id=Vol-3790/paper8
|storemode=property
|title=Generalized integro - differentiating controller for mechatronic devices of mobility nodes of humanoid robots
|pdfUrl=https://ceur-ws.org/Vol-3790/paper08.pdf
|volume=Vol-3790
|authors=Oleksandr Lysenko,Olena Tachinina,Oleksandr Guida,Iryna Alekseeva,Vladyslav Kutiepov
|dblpUrl=https://dblp.org/rec/conf/icst2/LysenkoTGAK24
}}
==Generalized integro - differentiating controller for mechatronic devices of mobility nodes of humanoid robots==
https://ceur-ws.org/Vol-3790/paper08.pdf
Generalized integro - differentiating controller for
mechatronic devices of mobility nodes of humanoid
robots
Oleksandr Lysenko1,, Olena Tachinina2 , Oleksandr Guida3, Iryna Alekseeva1 and Vladyslav
Kutiepov2
1
, 37, Prosp. Peremohy, Kyiv, 03056,
Ukraine
2
National Aviation University, 1, Liubomyra Huzara ave., Kyiv, 03058, Ukraine
3
Abstract
The article considers the generalized integro-differentiating controller (GID-controller) as an alternative
to the PID-controller for use in cascaded SISO LTI systems for automatic control of mechatronic devices
of mobility nodes of humanoid robots. GID - controller is set by a generalized integro-differentiating
circuit or a connection of an ideal integrator with generalized prejudice-delay compensators. The article
shows that the main positive property of the GID controller compared to the PID controller is that, in the
presence of the SISO LTI mathematical model of the control object, the primary parametric setting of the
GID controller gives a practically acceptable rational result of controlling the robot movements. That is,
the initial parametric setting of the GID controller does not require further additional adjustment of the
controller parameters. This positive quality of the GID - controller allows you to significantly reduce the
time for adjusting the controller parameters on a real object. Therefore, the method of parametric
adjustment of the GID - controller was called the method of express adjustment of the generalized
integro-differentiating controller (MEA GID - controller). The result of a computer experiment is
presented, which showed that the MEA GID - controller provides quality, simplicity, convenience and
time saving during parametric adjustment of the controller, which justifies the expediency of using the
GID controller for controlling mechatronic devices of robot mobility nodes in general and, in particular,
humanoid robots with increased requirements to human-like movements.
Keywords
Automatic control system, PID-controller, integro-differentiating circuit, prejudice-delay
compensators 1
1. Introduction
When making humanoid robots designed to work next to human (housework, nursing robots,
service jobs in customer service areas), one of the main requirements is the implementation of the
principle of safe interaction between humanoid robots and human [1-6]. This principle is
implemented thanks to an approach that can be called "smoothness + sensuality" ("S + S"): the
robots perform movements that resemble (practically do not differ from) human movements, that
means, that they are smooth and sensual in terms of strength [5-7]. The structure of cascade
(multi-loop) SISO LTI automatic control systems with the properties of quasi-invariance (quasi-
adaptability) to the action of external disturbances in the best way ensures the implementation of
the "S + S" approach [8-11] (see Figure 1). Usually, in each of the cascades, controller with
parametric adjustment are used with a structure of PID-controller varieties (from a proportional
controller to a full structure with proportional, integral, and differential signals) [12, 13]. The
presence of an integrating link provides the property of quasi-invariance to external disturbances
such as step action [8]. Considering the fact that in humanoid robots the number of mobility nodes
exceeds hundreds [6, 7, 9], and in cascade automatic control systems of drives in mobility nodes, at
least two cascades are used, the total number of controllers that need to be adjusted can exceed
thousands. It is clear that an urgent engineering problem arises regarding the rapid adjustment (or
ICST-2024: Information Control Systems & Technologies, September , 23 25, 2024, Odesa, Ukraine
lysenko.a.i.1952@gmail.com (O. Lysenko); tachinina5@gmail.com (O. Tachinina); guydasg@ukr.net (O. Guida);
alexir1@ukr.net (I. Alekseeva), vladcorvt@gmail.com (V. Kutiepov)
0000-0002-7276-9279 (O. Lysenko); 0000-0001-7081-0576 (O. Tachinina); 0000-0002-2019-2615 (Guida O.); 0000-0002-
2878-6514 (I. Alekseeva), 0000-0002-1055-9698 (V. Kutiepov)
Β© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
re-adjustment) of controllers. Let us emphasize that, if computer numerical tuning programs are
used for parametric tuning according to algorithmically set criteria, then the actual task of quick
adjustment of the controller turns into the actual task of finding the first successful approximation,
that is, finding the initial conditions from which the computer adjustment algorithms "starts" [14
17].
