Control method and system of resistance-inductance-capacitance circuit switching system

Abstract

The invention relates to the technical field of control, in particular to a control method and system of a resistor-inductor-capacitor circuit switching system. Taking the change rate of the capacitor voltage and the change rate of the inductive current as elements of a state vector of the RLC circuit switching system, and constructing a state-space equation through a semi-Markov switching process; the state-space equation is discretized through a zero-order retainer, nonlinear disturbance is constrained by adopting incremental quadratic constraint, the nonlinear constraint range of the system is wider, the universality of a feasible solution is improved, and based on the state vector of the current RLC circuit switching system and the state vector of the RLC circuit switching system at the interval of the preset time, the nonlinear disturbance is restrained by adopting incremental quadratic constraint, so that the nonlinear constraint range of the system is wider. And judging whether the RLC circuit switching system needs to be controlled or not through the event trigger, and if so, adjusting the control input of the current resistance-inductance-capacitance circuit switching system through the elastic controller. According to the invention, the communication burden of the system is reduced, the elasticity of the system is enhanced, and the accurate control of the RLC circuit switching system is realized.

Description

Technical Field

[0001] The present invention relates to the field of control technology, and in particular to a control method and system for a resistor-inductor-capacitor circuit switching system. Background Art

[0002] The resistance-inductance-capacitance (RLC) circuit system plays a vital role in the design of modern power systems and power conversion technology due to its simple structure, low cost, easy implementation and diverse functions. For example, in an uninterruptible power supply system, the RLC circuit can store a large amount of energy in a short period of time and release it quickly when the power is interrupted to maintain the operation of key equipment. In the design of electronic equipment, the RLC circuit helps to improve the electromagnetic compatibility of the system; through proper design, the RLC circuit can reduce electromagnetic interference and enable the equipment to operate stably in a complex electromagnetic environment. With the rapid development of industrial automation and intelligence, the power system has become more complex and sophisticated, and RLC switching circuits have become more common. It can be regarded as a complex RLC circuit system composed of multiple RLC circuit systems connected together through switches or other connectors. For example, in the application of computer technology, when using computer technology for complex calculations, RLC switching circuits are widely used as an integral differential analog circuit. Therefore, it is very necessary to study the control method of the resistance-inductance-capacitance circuit switching system. Obtaining a more practical modeling method is the premise for studying the control method of the RLC circuit switching system.

[0003] At present, the RLC circuit switching system has multiple modes, so it is necessary to use appropriate system theory to make it closer to reality. However, most of the existing literature adopts a simple linear switching theory based on time to model the RLC switching circuit as an approximate model of linear behavior in different time periods, which is not in line with reality. Linear switching theory often assumes that the response of the circuit is time-invariant, that is, the parameters of the circuit (such as resistance, inductance, capacitance, etc.) are constant in different time periods, and switching only changes the topology of the circuit. However, in reality, as the switch switches, the characteristics of the circuit will change dynamically, and these time-varying characteristics often have an important impact on the performance of the system in actual circuits. In order to improve the shortcomings of the simple linear switching theory based on time, scholars have adopted the Markov process to more accurately describe and analyze the switching behavior of complex systems. The Markov process uses a Markov chain to model the transition probability of the circuit from one state to another, and the transition probability matrix describes the switching rate of the circuit under different conditions, which is affected by the value of the circuit components. Through this modeling method, the Markov process can capture the random switching behavior between different working modes in the RLC circuit and analyze the long-term stable state or transient response of the circuit.

[0004] However, in the traditional Markov process, geometric distribution and exponential distribution are usually followed. In the actual circuit switching process, the jump between states may be affected by a variety of complex factors, which do not necessarily conform to the assumptions of geometric distribution or exponential distribution. In addition, the Markov process is memoryless. In the actual RLC circuit switching process, as the circuit is used for a longer time, circuit components will age, and cumulative changes in parasitic capacitance or inductance will occur. The changes in component parameters are related to the circuit's usage history. Therefore, the Markov system that follows the memoryless geometric distribution is not realistic. In addition, due to the increasing openness of network channels, if the RLC If the switching circuit is embedded in a more complex system, such as an electronic device, communication system or control system, it may become an indirect target of attack. The existing control methods of the resistor-inductor-capacitor circuit switching system mostly focus on the electrical characteristics of the circuit itself and the modeling and control of the switching behavior under normal conditions. They do not fully take into account the possibility of such external malicious attacks. They do not consider how the circuit should respond once an attack occurs and how to ensure its own stability and security. They also cannot allow the circuit to maintain normal working conditions when subjected to such nonlinear disturbances and random malicious attacks, thereby reducing the stability of the RLC circuit switching system. Summary of the invention

[0005] To this end, the technical problem to be solved by the present invention is to overcome the defect that the existing RLC circuit switching control method is difficult to adapt to the actual RLC circuit switching system, and lacks a control mechanism to deal with external malicious attacks to ensure stability and security, resulting in insufficient stability of the RLC circuit switching system.

