A control method for output reachable set of a direct current motor switching singular multi-agent system
By constructing a DC motor-switching singular model and performing feedback compensation, the problem of pulse effect caused by feedback loop delay and mode switching in the DC motor system was solved, ensuring the stability and control accuracy of the system.
Patent Information
- Application Number
- CN202610282059.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-10
- Publication Date
- 2026-06-30
Smart Images
Figure CN122316181A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a control method for the output reachable set of a DC motor switching singular multi-agent system, belonging to the field of DC motor control. Background Technology
[0002] Multi-agent systems (MASs) consist of multiple agents with independent decision-making and execution capabilities. These agents collaborate through local information exchange to complete complex global coordination tasks. In recent decades, MASs have received significant attention from the scientific community due to their widespread applications in cooperative control, distributed sensor networks, smart grids, and formation control. In robotics, DC motors are the core actuators driving joints, wheels, and propellers. To achieve position consistency and trajectory tracking in complex environments, the electromechanical dynamics of DC motors must be modeled. Crucially, the dynamic response of DC motors not only determines the control performance of individual nodes but also affects the stability of the entire MAS system through network coupling. Furthermore, introducing switching mechanisms can effectively characterize structural abrupt changes that occur during system operation. Therefore, the integration of switched systems, singular systems, and MASs plays an indispensable role in modern control theory and engineering, and can be used to solve control problems in complex scenarios such as interconnected power grids, distributed robotic systems, and cyber-physical systems.
[0003] Switching singular systems consist of differential equations, algebraic constraints, and switching mechanisms. For DC motor systems, a switching singular model can be constructed by characterizing the topological constraints of the armature circuit, the algebraic relationship between speed and current, and the electromechanical coupling characteristics. This model can effectively describe the discontinuous characteristics of DC motor operation, such as mode switching and load changes. Compared with traditional state-space models, switching singular models consider both the dynamic evolution of states and the static constraints described by algebraic equations, providing a more comprehensive characterization of the actual physical system. In theoretical analysis, to ensure system performance, each subsystem must possess regularity and pulse-free characteristics. When the system satisfies regularity, its solution exists and is unique; this property can be guaranteed under compatible initial conditions. Pulse-free characteristics suppress transient pulse effects caused by mode switching or structural changes, fundamentally avoiding sudden changes in DC motor speed and current, ensuring safe and robust system operation.
[0004] Due to physical limitations such as sensor sampling bandwidth, signal processing delay, and network communication latency, time delays inevitably occur in the closed-loop feedback loop of a DC motor. These delays can lead to DC motor speed instability and reduce the consistency control performance of multi-agent systems. Simultaneously, mode switching in a singular system can generate pulse effects due to abrupt changes in system structure and parameters, manifesting as transient jumps in current and voltage, posing significant challenges to system safety and control accuracy. To suppress these transient effects, a controller must be designed and introduced based on real-time data. During system operation, structural changes introduce unstable energy, requiring rapid control adjustments to offset its impact. The method proposed in this paper effectively reduces the complex coupling effect between feedback delay and pulse effects by processing feedback delay during normal system operation and applying pulse control at switching moments, thus ensuring the operational stability of the DC motor system.
[0005] The reachability set of a dynamic system refers to the set of all output states that the system can reach from initial conditions under bounded disturbances. Currently, numerous scholars have conducted research on the theoretical issues related to reachability sets for various system models, including singular systems, switched systems, TS fuzzy systems, Markov jump systems, and time-delay systems. For DC motor cooperative systems, reachability sets can be used to characterize the range of output fluctuations caused by external disturbances, thereby determining whether key physical quantities such as armature current and DC motor speed exceed preset safety thresholds, providing a direct theoretical criterion for DC motor fault early warning and safety constraint verification. However, most existing studies have failed to fully consider the coupling effect between the inherent impulse characteristics and control delay of switched singular multi-agent systems. Summary of the Invention
[0006] This invention proposes an output reachable set control method for a DC motor switching singular multi-agent system. The problem it solves is to provide feedback compensation for feedback loop delay and pulse effects generated by mode switching, and to limit the current and speed within the reachable set.