2. Problem Statement
Two-cascade control systems (Figure 1) have better indicators of control quality compared to
single-cascade systems [8]. Therefore, they should be used where they do not exist yet. If two-
cascade control is abandoned in those mobility nodes, where it exists, in order to reduce the
number of controllers to be adjusted, the following positive properties of cascade control will be
lost:
1. External disturbances acting on the part of the control object that is covered by local
feedback will directly affect the output coordinate, and won`t be reduced in the internal
auxiliary loop.
2. Parametric disturbances that occur in the internal circuit will significantly affect the output
signal.
3. The time of the transient response at the output of the system will increase significantly if
the internal feedback is turned off, due to which the dynamic properties of the mechatronic
devices of the mobility node are corrected.
Figure 1: Structural diagram of the cascade (multi-circuit) SISO LTI system of automatic control of
mechatronic devices in the mobility nodes of humanoid robots: ππ
π (π ), πππ (π ) ( π = 1,2) - scalar
continuous transfer functions that reflect the algorithm of the controller (index Rj) and
mathematical model of the control object (index Oj) corresponding to the first cascade (internal
circuit, j=1) and the second cascade (external circuit, j=2) of the automatic control system
Currently, in mechatronic devices of mobility nodes of humanoid robots are used (almost 100%)
as controllers in both cascades PID-controllers [8-12]. As known, the PID-controller forms its
output signal as the sum of proportional, integral and differential signals from the error applied to
its input. We will use the so-called standard form to display the mathematical model of the PID-
controller operation algorithm
1 πππ β π
πππΌπ·π (π ) = πππ β (1 + + ), (1)
πππ β π πππ β π + 1
where (according to recommendations [8]) we assume that the additional time constant can be
calculated from the following relation πππ = 0.15 β πππ (π = 1,2) .
Let us assume that the mathematical model of the control object is known πππ (π ) ( π = 1,2). As
a controller in both cascades, it is planned to use a PID controller, that is, the structure of the
controller is known: ππ
π (π ) = πππΌπ·π (π ) (π = 1,2). As a rule, a two-stage procedure is used to set
the parameters of both PID controllers, in which the smoothness (human-likeness) of movements is
implemented in the automatic control system: at the first stage, the initial adjustment is performed
using the Ziegler-Nichols or Cohen-Kun methods; at the second stage, the result of the initial
adjustment is improved using computer simulation. The duration and effectiveness of the second
stage significantly depends on the initial adjustment. The experience of adjusting the PID -
controller as a whole, shows that 90% of the time (and at the same time not always with the desired
result) is spent on the second stage of adjustment [8-12].
A scientific-technical problem arises: to reduce the time spent on such a setting of the
cascade system of automatic control of mechatronic devices in mobility nodes, which ensures the
smoothness of the movements of the humanoid robot, that means that almost human-like
movements are achieved.
The engineering experience of solving the problems of adjusting the structure and parameters
of the controllers indicates two effective approaches: first, to ensure a successful first
approximation to the acceptable structure and parameters of the controller (initial adjustment);
secondly, after the first approximation, adjust the minimum number of parameters.
3. Method of express adjustment of the generalized integro-
differentiating controller (MEA GID- controller)
The initial data for solving the scientific-technical problem is: the structure of the cascaded SISO
LTI automatic control system (ACS) (Figure 1) and the mathematical model of the control object
πππ (π ) ( π = 1,2).
An ACS with PID controllers is considered as a prototype ACS, which should be improved by
usage of a GID - controller. PID - controllers are connected to the internal and external cascades
respectively (Figure 1).
The task of synthesizing a cascade ACS (Figure 1) is considered solved if the algorithms of the
ππ
π (π ) (π = 1,2) .
The general approach to the synthesis of transfer functions of regulators ππ
π (π ) (π = 1,2) is as
follows. First, the regulator for the internal cascade (circuit) is synthesized with the mathematical
model of its operation algorithm, which is specified by the transfer function ππ
1 (π ) , where as a
mathematical model of the control object is considered ππ1 (π ) (Figure1). After that, the synthesis
of the regulator of the external cascade (circuit) is performed, which means that the transfer
function is found ππ
2 (π ). As a mathematical model of the control object, the serial connection of
the transfer functions of the internal cascade (circuit) and ππ2 (π ) .