[0006] In order to solve the above technical problems, the present invention provides a control method for a resistor-inductor-capacitor circuit switching system, comprising the following steps:

[0007] Through Kirchhoff's theorem, the mathematical model of the RLC circuit switching system is established;

[0008] Based on the mathematical model of the RLC circuit switching system, the change rate of the capacitor voltage and the change rate of the inductor current are used as elements of the state vector of the RLC circuit switching system, and the state space equation is constructed through the semi-Markov switching process;

[0009] The state space equation is discretized by a zero-order holder, and the nonlinear disturbance of the RLC circuit switching system is constrained by an incremental quadratic constraint, thus obtaining a discretized semi-Markov process switching system model.

[0010] Obtain the current capacitor voltage, inductor current, inductance of the inductor, capacitance of the capacitor, resistance value of the resistor and output voltage, and input the mathematical model of the RLC circuit switching system to obtain the state vector of the current RLC circuit switching system;

[0011] Inputting the state vector of the current RLC circuit switching system into the discretized semi-Markov process switching system model to obtain the state vector of the RLC circuit switching system at a preset time interval;

[0012] Based on the state vector of the current RLC circuit switching system and the state vector of the RLC circuit switching system at a preset time interval, an event trigger is used to determine whether the RLC circuit switching system needs to be controlled. If so, the control input of the current resistor-inductor-capacitor circuit switching system is adjusted through an elastic controller.

[0013] Preferably, a mathematical model of the RLC circuit switching system is established by Kirchhoff's theorem, including:

[0014]

[0015] in, for u c The rate of change, for i L The rate of change, u c is the capacitor voltage, i L is the inductor current, t is the time, L is the inductance of the inductor, C is the capacitance of the capacitor, R is the resistance of the resistor, u d is the input voltage.

[0016] Preferably, based on the mathematical model of the RLC circuit switching system, the change rate of the capacitor voltage and the change rate of the inductor current are used as elements of the state vector of the system, and the state space equation is constructed through the semi-Markov switching process, including:

[0017] Let the state vector of the RLC circuit switching system be Through the semi-Markov switching process, the state space equation is constructed, and the formula of the state space equation is:

[0018]

[0019] in, is the rate of change of x, [.] T is the transpose, x is the state vector of the RLC circuit switching system, u is the control input of the resistor-inductor-capacitor circuit switching system, and r k is the switching signal of the RLC circuit switching system at the kth sampling, f(.) is the nonlinear disturbance, ω is the external disturbance, k is the kth sampling, A(r k ) is r kThe corresponding first coefficient matrix, B(r k ) is r k The corresponding second coefficient matrix, f(x), is the nonlinear perturbation of the RLC circuit switching system.

[0020] Preferably, the state space equation is discretized by passing it through a zero-order holder, and the nonlinear disturbance is constrained by using an incremental quadratic constraint to obtain a discretized semi-Markov process switching system model. The formula of the discrete-time semi-Markov process switching system model is:

[0021] x(k+1)=A(r k )x(k)+B(r k )u(k,r k )+f(x(k))+ω(k),

[0022] Where x(k+1) is the state vector of the RLC circuit switching system at the k+1th sampling, x(k) is the state vector of the RLC circuit switching system at the kth sampling, and r k is the switching signal of the RLC circuit switching system at the kth sampling, ω(k) is the external disturbance at the kth sampling, u(k,r k ) is the control input of the resistor-inductor-capacitor circuit switching system at the kth sampling time, and f(x(k)) is the nonlinear disturbance of the RLC circuit switching system at the kth sampling time.

[0023] Preferably, an incremental quadratic constraint is used to constrain the nonlinear disturbance f(x(k)) of the RLC circuit switching system, and the constraint function is:

[0024]

[0025] in, W 22 <0, W is the incremental quadratic constraint matrix, W 11 is the element in the first row and first column of the incremental quadratic constraint matrix, W 12 is the element in the first row and second column of the incremental quadratic constraint matrix, W 21 is the element in the second row and first column of the incremental quadratic constraint matrix, W 22 is the element in the second row and second column of the incremental quadratic constraint matrix.

[0026] Preferably, the switching signal r of the RLC circuit switching system k The residence time τ satisfies the following state transition probability matrix:

[0027] Pr{s k+1 -s k =τ,r k+1 =j|r k=i,…,r0=r0}=

[0028] Pr{s k+1 -s k =τ,r k+1 =j|r k =i}=π ij (τ),

[0029] π ij (τ) = Pr{r k+1 =j|r k =i}*Pr{s k+1 -s k =τ|r k+1 =j,r k =i},

[0030] Among them, s k+1 is the time of the k+1th sampling, s k is the kth sampling time, τ is the retention time of the switching signal r(k) of the RLC circuit switching system, θ ij =Pr{r k+1 =j|r k =i} is the state transfer matrix of the RLC circuit switching system, ω ij (τ) = Pr{s k+1 -s k =τ|r k+1 =j,r k =i} is the switching signal r of the RLC circuit switching system k The probability density function of the residence time τ distribution, i is the i-th mode, j is the j-th mode, Pr{.} is the probability, π ij (τ) is the state transition probability matrix, r k+1 is the switching signal of the RLC circuit switching system at the k+1th sampling.