[0007] This invention includes the following steps: S1. Construct a DC motor-switching singular model; S2. Monitor the current and speed of the DC motor in the execution system, and construct a pulse reset map to capture the transient jumps in the current; S3. After a jump occurs, the voltage is compensated by feedback through the switching singular model. S4. Ensure that the system state is within a preset bounded set, further limiting the current and speed to within safe thresholds, and protecting the normal operation of the DC motor.
[0008] Furthermore, the DC motor-switching singular model is as follows: DC motor current and DC motor shaft speed Used as the system state vector Power supply voltage As control input The output current is considered as the system output vector. Voltage fluctuations caused by external load disturbances Modeled as system disturbance input vector , No. The dynamic characteristics of a DC motor are described by the following formula: , , in , , , , .
[0009] Furthermore, the execution system includes N DSP controllers, N DC motors, and N sensors. The DC motor and the first The first DSP controller, the first The sensors are connected together, including a current sensor and a speed sensor.
[0010] Furthermore, due to mechanical inertia, the shaft speed of a DC motor... Maintain continuity, while armature current A transient jump will occur. To capture this transient jump, the pulse reset mapping is introduced:
[0011] in and These represent the error states before and after the switch, respectively. Specifically, the jump matrix is selected as follows: , , .
[0012] Furthermore, the switching singularity model includes delay compensation and impulse compensation.
[0013] Furthermore, disturbance input Bounded, satisfied ,in Given a known positive real constant, for the th singularity in the switching model The distributed output delay compensation feedback control protocol for a DC motor is designed as follows:
[0014] in For the switching controller gain to be determined, Represents time-varying delay, satisfying .
[0015] Furthermore, the system pulse compensation is as follows:
[0016] in The switching controller gain is to be determined.
[0017] Furthermore, the reachable set is defined as: , The ellipsoidal boundary of the system's reachable set can be characterized by the intersection of a family of ellipsoids:
[0018] Among the requirements .
[0019] Beneficial effects: 1. A novel hybrid control strategy is proposed to address the coupling problem between time delay and impulse dynamics. The proposed strategy not only designs a state-output feedback loop with time delay to suppress consistency errors caused by communication delay, but also introduces an impulse state feedback loop at the switching moment to respond to the energy jump problem caused by abrupt changes in system structure.
[0020] 2. A DC motor model was constructed to verify the validity of the theoretical results. A corresponding switching singular multi-agent model was established by characterizing the armature circuit resistance switching structure and electromechanical coupling characteristics. The proposed reachability set theory scheme realizes the safety domain constraint on the DC motor speed and current, effectively eliminating the adverse effects of structural abrupt changes and time delays.
[0021] 3. Sufficient conditions were derived through linear matrix inequalities, and a theoretical framework for the output reachable set was established to ensure that the output reachable set of the closed-loop system is always constrained within the ellipsoidal region. This further restricts the current and speed, ensuring the safe operation of the DC motor. Attached Figure Description
[0022] Figure 1 This is a flowchart of the present invention; Figure 2 Block diagram of DC motor followers: Follower 1 and 2; Figure 3 This is the directed switching graph of the present invention; Figure 4 This is the set of output error trajectories achievable by the present invention; Figure 5 This invention involves switching signals and pulse effects; Figure 6 For the present invention when switching signal System state trajectory; Figure 7 For the present invention when switching signal System state trajectory; Figure 8 The present invention has a switching signal The output error trajectory. Detailed Implementation
[0023] Combination Figure 1-8 This implementation method is explained below. Symbol explanation: In this text, Rn denotes an n-dimensional Euclidean space. For any real symmetric matrix P, P>0 (or P ≥ 0) indicates that it is a positive definite matrix (or a semi-definite matrix). The identity matrix and the zero matrix with appropriate dimensions are denoted by I and 0, respectively. The Kronecker product is... The superscript "T" indicates the transpose of a matrix or vector. In a symmetric matrix, the asterisk (*) represents the transpose. Let denote the term derived from symmetry. We define He(A) = A + AT, and denote the Euclidean norm as ∥ · ∥. Unless otherwise stated, all matrices are assumed to have compatible dimensions.