In order to solve the scientific-technical problem set above, it is proposed: replace the PID-
controllers in the cascade system-prototype with generalized integro-differentiating controllers
(GID - controllers), for the initial adjustment of which use a special method of initial express
adjustment with increased adjustment quality.
Content of the main material: structure and parameters of GID - controller; method of express
adjustment of GID - controller; an example of the initial setting of PID and GID - controllers for a
cascade ACS and comparative modeling of transient response in a cascade ACS with synthesized
regulators.
Structure and parameters of GID - controllers.
As an alternative to the PID-controller algorithm, it is proposed to apply the algorithm, which is
given by the transfer function of the GID-controller:
(2)
ππΊπΌπ· (π1 π + 1)π1 β (π3 π + 1)π3
πππΌπ· (π ) = π£ β
π (π2 π + 1)π2 β (π4 π + 1)π4
parametric synthesis of which (search of parameters πππΌπ· > 0; π£, π1,2,3,4 β {0; 1; 2; β¦ }; π1,2,3,4 >
0) is proposed to be carried out by the method of express adjustment of the GID - controller (MEA
GID-controller). We emphasize once again that the MEA GID-controller is considered as a method
of primary parametric adjustment of the regulator.
We will remind, that according to the terminology used in the national or English-language
scientific literature, the GID - controller is also called a generalized integro-differentiating circuit
or a connection of an ideal integrator with generalized prejudice-delay compensators.
3.1. Stages of MEA GID-controller
Stage 1. Create a mathematical model of an open circuit.
Consider the open circuit in the form of a serial connection of mathematical models of the GID -
controller and control object and calculate the transfer function of the open circuit:
(π π +1)π1 β(π π +1)π3 1
β (π )
ππ (π ) = ππΊπΌπ· (π ) β ππ (π ) = ππΊπΌπ· β (π1 π +1)π2 β(π3 π +1)π4 β π π£ ππ (π ) = ππΊπΌπ· β ππβ (π ), (3)
2 4
where
β (π ) (π π +1)π1 β(π π +1)π3
πππΌπ· = ππΊπΌπ· β (π1 π +1)π2 β(π3 π +1)π4 ;
2 4
1
ππβ (π ) = π π£ ππ (π ) ;
1 π π π +π π πβ1 +β―+π π +π
ππ (π ) = π π β ππ π π +ππβ1π πβ1 +β―+π 1π +π 0,
π πβ1 1 0
ππ transfer function of the control object. We will remind that considered as known: π the
number of ideal integrators in the mathematical model of control object; π and π - orders of
polynomials in the numerator and denominator ππ (π ) and the coefficients of these polynomials in
the corresponding powers π .
Stage 2. Set the structural parameters of the transfer function ππΊπΌπ· (π ) of GID-controller π£ and
π1,2,3,4 .
Usually, π£ and π1,2,3,4 β {0; 1; 2}.
We choose π£ (π£ the number of ideal integrators in the controller) to fulfill the requirement to
ensure the given order of astatism of the closed circuit (Figure 1) taking into account the number of
ideal integrators in the control object.
We choose π1,2,3,4 taking into account the properties of prejudice-delay compensators (PDC)
π π +1 π π +1
π12 (π ) = π1 π +1 and π34 (π ) = π3 π +1 .
2 4
Analysis of the amplitude and phase-frequency characteristics of bias-delay compensators
allows us to draw the following conclusions:
1. A PDC with the properties of an advance link allows you to increase the phase margin.
2. A PDC with the properties of a delay link allows you to reduce the impact of high-
frequency disturbances.
3. The sequential inclusion of the prejudice-delay links with raising the binomials to the
appropriate power π1,2,3,4 allows you to obtain and strengthen both positive effects.
Stage 3. Calculate the cutoff frequency ππ§ for the transfer function ππβ (π ), that means, the
frequency at which |ππβ (π β ππ§ )| = 1.
For designing the transfer function
1 π π π +π π πβ1 +β―+π π +π
ππβ (π ) = π π£+π β ππ π π +ππβ1π πβ1 +β―+π 1π +π 0 (4)
π πβ1 1 0
and calculating the cutoff frequency, corresponding functions of the computer mathematics system
MATLAB+Simulink can be used.
Stage 4. Calculation of the GID-controller parameters.
Based on the known cut-off frequency ππ , calculate the parameters of the transfer function of
the GID-controller:
3.3 1 1 1
π1 = ; π3 = ; π2 = ; π4 = .