[0031] Preferably, the determining whether the RLC circuit switching system needs to be controlled through an event trigger based on the state vector of the current RLC circuit switching system and the state vector of the RLC circuit switching system at a preset time interval includes:

[0032] judge Is it true? If so, the RLC circuit switching system needs to be controlled, and the control input of the current resistor-inductor-capacitor circuit switching system is adjusted through the elastic controller;

[0033] in, k m is the event triggering time, k m The state vector of the RLC circuit switching system at time , km The switching signal of the RLC circuit switching system at time, is the state vector of the RLC circuit switching system at intervals of preset time, for The corresponding first weight matrix, for The corresponding event trigger threshold constant, h is the preset time.

[0034] Preferably, adjusting the control input of the current resistor-inductor-capacitor circuit switching system by the elastic controller includes:

[0035]

[0036] in, k m The control input of the resistor-inductor-capacitor circuit switching system at the moment, for The corresponding preset positive number, for The corresponding gain matrix is, for The corresponding second weight matrix, for The corresponding third weight matrix, x(k m ) is the kth m The state vector of the RLC circuit switching system at the sampling time.

[0037] Preferably, the first weight matrix, the second weight matrix, the third weight matrix, and the gain matrix are solved by matrix inequalities, and the matrix inequalities include:

[0038] make

[0039]

[0040] Λ(i)=diag{-ρ(i)},

[0041]

[0042] Then the matrix inequality is:

[0043]

[0044] Wherein, η is a first constant greater than 0, ε is a second constant greater than 0, β is a third constant, β=1+ε, ζ is a fourth constant, ζ=1+η, μ is a setting parameter, μ=1+ε -1 +η -1, diag{.} represents the construction of a diagonal matrix, Υ is the total number of modes of the RLC circuit switching system, Φ(i) is the first weight matrix corresponding to the i-th mode, W 22 <0, W is the incremental quadratic constraint matrix, W 11 is the element in the first row and first column of the incremental quadratic constraint matrix, W 12 is the element in the first row and second column of the incremental quadratic constraint matrix, W 21 is the element in the second row and first column of the incremental quadratic constraint matrix, W 22 is the element in the second row and second column of the incremental quadratic constraint matrix, K(i) is the gain matrix corresponding to the i-th mode, M δ (i) is the second weight matrix corresponding to the i-th mode, N δ (i) is the third weight matrix corresponding to the i-th mode, P(i) is the positive definite matrix corresponding to the i-th mode, P(j) is the positive definite matrix corresponding to the j-th mode, is the maximum residence time, ρ(i) is the fifth constant greater than 0, I is the unit diagonal matrix, is the third equivalent coefficient matrix corresponding to the i-th mode, A i is the first coefficient matrix corresponding to the i-th mode, B i is the second coefficient matrix corresponding to the i-th mode, and γ(i) is the event trigger threshold constant under the i-th mode.

[0045] The present invention also provides a control system for a resistor-inductor-capacitor circuit switching system, comprising:

[0046] Mathematical module building module, used to build mathematical model of RLC circuit switching system through Kirchhoff's theorem;

[0047] A state space equation building module is used to build a state space equation based on the mathematical model of the RLC circuit switching system, taking the change rate of the capacitor voltage and the change rate of the inductor current as the elements of the state vector of the RLC circuit switching system, and through the semi-Markov switching process;

[0048] A discrete module is used to discretize the state space equation through a zero-order holder, and to constrain the nonlinear disturbance of the RLC circuit switching system using incremental quadratic constraints to obtain a discretized semi-Markov process switching system model;

[0049] The current state vector acquisition module is used to acquire the current capacitor voltage, inductor current, inductance of the inductor, capacitance of the capacitor, resistance value of the resistor and output voltage, and input the mathematical model of the RLC circuit switching system to obtain the current state vector of the RLC circuit switching system;

[0050] A future state vector acquisition module is used to input the state vector of the current RLC circuit switching system into a discretized semi-Markov process switching system model to obtain the state vector of the RLC circuit switching system at a preset time interval;

[0051] The control module is used to determine whether the RLC circuit switching system needs to be controlled based on the state vector of the current RLC circuit switching system and the state vector of the RLC circuit switching system at a preset interval through an event trigger, and if so, adjust the control input of the current resistor-inductor-capacitor circuit switching system through an elastic controller.

[0052] The above technical solution of the present invention has the following beneficial effects compared with the prior art:

[0053] The present invention discloses a control method and system for a resistor-inductor-capacitor circuit switching system. The present invention adopts a discrete-time semi-Markov process to model the RLC circuit switching system. Compared with the traditional random switching process and Markov process, the semi-Markov process breaks through the limitation that the jump model can only adopt geometric distribution and exponential distribution, and uses different probability distribution types to describe the system jump process, so that the system modeling has memory, and can better fit the situation that the state jump in the actual circuit switching is affected by multiple complex factors, thereby improving the accuracy of the control of the RLC circuit switching system, and adopts incremental quadratic constraints to describe the nonlinearity of the system, so that the nonlinear constraint range of the system is wider, thereby improving the universality of feasible solutions.