[0024] Consider a directed graph , which includes 10 followers ,in and a leader To analyze the interaction structure among followers in detail, we introduce a directed graph. , where the node set Describing followers, edge sets This represents the connection between them. Directed edge. Indicates following the node To follow the node The information flow, which means yes The neighbors. Follow the node. The neighbor set is represented as The adjacency matrix of the following nodes is represented as follows: ,in hour, Otherwise. The Laplace matrix of a directed graph. Defined as ,in It is the degree matrix of the graph, and And for all The leader adjacency matrix is a diagonal matrix. It means that among them Indicates the leader Followers Neighbors Indicates other cases. Information exchange matrix. Defined as Used to describe directed graphs The information flow topology in a graph. A graph is called a graph if there exists a root node and all other nodes have directed paths from that root node. It has a directional spanning tree.
[0025] Consider a class of switching singular multi-agent systems consisting of N followers and one leader. The dynamics of the i-th follower are expressed as:
[0026] in For state vectors, To control the input, As a disturbance input, For measurement output. Matrix Given a real matrix of appropriate dimensions. It is a singular matrix that satisfies Switching signals It is a piecewise constant function that takes values from the set For each For what have ,have The switching time satisfies... And recursively defined as Furthermore, the switching time satisfies the non-Zeno condition. .
[0027] The dynamic characteristics of a leader are described as follows:
[0028] in and These are the leader's status and measured output, respectively.
[0029] Matrix pairs It is called: A regular matrix, if ; No pulse matrix, if
[0030] .
[0031] Definition 2: A switching singular multi-agent system consisting of followers and leaders is called regular and impulsive if defined... For all Both are valid.
[0032] Assumption: For each Matrix pairs It is sedative, and the matrix pairs It is detectable, where stabilization is relative to the singular matrix. Defined.
[0033] To address the leader-follower consistency problem under perturbation input, the consistency errors of the state and output are defined as follows: .
[0034] make
[0035]
[0036]
[0037]
[0038] The error dynamic equation of a multi-agent system can then be written in the following compact form:
[0039] It is an N×N identity matrix.
[0040] Assumption: Disturbance input Bounded, satisfied ,in It is a known positive real constant.
[0041] For the first in the follower system The distributed output feedback control protocol with one follower is designed as follows:
[0042] in For the switching controller gain to be determined, Represents time-varying delay, satisfying .
[0043] Substituting equation (4) into equation (3), we obtain the dynamic equation for the closed-loop error as follows:
[0044] Within the leader-follower consensus framework, the reachable set of switching singular multi-agent systems was investigated. Synthesis. Specifically, the impulse effect is modeled as follows:
[0045] in and It is a known real matrix with appropriate dimensions. express The pulse jump at time, assuming state It is left-continuous and satisfies +
[0046] and + .
[0047] Considering the pulse timing, a control protocol based on system pulses The design is as follows:
[0048] in The switching controller gain is to be determined.
[0049] Based on the impulse effect model (5), combined with the control protocol and The closed-loop error dynamic equation for the switching singular multi-agent system can be established as follows: when hour
[0050] when hour
[0051] Bounded Lemma, for any ,set up and Let be a given positive scalar. Assume that holds. If a positive definite symmetric matrix exists... and piecewise continuous functions , making
[0052] in Indicates pulse
[0053] Switching time. Therefore, for any... ,in , This represents a bounded perturbation term.
[0054] Determine the real-time output reachable set that limits the output consistency error system. The trajectory. The reachable set is defined as:
[0055] The ellipsoidal boundary of the system's reachable set can be characterized by the intersection of a family of ellipsoids:
[0056] Among the requirements .
[0057] Objective: To determine the leader-follower consistency in a switching singular multi-agent system (3), if the closed-loop error... The difference system (7) is regular and impulsive, and under control protocol (4), the output consistency error is...
[0058] If the trajectory is strictly restricted to the ellipsoid family defined in (13), then it is said that the real-time output reachable set boundary has been obtained.