ππ§ 3.3βππ§ 33βππ§ 330βππ§
Written down ratios make it possible to obtain a successful first approximation to the
acceptable values of the GID-controller parameters at any values of its structural parameters π and
ππ,π,π,π . These ratios are obtained as a result of empirical generalization of the experience of
synthesis of GID - controllers.
Stage 5. Selection of structural parametersπ1,2,3,4 and the gain of the regulator ππΊπΌπ· .
First step: set π1,2,3,4 = 1.
Design a computer mathematical model and perform a simulation experiment for selection ππΊπΌπ·
. Recommended: Start with a value ππΊπΌπ· β [0.1 β πππΎπβπ ; 0.5 β πππΎπβπ ], where πππΎπβπ gain
coefficient, which is calculated by the method of Ziegler-Nichols oscillations [8], and choose such a
value of ππΊπΌπ· , at which the duration of the transient response, oscillation and overregulation will
have acceptable values for the specific task.
If it was successful in choose ππΊπΌπ· , in which the above stated parameters of the transient
response satisfy the requirements of a specific task, then we consider that stage 5 is completed.
If it was not possible to meet the requirements of a specific task, then we change one of the
structural parameters π1,2,3,4 and repeat the selection ππΊπΌπ· .
During the initial setup, stage 5 is performed in the interactive "manual" mode. Experience
shows that no more than a few "runs" of a computer mathematical model are enough to obtain a
result acceptable for practical use, that is, before stopping the adjustment as a whole. Let us
emphasize that the "human-likeness" of movements is assessed by experts, although formally the
smoothness of movements can be specified using well-known standard forms [12].
4. Results and discussions
In this section, we will consider an example of the initial setting of the PID- and GID-
controllers for a cascade ACS (Figure 1) and perform a comparative simulation of transient
responses in a cascade ACS with synthesized controllers. Let us start with the initial setting of the
PID - controllers for the cascade ACS (Figure 1).
The initial setting of the PID - controllers for the cascade ACS (Figure 1). For the initial setting
of the PID-controller parameters (that is, determination of the gain ππ , constant of integration ππ
and constant of differentiation ππ ) we will use well-known methods [8]: Ziegler-Nichols
oscillations (KZ-N); Ziegler - Nichols when using the transient response (Z-NPP); Cohen Kuhn
using the transient response (K-KPP). To demonstrate the exact method by which the parameters
of the PID controller were determined, we will use the corresponding indices for each of the
methods: πππΎπβπ , πππΎπβπ , πππΎπβπ ; πππβπππ , πππβπππ , πππβπππ ; πππΎβπΎππ , πππΎβπΎππ , πππΎβπΎππ .
The above-mentioned methods require conducting a computer or field experiments [8-12].
According to the results of the experiment, auxiliary parameters are determined, which we will
denote as πΎ0 , π0 ; π₯0 (π‘0 ), π₯0β = lim π₯0 (π‘) , π‘0 , π‘1 , π‘2 . Physical and mathematical content of these
π‘ββ
parameters is illustrated with the help of figures 2 and 3.
Figure 2: A transient response with constant oscillations with a period of π0 at the output of a
closed system consisting of a proportional controller with a gain factor of πΎ0 and a control object:
the values πΎ0 , π0 are used to calculate the parameters (initial setting) of the PID - controller using
the Ziegler-Nichols oscillation method
According to the known πΎ0 , π0 πππ π₯0 (π‘0 ), π₯0β = lim π₯0 (π‘) , π‘0 , π‘1 , π‘2 parameters of the PID-
π‘ββ
controller are calculated using the above-mentioned methods [8]:
π
πππΎπβπ = 0.6 β πΎ0 , πππΎπβπ = 0.5 β π0 , πππΎπβπ = 80;
π·
2
πππβπππ = 1.2 β π· βπ· , πππβπππ = 2 β π·1 , πππβπππ = 0.5 β π·1;
0 1
π·2 π·1
πππΎβπΎππ = β (0.9 + ),
π·0 β π·1 12 β π·2
30 β π·2 + 3 β π·1
πππΎβπΎππ = π·1 β ,
9 β π·2 + 20 β π·1
4βπ· βπ·
1 2
πππΎβπΎππ = 11βπ· +0.2βπ· ,
2 1
where π·0 = π₯0β β π₯0 (π‘0 ), π·1 = π‘1 β π‘0 , π·2 = π‘2 β π‘1 .