[0054] In addition, the present invention determines whether the RLC circuit switching system needs to be controlled through an event trigger based on the state vector of the current RLC circuit switching system and the state vector of the RLC circuit switching system at a preset time interval, thereby reducing the communication burden of the system. At the same time, an elastic controller is introduced to adjust the control input of the current resistor-inductor-capacitor circuit switching system through the elastic controller. Taking into account nonlinear disturbances and random interference such as external malicious attacks, it can be determined whether the circuit needs to be controlled and the control input can be adjusted in time, so that the circuit can still maintain a normal working state when facing such external attacks, thereby ensuring the stability and safety of the circuit, overcoming the shortcomings of the prior art in dealing with external malicious attacks, and improving the stability and reliability of the RLC circuit switching system in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein:

[0056] Figure 1 It is a flow chart of a control method of a resistor-inductor-capacitor circuit switching system of the present invention.

[0057] Figure 2 It is the circuit diagram of RLC circuit switching system. DETAILED DESCRIPTION

[0058] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0059] like Figure 1 As shown, Figure 1 The present invention is a flow chart of a control method of a resistor-inductor-capacitor circuit switching system.

[0060] Embodiment 1 of the present invention provides a control method for a resistor-inductor-capacitor circuit switching system, comprising the following steps:

[0061] like Figure 2 As shown, Figure 2 Circuit diagram for RLC circuit switching system.

[0062] Step S1: Establish a mathematical model of the RLC circuit switching system through Kirchhoff's theorem;

[0063] In this embodiment, specifically, the mathematical model of the RLC circuit switching system is:

[0064]

[0065] in, for u c The rate of change, for i L The rate of change, u c is the capacitor voltage, i L is the inductor current, t is the time, L is the inductance of the inductor, C is the capacitance of the capacitor, R is the resistance of the resistor, u d is the input voltage.

[0066] Step S2: Based on the mathematical model of the RLC circuit switching system, the change rate of the capacitor voltage and the change rate of the inductor current are used as elements of the state vector of the RLC circuit switching system, and a state space equation is constructed through a semi-Markov switching process;

[0067] Let the state vector of the RLC circuit switching system be [.] T To transpose, the state space equation is constructed through the semi-Markov switching process. The formula of the state space equation is:

[0068]

[0069] in, is the rate of change of x, x is the state vector of the RLC circuit switching system, u is the control input of the resistor-inductor-capacitor circuit switching system, r k is the switching signal of the RLC circuit switching system at the kth sampling, f(.) is the nonlinear disturbance, ω is the external disturbance, k is the kth sampling, A(r k ) is r k The corresponding first coefficient matrix, B(r k ) is r k The corresponding second coefficient matrix, f(x), is the nonlinear perturbation of the RLC circuit switching system.

[0070] Step S3: discretizing the state space equation by a zero-order holder, and constraining the nonlinear disturbance of the RLC circuit switching system by using an incremental quadratic constraint to obtain a discretized semi-Markov process switching system model;

[0071] In this embodiment, specifically, the formula of the discrete-time semi-Markov process switching system model is:

[0072] x(k+1)=A(r k )x(k)+B(r k )u(k,r k )+f(x(k))+ω(k),

[0073] Where x(k+1) is the state vector of the RLC circuit switching system at the k+1th sampling, x(k) is the state vector of the RLC circuit switching system at the kth sampling, and r k is the switching signal of the RLC circuit switching system at the kth sampling, ω(k) is the external disturbance at the kth sampling, u(k,r k ) is the control input of the resistor-inductor-capacitor circuit switching system at the kth sampling time, and f(x(k)) is the nonlinear disturbance of the RLC circuit switching system at the kth sampling time.

[0074] The present invention adopts a discrete-time semi-Markov process to model the RLC circuit switching system. Compared with the traditional random switching process and Markov process, the semi-Markov process breaks through the limitation that the jump model can only use geometric distribution and exponential distribution, and uses different probability distribution types to describe the system jump process, so that the system modeling has memory and can better fit the situation in which the state jump in the actual circuit switching is affected by multiple complex factors, thereby improving the accuracy of the control of the RLC circuit switching system.

[0075] In this embodiment, preferably, an incremental quadratic constraint is used to constrain the nonlinear disturbance f(x(k)) of the RLC circuit switching system, and the constraint function is:

[0076]

[0077] in, W 22 <0, W is the incremental quadratic constraint matrix, W 11 is the element in the first row and first column of the incremental quadratic constraint matrix, W 12 is the element in the first row and second column of the incremental quadratic constraint matrix, W 21 is the element in the second row and first column of the incremental quadratic constraint matrix, W 22 is the element in the second row and second column of the incremental quadratic constraint matrix.

[0078] The present invention adopts incremental quadratic constraints to describe the nonlinearity of the system, so that the nonlinear constraint range of the system is wider, thereby improving the universality of feasible solutions.