[0059] This section aims to obtain the real-time output reachable set bounds for leader-follower consistency in a switching singular multi-agent system (3). We establish sufficient conditions in the form of a corresponding strict linear matrix inequality (LMI) to ensure that the output consistency error is constrained within a specified family of ellipsoids.
[0060] Theorem 1: For ,set up and Given a scalar, and If there exists a positive definite symmetric matrix and and arbitrary matrices and and ,That middle This makes the following inequality valid:
[0061]
[0062]
[0063]
[0064]
[0065]
[0066]
[0067]
[0068]
[0069] in , It is a full-rank matrix and satisfies = 0 (rank( ) = ≤ Therefore, given the existence of a state feedback controller, under the assumption that the reachable output states of system (7) can be contained in a family of ellipsoids, as follows:
[0070] The execution system includes N DSP controllers, N DC motors, and N sensors, wherein the... The DC motor and the first The first DSP controller, the first The sensors are connected together, including a current sensor and a speed sensor.
[0071] Example: like Figure 2 As shown, a DC motor experimental verification platform was built. This experimental setup is based on a DSP control core. The main hardware components include a DSP controller, a DC motor driver, a monitoring interface, and a 2342S012CR-158 DC motor. The rated parameters of the DC motor are: rated voltage 12V, rated current 1.6A, rated speed 500 r / min, and no-load current less than 0.0694A.
[0072] The parameter name for a DC motor is: armature resistance. armature inductance torque constant back electromotive force constant gear ratio DC motor efficiency Gearbox efficiency DC motor shaft inertia .
[0073] This multi-agent system comprises three agents: a virtual leader (node) ) and two physical followers (nodes) and Specifically, the two physical followers are independent DC motors, while the virtual leader is implemented as a computing node running on a central controller. To model the dynamics of the followers, a graph-based approach is used. The following dynamic equations are derived from the block diagram of the armature circuit and gear transmission mechanism shown: Using Kirchhoff's laws, the circuit equation for the i-th DC motor can be derived as follows:
[0074] Due to armature inductance Much smaller than resistance Therefore, it can be ignored. Thus, the circuit equations can be modified. Write as follows:
[0075] Using Newton's second law, the equation of motion for the load of the i-th DC motor can be expressed as follows:
[0076] in
[0077]
[0078]
[0079] This is the rotor inertia of the motor. For load inertia, The internal friction coefficient of the motor. This represents the load friction number.
[0080] The above analysis allows us to establish a switching singular multi-agent system model of a DC motor. In this model, the DC motor current... and DC motor shaft speed Used as the system state vector Power supply voltage As control input The output current is considered as the system output vector. Voltage fluctuations caused by external load disturbances Modeled as system disturbance input vector , No. The dynamic characteristics of a DC motor are described by the following formula:
[0081] in , , , , .
[0082] This refers to the shaft inertia of the DC motor. It is the coefficient of viscous friction; It is the back electromotive force constant; For gearbox efficiency; Efficiency of DC motor; Armature resistance; This refers to the gear ratio; The torque constant; This is the coupling coefficient between load fluctuation and rotational speed.
[0083] Due to mechanical inertia, the shaft speed of a DC motor... Maintain continuity, while armature current A transient jump will occur. To capture this transient jump, the pulse reset mapping is introduced:
[0084] in and These represent the error states before and after the switch, respectively. Specifically, the jump matrix is selected as follows: , ; Furthermore, the communication topology is modeled as follows: Figure 3 The fixed directed graph shown is related to the switching signal. Irrelevant. From Figure 3 The communication matrix can be obtained. .
[0085]
[0086] The parameters for the DC motor system are specified as follows: , , , , , , , , , , , The time-varying delay is due to Give; External disturbances are Other relevant parameters are set to... .