Figure 3: Transient response at the output of the control object: value π₯0 (π‘0 ), π₯0β =
lim π₯0 (π‘) , π‘0 , π‘1 , π‘2 are used to calculate parameters (initial setting) of the PID - controller by
π‘ββ
methods of Ziegler-Nichols and Cohen Kuhn when using a transient response (a tangent is
drawn at point A (the inflection point of the transient response))
We consider that the mathematical model of the mechatronic device in each of the mobility
nodes is given by the continuous transfer functions ππ1 (π ) and ππ2 (π ) (Figure 1). The transfer
function ππ1 (π ) can be calculated as the transfer function of serially connected links of directed
action. These links are a power transformator with a transfer function ππ (π ) and a direct current
motor (DC) with a transfer function ππ·ππ (π ), where the output signal is considered to be the
angular speed of the rotor, i.e.:
ππ1 (π ) = ππ (π ) β ππ·ππ (π ).
The first cascade (circuit) consists of a controller with a transfer function ππ
1 (π ) and a control
object with a transfer function ππ1 (π ) (Figure 1). The second cascade consists of a controller with
a transfer function ππ
2 (π ) and a control object with a transfer function equal to the product of the
π (π )βππ1 (π )
transfer functions of the first cascade (circuit), π»1 (π ) = π
1 (π )βπ
1+ππ
1
to the transfer function
π1 (π )
1
ππ2 (π ) = π , where the output signal is the rotation angle of the DC motor rotor.
When performing computer experiments, typical transfer functions of mechatronic devices of
mobility nodes of humanoid robots were used [8-12]:
10 1
ππ (π ) = 0.0003βπ 2 +0.04βπ +1 ;ππ·ππ (π ) = 0.4βπ 2 +1.3βπ +1 .
Let us perform the initial setting of the PID - controller of the first cascade using the above
stated methods. During the initial setting of the PID - controller of the first cascade (internal
circuit), the following auxiliary values of parameters were obtained:
πΎ0 = 3.5, π0 = 0.72 π ; π₯0 (π‘0 ) = 0, π₯0β = 10, π‘0 = 0 π , π‘1 = 0.25 π, π‘2 = 2 π .
The result of calculating the parameters of PID - controller of the first cascade (internal circuit):
πππΎπβπ1 = 2.100 , πππΎπβπ1 = 0.3600 π , πππΎπβπ1 = 0.0900 π ;
πππβπππ1 = 0.8400 , πππβπππ1 = 0.500 π , πππβπππ1 = 0.1250 π ;
πππΎβπΎππ1 = 0.6383 , πππΎβπΎππ1 = 0.6416 π , πππΎβπΎππ1 = 0.0907 π .
Let us perform the initial setting of the GID - controller of the first cascade using the MEN UID
- regulator. Assume that π£ and π1,2,3,4 are equal to one. We will calculate the cut-off frequency
and parameters of the GID - regulator of the first cascade (internal circuit). We will use the
positioning of the MEA GID-controller and as a result we will get:
πππ
ππ§1 = 2.61 π ,π11 = 1.2644 π , π31 = 0.1161 π , π21 = 0.0116 π ,
π41 = 0.0012 π . We assume, that πππΌπ·1 = 0.1 β πππΎπβπ1 =0.21 .
Before moving on to adjusting the parameters of the controller of the second cascade (Figure 1),
consider the transient response at the output of the two-cascade ACS under the condition that
ππ
2 (π ) = 1. Let us clarify the issue of the necessity to complicate the general procedure for
setting up a two-stage ACS by adjusting the controller for the second cascade.
Let us perform a visual analysis of the transient responses (see Figure 4) at the output of the
two-stage ACS (Figure 1).
This analysis shows: when using the GID-controller, the initial setting of which is performed
using the proposed method, the smoothness of movements in the mobility node of the humanoid
robot will be better than when using the PID-controller.
Thus, if there is no need to reduce the readjustment and the duration of the transient response,
then it can be assumed that the cascade ACS can be designed with the connection of only one GID-
controller in the internal cascade of the ACS (we consider the external cascade as having a
proportional controller with a gain factor connected to it, which is equal to one).
We especially emphasize that it is not necessary to adjust the GID - controller: only the initial
setting is enough.
Let us assume that there is still a necessity to reduce the duration of the transient response
while maintaining the smoothness of the movements in the mobility node. Then we will perform
1
the initial setting of the PID and GID-controllers for the second cascade (circuit). Since ππ2 (π ) = π
, then only the Ziegler-Nichols oscillation method can be used to adjust PID-controller.