[0079] In this embodiment, preferably, the switching signal r of the RLC circuit switching system k The residence time τ satisfies the following state transition probability matrix:

[0080] Pr{s k+1 -s k =τ,r k+1 =j|r k =i,…,r0=r0}=

[0081] Pr{s k+1 -s k =τ,r k+1 =j|r k =i}=π ij (τ),

[0082] π ij (τ) = Pr{r k+1 =j|r k =i}*Pr{s k+1 -s k =τ|r k+1 =j,r k =i},

[0083] Among them, s k+1 is the time of the k+1th sampling, s k is the k+1th sampling time, τ is the retention time of the switching signal r(k) of the RLC circuit switching system, θ ij =Pr{r k+1 =j|r k =i} is the state transfer matrix of the RLC circuit switching system, ω ij (τ) = Pr{s k+1 -s k =τ|r k+1 =j,rk =i} is the switching signal r of the RLC circuit switching system k The probability density function of the residence time τ distribution, i is the i-th mode, j is the j-th mode, Pr{.} is the probability, π ij (τ) is the state transition probability matrix, r k+1 is the switching signal of the RLC circuit switching system at the k+1th sampling.

[0084] The switching signal r of the RLC circuit switching system k The residence time τ determines the transition probability of the system. The residence time τ can obey a memoryless geometric distribution or a memory-based probability distribution.

[0085] Step S4: obtaining the current capacitor voltage, inductor current, inductance of the inductor, capacitance of the capacitor, resistance of the resistor and output voltage, and inputting the mathematical model of the RLC circuit switching system to obtain the state vector of the current RLC circuit switching system;

[0086] Step S5: inputting the state vector of the current RLC circuit switching system into the discretized semi-Markov process switching system model to obtain the state vector of the RLC circuit switching system at a preset time interval;

[0087] Step S6: Based on the state vector of the current RLC circuit switching system and the state vector of the RLC circuit switching system at a preset time interval, determine whether the RLC circuit switching system needs to be controlled through an event trigger, and if so, adjust the control input of the current resistor-inductor-capacitor circuit switching system through the elastic controller.

[0088] In this embodiment, preferably, the determining whether the RLC circuit switching system needs to be controlled through an event trigger based on the state vector of the current RLC circuit switching system and the state vector of the RLC circuit switching system at a preset time interval includes:

[0089] judge Is it true? If so, the RLC circuit switching system needs to be controlled, and the control input of the current resistor-inductor-capacitor circuit switching system is adjusted through the elastic controller;

[0090] in, k m is the event triggering time, k m The state vector of the RLC circuit switching system at time , k m The switching signal of the RLC circuit switching system at time, is the state vector of the RLC circuit switching system at intervals of preset time, for The corresponding first weight matrix, for The corresponding event trigger threshold constant, h is the preset time.

[0091] The present invention determines whether the RLC circuit switching system needs to be controlled through an event trigger, thereby reducing the communication burden of the system. The event trigger can accurately determine whether the current RLC circuit switching system needs control intervention. This judgment mechanism is not based on a fixed time interval or a simple threshold comparison, but comprehensively considers the relationship between the state vector of the current RLC circuit switching system and the state vector after a preset time interval, thereby avoiding unnecessary control operations and significantly reducing the control resource consumption of the system.

[0092] In this embodiment, preferably, adjusting the control input of the current resistor-inductor-capacitor circuit switching system by the elastic controller includes:

[0093]

[0094] in, k m The control input of the resistor-inductor-capacitor circuit switching system at the moment, for The corresponding preset positive number, for The corresponding gain matrix is, for The corresponding second weight matrix, for The corresponding third weight matrix, x(k m ) is the kth m The state vector of the RLC circuit switching system at the sampling time.

[0095] By adjusting the control input of the current resistor-inductor-capacitor circuit switching system through an elastic controller, it is possible to determine whether the circuit needs to be controlled and adjust the control input in time, taking into account nonlinear disturbances and random interference such as external malicious attacks, so that the circuit can still maintain a normal working state when facing such external attacks, thereby ensuring the stability and safety of the circuit, overcoming the shortcomings of the existing technology in dealing with external malicious attacks, and improving the stability and reliability of the RLC circuit switching system in complex environments.

[0096] In this embodiment, preferably, the first weight matrix, the second weight matrix, the third weight matrix, and the gain matrix are solved by matrix inequalities, and the matrix inequalities include:

[0097] make

[0098]

[0099] Λ(i)=diag{-ρ(i)},

[0100]

[0101] Then the matrix inequality is:

[0102]

[0103] Wherein, η is a first constant greater than 0, ε is a second constant greater than 0, β is a third constant, β=1+ε, ζ is a fourth constant, ζ=1+η, μ is a setting parameter, μ=1+ε -1 +η -1 , diag{.} represents the construction of a diagonal matrix, Υ is the total number of modes of the RLC circuit switching system, Φ(i) is the first weight matrix corresponding to the i-th mode, W 22 <0, W is the incremental quadratic constraint matrix, W 11 is the element in the first row and first column of the incremental quadratic constraint matrix, W 12 is the element in the first row and second column of the incremental quadratic constraint matrix, W 21 is the element in the second row and first column of the incremental quadratic constraint matrix, W 22 is the element in the second row and second column of the incremental quadratic constraint matrix, K(i) is the gain matrix corresponding to the i-th mode, M δ (i) is the second weight matrix corresponding to the i-th mode, N δ (i) is the third weight matrix corresponding to the i-th mode, P(i) is the positive definite matrix corresponding to the i-th mode, P(j) is the positive definite matrix corresponding to the j-th mode, is the maximum residence time, ρ(i) is the fifth constant greater than 0, I is the unit diagonal matrix, is the third equivalent coefficient matrix corresponding to the i-th mode, A i is the first coefficient matrix corresponding to the i-th mode, B i is the second coefficient matrix corresponding to the i-th mode, and γ(i) is the event trigger threshold constant under the i-th mode.