[0087] The leader's initial state is The initial states of the two followers are respectively and The corresponding ellipsoid matrix and As shown in Table 2. By solving the linear matrix inequality of the error system (2) in Theorem 1. To obtain the minimum value The controller gain for different switching signals is calculated as follows:
[0088] The corresponding ellipsoid matrix and As shown below:
[0089] Using the obtained matrix and Construct the three-dimensional boundary of the reachable set, such as Figure 4 As shown, analysis of the reachable set boundary reveals that all state trajectories of the error system lie within the ellipsoidal region. This indicates that the error system consistently satisfies the pre-defined performance constraints during operation, thus validating the effectiveness of the proposed method.
[0090] Figure 5 The evolution of the switching signal and its corresponding impulse effect are depicted. It can be seen that the impulse effect causes instantaneous state jumps at each switching moment. However, due to the designed state feedback compensation, these jumps are effectively controlled within acceptable limits without affecting the stability of the hybrid system.
[0091] The speed and current trajectories of the DC motor system are as follows: Figure 6 and Figure 7 As shown in the figure. The results indicate that the physical variables maintain good transient response characteristics during the switching process. Furthermore, the output trajectory of the error system is shown in the figure. Figure 8 As shown in the figure, these results confirm that the state variables of both Follower 1 and Follower 2 can successfully track the state of the leader. Moreover, the consistency error converges rapidly to a small neighborhood near zero within a finite time, demonstrating excellent cooperative tracking performance and strong anti-interference ability.
[0092] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.
Claims
1. A method for controlling the output reachable set of a switched singular multi-agent system of direct current motors, characterized in that, Includes the following steps: S1. Construct a DC motor-switching singular model; S2. Monitor the current and speed of the motor in the execution system, and construct a pulse reset map to capture the transient jumps in the current; S3. After a jump occurs, the voltage is compensated by feedback through the switching singular model. S4. Ensure that the system state is within a preset bounded set, further limiting the current and speed to within safe thresholds to protect the normal operation of the motor.
2. The output reachability set control method for a DC motor switching singular multi-agent system according to claim 1, characterized in that, The DC motor - switched singular model is: DC motor current and DC motor shaft speed are used as system state vector , supply voltage as control input , while the output current is considered as system output vector , voltage fluctuations caused by external load disturbances are modeled as system disturbance input vector , the dynamic behavior of the th DC motor is described by the following equation: ， in ， ， ， ， Jm is the inertia of the DC motor shaft; vis is the viscous friction coefficient; Kem is the back EMF constant; gc is the gearbox efficiency; DCm is the DC motor efficiency; Rb is the armature resistance; gr is the gear ratio; Kt is the torque constant; K is the coupling coefficient of load fluctuations on the speed.
3. The output reachability set control method for a DC motor switching singular multi-agent system according to claim 2, characterized in that, The execution system includes N DSP controllers, N DC motors, and N sensors, wherein the... The DC motor and the first The first DSP controller, the first The sensors are connected together, including a current sensor and a speed sensor.
4. The output reachability set control method for a DC motor switching singular multi-agent system according to claim 3, characterized in that, Due to mechanical inertia, the shaft speed of a DC motor... Maintain continuity, while armature current A transient jump will occur. To capture this transient jump, the pulse reset mapping is introduced: in and These represent the error states before and after the switch, respectively. Specifically, the jump matrix is selected as follows: ， ， 。 5. The output reachability set control method for a DC motor switching singular multi-agent system according to claim 4, characterized in that, The switching singularity model includes delay compensation and impulse compensation.
6. The output reachability set control method for a DC motor switching singular multi-agent system according to claim 5, characterized in that, Disturbance input Bounded, satisfied ,in Given a known positive real constant, for the th singularity in the switching model The distributed output delay compensation feedback control protocol for a DC motor is designed as follows: in For the switching controller gain to be determined, Represents time-varying delay, satisfying .
7. The output reachability set control method for a DC motor switching singular multi-agent system according to claim 6, characterized in that, The system pulse compensation is as follows: in The switching controller gain is to be determined.
8. The output reachability set control method for a DC motor switching singular multi-agent system according to claim 7, characterized in that, The reachable set is defined as: ， The ellipsoidal boundary of the system's reachable set can be characterized by the intersection of a family of ellipsoids: Among the requirements .