Figure 4. Transient response at the output of the two-cascade ACS (Figure 1) under the
condition that ππ
2 (π ) = 1 and different ππ
1 (π ): 1, 2, 3, transfer function ππ
1 (π ) is equal to the
transfer function of the PID - controller, the parameters of which are adjusted by the methods of
Ziegler-Nichols oscillations, Ziegler-Nichols when using a transient response, and Cohen-Kuhn
when using a transient response respectively; 4 - transfer function ππ
1 (π ) is equal to the transfer
function of the GID - controller.
During the initial setting of the PID - controller of the second cascade (external circuit), the
following auxiliary values of parameter were obtained
πΎ0 = 3.5, π0 = 0.72 π .
Based on these values, the parameters of the PID-controller of the second cascade were
calculated:
πππΎπβπ2 = 1.800 , πππΎπβπ2 = 0.3300 π , πππΎπβπ2 = 0.0825 π .
Let us move on to setting up the GID-controller. Assume, that π£ and π1,2,3,4 equal to one.
During the initial setting of the GID-controller of the second cascade (external circuit), the
πππ
following value of the cutoff frequency was obtained ππ§2 = 0.99 π and the values of the GID-
controller were calculated:
π12 = 3.3333 π , π32 = 0.3061 π , π22 = 0.0306 π , π42 = 0.0031 π .
Let us assume, that πππΌπ·2 = 0.2 β πππΎπβπ2 =0.36 . As we can see (see Figure 5), the use in the
second cascade of the GID-controller with the initial setting of parameters allows to obtain
smoother movements in the mobility node of the humanoid robot compared to the use of the
initially configured PID-controller. We note, that there will be almost no readjustment. In order to
improve the result of the GID-controllers application, we will change the structural parameters of
the GID-regulators in both cascades (circuits). Let us assume, that π£ = 1 and π1,2 = 1, π3,4 = 2
provided that the parameter values π1π , π3π , π2π , π4π (π = 1,2) and πππΌπ·1 remained unchanged.
Let us assume, that πππΌπ·2 = 0.5 β πππΎπβπ2 . It was possible to reduce the duration of the transient
response by almost two times while maintaining the smoothness of the movement and the absence
of readjustment (Figure 6).
Figure 5. Transient responses at the output of the two-cascade ACS (Figure 1) under the condition
that: 1 transfer functions ππ
1 (π )and ππ
2 (π )are equal to the transfer functions of the PID -
controllers, parameters of which are adjusted by the Ziegler - Nichols oscillation method; 2
transfer functions ππ
1 (π ) and ππ
2 (π ) are equal to the transfer functions of the GID - controllers,
under the condition that the structural parameters of the GID - controllers π£ and π1,2,3,4 are equal
to one
Figure 6. Transient responses at the output of the two-cascade ACS (Figure 1) under the condition
that: 1 transfer functions ππ
1 (π ) and ππ
2 (π ) are equal to the transfer functions of the PID -
controllers, parameters of which are adjusted by the Ziegler - Nichols oscillation method; 2 the
transfer functions ππ
1 (π ) and ππ
2 (π ) are equal to the transfer functions of the GID - controllers,
under the condition that the structural parameters of the GID - controllers π£ v and π1,2,3,4 are
equal to one, and π3,4 = 2
5. Conclusions
As an alternative to the PID-controller for usage in cascaded SISO LTI systems for automatic
control of the mobility nodes of humanoid robots, it is proposed to use a controller, which is set by
a generalized integro-differentiating circuit or a connection of an ideal integrator with generalized
prejudice-delay compensators. This controller was called a generalized integro-differentiating
controller (GID - controller).
The main positive property of the GID-controller compared to the PID -controller is that when
SISO LTI mathematical model of the control object is available, the primary parametric setting of
the GID-controller gives an almost acceptable rational result of control that does not require
additional adjustment. Therefore, the method of parametric adjustment of the GID - controller was
named the method of express adjustment of the generalized integro-differentiating regulator (MEA
GID-controller).
MEA GID-controller provides quality, simplicity, convenience and time saving during
parametric adjustment of the controller, which justifies the expediency of using the GID -
controller for controlling mechatronic devices of robot mobility nodes in general and, in particular,
humanoid robots with increased requirements for human-like movements.
The computer experiment presented in the article illustrated and confirmed the positive
properties of the GID - controller, which give it an advantage compared to the PID - controller.
Further research will be aimed at developing a method of structural-parametric synthesis of the
GID - controller and its application in automatic control systems with significant nonlinearities.
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