[0104] The proof process of solving the first weight matrix, the second weight matrix, the third weight matrix, and the gain matrix by matrix inequality in this embodiment is as follows:

[0105] The lemmas required for the proof are:

[0106] Lemma 1: For the first matrix z, the second matrix M, the third matrix N and the fourth matrix Δ, there is a first positive number α such that the following inequality holds:

[0107] z+N T ΔM T +MΔN≤z+α -1 N T N+αM T M.

[0108] Lemma 2: For the fifth matrix J and the sixth matrix G, the following inequality holds for any positive number φ:

[0109]

[0110] Lemma 3: For a block matrix if The following formula holds:

[0111]

[0112] Consider the event trigger, and set the current event trigger time to be k m , the next event triggering time is k m+1 , let the preset time h = k m+1 -k m ,but in, k m +h+1 time RLC circuit switching system state vector, k m +h time RLC circuit switching system state vector;

[0113] Based on the elastic controller, we get k m Control input of a momentary resistor-inductor-capacitor circuit switching system The corresponding gain matrix include:

[0114]

[0115] Set ω(k m )=0,ω(k m ) is k m Therefore, the discrete-time semi-Markov process switching system model is:

[0116]

[0117] in, for The corresponding first coefficient matrix, for The corresponding second coefficient matrix, k m +h time RLC circuit switching system switching signal, k m The switching signal of the RLC circuit switching system at time, k m +h time RLC circuit switching system external disturbance, k m The nonlinear disturbance of the RLC circuit switching system at time +h, for The corresponding system first equivalent coefficient matrix is, for The corresponding system gain matrix is, for The corresponding system second coefficient matrix is, for The corresponding system first equivalent gain matrix.

[0118] Construct a Lyapunov function:

[0119]

[0120] when hour,

[0121] therefore:

[0122]

[0123] in, k m +h time RLC circuit switching system corresponding to the positive definite matrix, k m +h+1 time RLC circuit switching system corresponding to the positive definite matrix, is the second equivalent coefficient matrix of the system under the i-th mode, is the first equivalent gain matrix of the system under the i-th mode, For and is the Lyapunov function of the independent variable, ΔV is k m +h+1 moment and k m The difference of the Lyapunov function at time +h, is the mathematical expectation, B i is the second coefficient matrix of the system under the i-th mode, It is the first abbreviation symbol.

[0124] make Among them, (1) is the constraint function, (2) is the judgment condition of the event trigger, that is, (3)

[0125] According to Lemma 2,

[0126]

[0127] Write in matrix form, specifically:

[0128]

[0129] Among them, β=1+ε, ζ=1+η, μ=1+ε -1 +η -1 , using Lemma 3, we get:

[0130]

[0131] make So the inequality is:

[0132]

[0133] Construct the correlation matrix:

[0134]

[0135] Using Lemma 3, the above inequality is equivalent to:

[0136]

[0137] Applying Lemma 1, we can obtain:

[0138]

[0139] Applying Lemma 2, we can see that the above formula ≤0 is equivalent to the following matrix ≤0.

[0140]

[0141] Obviously easy to hour, The gain matrix and the related weight matrix can be obtained by the following matrix inequality:

[0142]

[0143] in

[0144]

[0145] The proof is now complete.

[0146] The present invention adopts a discrete-time semi-Markov process with memory to model the RLC circuit switching system to solve the shortcoming that the existing modeling form is not practical. Furthermore, the incremental quadratic constraint is used to represent the nonlinear constraint of the system, so that the nonlinear constraint range of the system is wider, thereby improving the universality of feasible solutions. At the same time, compared with the traditional closed-loop control, the present invention also designs a flexible controller to enhance the elasticity of the system, so that the system can restore the performance of the system more quickly when facing external disturbances. At the same time, the event trigger mechanism is introduced to reduce the communication burden of the system and save system resources.

[0147] The second embodiment provides a control system for a resistor-inductor-capacitor circuit switching system, including:

[0148] Mathematical module building module, used to build mathematical model of RLC circuit switching system through Kirchhoff's theorem;

[0149] A state space equation building module is used to build a state space equation based on the mathematical model of the RLC circuit switching system, taking the change rate of the capacitor voltage and the change rate of the inductor current as the elements of the state vector of the RLC circuit switching system, and through the semi-Markov switching process;

[0150] A discrete module is used to discretize the state space equation through a zero-order holder, and to constrain the nonlinear disturbance of the RLC circuit switching system using incremental quadratic constraints to obtain a discretized semi-Markov process switching system model;

[0151] The current state vector acquisition module is used to acquire the current capacitor voltage, inductor current, inductance of the inductor, capacitance of the capacitor, resistance value of the resistor and output voltage, and input the mathematical model of the RLC circuit switching system to obtain the current state vector of the RLC circuit switching system;

[0152] A future state vector acquisition module is used to input the state vector of the current RLC circuit switching system into a discretized semi-Markov process switching system model to obtain the state vector of the RLC circuit switching system at a preset time interval;

[0153] The control module is used to determine whether the RLC circuit switching system needs to be controlled based on the state vector of the current RLC circuit switching system and the state vector of the RLC circuit switching system at a preset interval through an event trigger, and if so, adjust the control input of the current resistor-inductor-capacitor circuit switching system through an elastic controller.

[0154] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0155] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0156] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0157] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0158] Obviously, the above embodiments are merely examples for the purpose of clear explanation and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the present invention.

Claims

1. A control method for a resistor-inductor-capacitor circuit switching system, characterized in that: The following steps are involved: Through Kirchhoff's theorem, the mathematical model of the RLC circuit switching system is established; Based on the mathematical model of the RLC circuit switching system, the change rate of the capacitor voltage and the change rate of the inductor current are used as elements of the state vector of the RLC circuit switching system, and the state space equation is constructed through the semi-Markov switching process; The state space equation is discretized by a zero-order holder, and the nonlinear disturbance of the RLC circuit switching system is constrained by an incremental quadratic constraint, thus obtaining a discretized semi-Markov process switching system model. Obtain the current capacitor voltage, inductor current, inductance of the inductor, capacitance of the capacitor, resistance value of the resistor and output voltage, and input the mathematical model of the RLC circuit switching system to obtain the state vector of the current RLC circuit switching system; Inputting the state vector of the current RLC circuit switching system into the discretized semi-Markov process switching system model to obtain the state vector of the RLC circuit switching system at a preset time interval; Based on the state vector of the current RLC circuit switching system and the state vector of the RLC circuit switching system at a preset time interval, an event trigger is used to determine whether the RLC circuit switching system needs to be controlled. If so, the control input of the current resistor-inductor-capacitor circuit switching system is adjusted through an elastic controller.

2. The control method of a resistor-inductor-capacitor circuit switching system according to claim 1, characterized in that: Through Kirchhoff's theorem, the mathematical model of the RLC circuit switching system is established, including: in, for u c The rate of change, for i L The rate of change, u c is the capacitor voltage, i L is the inductor current, t is the time, L is the inductance of the inductor, C is the capacitance of the capacitor, R is the resistance of the resistor, u d is the input voltage.

3. The control method of a resistor-inductor-capacitor circuit switching system according to claim 2, characterized in that: Based on the mathematical model of the RLC circuit switching system, the change rate of the capacitor voltage and the change rate of the inductor current are used as elements of the state vector of the system. Through the semi-Markov switching process, the state space equation is constructed, including: Let the state vector of the RLC circuit switching system be Through the semi-Markov switching process, the state space equation is constructed, and the formula of the state space equation is: in, is the rate of change of x, [.] T is the transpose, x is the state vector of the RLC circuit switching system, u is the control input of the resistor-inductor-capacitor circuit switching system, and r k is the switching signal of the RLC circuit switching system at the kth sampling, f(.) is the nonlinear disturbance, ω is the external disturbance, k is the kth sampling, A(r k ) is r k The corresponding first coefficient matrix, B(r k ) is r k The corresponding second coefficient matrix, f(x), is the nonlinear perturbation of the RLC circuit switching system.

4. The control method of a resistor-inductor-capacitor circuit switching system according to claim 3, characterized in that: The state space equation is discretized by passing it through a zero-order holder, and the nonlinear disturbance is constrained by incremental quadratic constraints to obtain a discretized semi-Markov process switching system model. The formula of the discrete-time semi-Markov process switching system model is: x(k+1)=A(r k )x(k)+B(r k )u(k,r k )+f(x(k))+ω(k), Where x(k+1) is the state vector of the RLC circuit switching system at the k+1th sampling, x(k) is the state vector of the RLC circuit switching system at the kth sampling, and r k is the switching signal of the RLC circuit switching system at the kth sampling, ω(k) is the external disturbance at the kth sampling, u(k, r k ) is the control input of the resistor-inductor-capacitor circuit switching system at the kth sampling time, and f(x(k)) is the nonlinear disturbance of the RLC circuit switching system at the kth sampling time.

5. The control method of a resistor-inductor-capacitor circuit switching system according to claim 4, characterized in that: The incremental quadratic constraint is used to constrain the nonlinear disturbance f(x(k)) of the RLC circuit switching system. The constraint function is: in, W 11 >0, W 22 <0, W is the incremental quadratic constraint matrix, W11 is the element of the first row and first column in the incremental quadratic constraint matrix, W 12 is the element in the first row and second column of the incremental quadratic constraint matrix, W 21 is the element in the second row and first column of the incremental quadratic constraint matrix, W 22 is the element in the second row and second column of the incremental quadratic constraint matrix.

6. The control method of a resistor-inductor-capacitor circuit switching system according to claim 4, characterized in that: The switching signal r of the RLC circuit switching system k The residence time T satisfies the following state transition probability matrix: Pr{s k+1 -s k =τ,r k+1 =j|r k =i,...,r0=r0}= Pr{s k+1 -s k =τ,r k+1 =j|r k =i}=π ij (τ), π ij (T)=Pr{r k+1 =j|r k =i}*Pr{s k+1 -s k =τ|r k+1 =j,r k =i}, Among them, s k+1 is the time of the k+1th sampling, s k is the kth sampling time, T is the retention time of the switching signal r(k) of the RLC circuit switching system, θ ij =Pr{r k+1 =j|r k =i} is the state transfer matrix of the RLC circuit switching system, ω ij (τ) = Pr{s k+1 -s k =τ|r k+1 =j,r k =i} is the switching signal r of the RLC circuit switching system k The probability density function of the residence time τ distribution, i is the i-th mode, j is the j-th mode, Pr{.} is the probability, π ij (τ) is the state transition probability matrix, r k+1 is the switching signal of the RLC circuit switching system at the k+1th sampling.

7. The control method of a resistor-inductor-capacitor circuit switching system according to claim 6, characterized in that: The determining whether the RLC circuit switching system needs to be controlled by an event trigger based on the state vector of the current RLC circuit switching system and the state vector of the RLC circuit switching system at a preset time interval includes: judge Is it true? If so, the RLC circuit switching system needs to be controlled, and the control input of the current resistor-inductor-capacitor circuit switching system is adjusted through the elastic controller; in, k m is the event triggering time, k m The state vector of the RLC circuit switching system at time , k m The switching signal of the RLC circuit switching system at time, is the state vector of the RLC circuit switching system at intervals of preset time, for The corresponding first weight matrix, for The corresponding event trigger threshold constant, h is the preset time.

8. The control method of a resistor-inductor-capacitor circuit switching system according to claim 7, characterized in that: The control input of the current resistor-inductor-capacitor circuit switching system is adjusted by an elastic controller, including: in, k m The control input of the resistor-inductor-capacitor circuit switching system at the moment, for The corresponding preset positive number, for The corresponding gain matrix is, for The corresponding second weight matrix, for The corresponding third weight matrix, x(k m ) is the kth m The state vector of the RLC circuit switching system at the sampling time.

9. The control method of a resistor-inductor-capacitor circuit switching system according to claim 8, characterized in that: The first weight matrix, the second weight matrix, the third weight matrix, and the gain matrix are solved by matrix inequalities, and the matrix inequalities include: make Λ(i)=diag{-ρ(i)}, Then the matrix inequality is: Wherein, η is a first constant greater than 0, ε is a second constant greater than 0, β is a third constant, β=1+ε, ζ is a fourth constant, ζ=1+η, μ is a setting parameter, μ=1+ε -1 +η -1 , diag{.} represents the construction of a diagonal matrix, Y is the total number of modes of the RLC circuit switching system, Φ(i) is the first weight matrix corresponding to the i-th mode, W 11 >0, W 22 <0, W is the incremental quadratic constraint matrix, W 11 is the element in the first row and first column of the incremental quadratic constraint matrix, W 12 is the element in the first row and second column of the incremental quadratic constraint matrix, W 21 is the element in the second row and first column of the incremental quadratic constraint matrix, W 22 is the element in the second row and second column of the incremental quadratic constraint matrix, K(i) is the gain matrix corresponding to the i-th mode, M δ (i) is the second weight matrix corresponding to the i-th mode, N δ (i) is the third weight matrix corresponding to the i-th mode, P(i) is the positive definite matrix corresponding to the i-th mode, P(j) is the positive definite matrix corresponding to the j-th mode, is the maximum residence time, ρ(i) is the fifth constant greater than 0, I is the unit diagonal matrix, is the third equivalent coefficient matrix corresponding to the i-th mode, A i is the first coefficient matrix corresponding to the i-th mode, B i is the second coefficient matrix corresponding to the i-th mode, and γ(i) is the event trigger threshold constant under the i-th mode.

10. A control system for a resistor-inductor-capacitor circuit switching system, characterized in that: include: Mathematical module building module, used to build mathematical model of RLC circuit switching system through Kirchhoff's theorem; A state space equation building module is used to build a state space equation based on the mathematical model of the RLC circuit switching system, taking the change rate of the capacitor voltage and the change rate of the inductor current as the elements of the state vector of the RLC circuit switching system, and through the semi-Markov switching process; A discrete module is used to discretize the state space equation through a zero-order holder, and to constrain the nonlinear disturbance of the RLC circuit switching system using incremental quadratic constraints to obtain a discretized semi-Markov process switching system model; The current state vector acquisition module is used to acquire the current capacitor voltage, inductor current, inductance of the inductor, capacitance of the capacitor, resistance value of the resistor and output voltage, and input the mathematical model of the RLC circuit switching system to obtain the current state vector of the RLC circuit switching system; A future state vector acquisition module is used to input the state vector of the current RLC circuit switching system into a discretized semi-Markov process switching system model to obtain the state vector of the RLC circuit switching system at a preset time interval; The control module is used to determine whether the RLC circuit switching system needs to be controlled based on the state vector of the current RLC circuit switching system and the state vector of the RLC circuit switching system at a preset interval through an event trigger, and if so, adjust the control input of the current resistor-inductor-capacitor circuit switching system through an elastic controller.

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