Direct order identification method for low-order dissimilar real pole linear system with small operand

Abstract

The invention discloses a low-operand low-order dissimilar real pole linear system order direct type identification method, which comprises the following steps: step 1, preparing a constant value input excitation and output quantity acquisition system, step 2, applying the constant value input excitation to a system to be detected and acquiring and outputting, step 3, calculating a sample element h (r, j), step 4, calculating an identification element g (a, b), and step 5, calculating the identification element g (a, b). 5-7, respectively calculating first-level, second-level and third-level identification elements and first-level, second-level and third-level identification elements, 8, calculating identification factors xRecc (1), xRecc (2) and xRecc (3), 9, analyzing the order number Num of the system to be tested according to the identification factors, 10, if Num =-1 and Recc = 1, if Recc = 2, turning to the step 4, and otherwise, ending; the method lays a solid foundation for safe, efficient and high-performance control and operation of the low-order dissimilar real pole linear system.

Description

Technical Field

[0001] The present invention relates to the technical field of order identification of linear systems, and particularly to a direct method for identifying the order of a low-order linear system with distinct real poles and small computational complexity. Background Art

[0002] System automation and intelligence are the foundation of today's intelligent society, which is based on the system model. People usually obtain the system model through system identification. System identification includes two key links: system order identification and system parameter identification. System order identification mainly determines the order of the system, that is, the complexity of the system model, while the core task of system parameter identification is to estimate the specific parameters in the system model. The former is often the basis for the latter. Most high-order linear systems are composed of low-order sub-modules or systems with distinct real poles whose order does not exceed three. Therefore, studying the order identification of low-order linear systems with distinct real poles whose order does not exceed three has very important practical significance for promoting the process of automation and intelligence in China.

[0003] At present, the methods for identifying the order of a linear system with distinct real poles include estimating the order of the model by constructing a Hankel matrix and finding its rank or using the ratio of the determinants of product moment matrices; inferring the order of the system model according to the loss function method; and estimating the model order according to the information criterion.

[0004] These methods usually involve matrix operations, which have a large amount of calculation, require high hardware costs or long time overheads, and are increasingly difficult to meet people's requirements for hardware costs and real-time performance in automated and intelligent systems. The identification accuracy depends on relevant criteria and is not direct. Therefore, the present invention proposes a direct method for identifying the order of a low-order linear system with distinct real poles and small computational complexity to solve the problems existing in the prior art. Summary of the Invention

[0005] In view of the above problems, the object of the present invention is to propose a direct method for identifying the order of a low-order linear system with distinct real poles and small computational complexity. This method can identify the order of a low-order linear system with distinct real poles, and has the advantages of strong anti-interference ability, high identification accuracy, stable and reliable identification, economy, simplicity, high efficiency and directness, laying a solid foundation for automatically and intelligently controlling these low-order linear systems with distinct real poles quickly, accurately, reliably and with high performance, and enabling them to operate safely, efficiently and with high performance.

[0006] To achieve the object of the present invention, the present invention is realized through the following technical solutions: First, denote a n 、a n-1 、a n-2 、…、a 2 、a 1 、a 0, where \(a\) and \(b\) are constant coefficients. For an \(n\)-th order linear system with input \(bu(t)\) and output \(y(t)\), it can be expressed as:

[0007]

[0008] where \(u(t)\) is the unit step signal, i.e.,

[0009] When \(n = 3\), the system is a third-order system, and there is

[0010] When \(n = 2\), the system is a second-order system, and there is

[0011] When \(n = 1\), the system is a first-order system, and there is When \(n = 0\), the system is a proportional system or a zero-order system, and there is \(a\) 0 y(t)=bu(t).

[0012] If the initial state of the system is 0, i.e., m = 0, 1, 2, 3, y(0)=0, then the step response \(y(t)\) of the above zero-order to third-order systems can be analyzed. For low-order systems with distinct poles, using the characteristics of the poles of each order system and its step response \(y(t)\), supplemented by the idea of digital anti-interference is the idea of the present invention.

[0013] A method for directly identifying the order of a low-order linear system with distinct real poles and small computational complexity includes the following steps:

[0014] Step 1: Set the input of the system to be measured to zero, and release the restraint to make the system in a zero equilibrium state, that is, the output and state of the system are equal to zero and remain unchanged in equilibrium. Then prepare a constant input excitation with an amplitude of \(b\) and a system for collecting the output quantity \(y(t)\).

[0015] Step 2: Apply the constant input excitation prepared in Step 1 to the input end of the system to be measured. At the same time, use the prepared collection system to collect the output \(y(t)\) and save it. Denote \(f(r)=y(rT)\) as the output value \(y(t)\) of the system collected in the \(r\)-th cycle, \(r = 1, 2, 3,\cdots,N\), \(T\) is the sampling period, and \(N\) is the number of collected samples.

[0016] Step 3: Calculate the sample element \(h(r,j)\), \(h(r,j)=f(r)-f(j)\), where \(r = 1, 2, 3,\cdots,N\), \(j = 2, 3,\cdots,N\), \(r\neq j\). Initialize the identification times \(Rec = 1\) and the order \(Num=-1\).

[0017] Step 4: Let \(m = BasicL\times Rec\), \(r\) 0= m - BasicL + 1, MaxL is an integer of 0.5N, 20 < BasicL < MaxL, calculate the identification primitive g(a, c), a = 1, 2, 3, c = 1, 2, 3, 4, where,

[0018]

[0019] where b = 1, 2, 4;

[0020] Step Five: Calculate the first-level identification element D11 1 、D11 2 、D12 1 、D12 2 , and the first-level identification factors D11, D12, where D11 = D11 1 - D11 2 、D12 = D12 1 - D12 2 ;

[0021] Step Six: Calculate the second-level identification element D21 1 、D21 2 、D22 1 , and the second-level identification factors D21, D22, where D21 = D21 1 - D21 2 、D22 = g(2, 3)g(2, 4)D12 - g(2, 4)g(3, 3)D12;

[0022] Step Seven: Calculate the third-level identification element D3 1 、D3 2 、D3 3 、D3 4 、D3 5 、D3 6 , and the third-level identification factor D3, where D3 = D3 1 + D3 2 + D3 3 - D3 4 - D3 5 - D3 6 ;

[0023] Step Eight: Calculate the identification factor χ Rec (1)、χ Rec (2)、χ Rec (3); If D12 = 0, then χ Rec (1) = 3, otherwise If D22 = 0, then χ Rec (2) = 3, χ Rec (3) = 1, otherwise,

[0024] Step Nine: Denote the allowable error as Tol, and according to χ Rec (1) χ Rec (2) χ Rec (3) Analyze the order Num of the system under test;

[0025] Step Ten: If Num = -1 and Rec = 1, then Rec = 2, and go to Step Four for calculation; otherwise, end. At this time, if Num = -1, the system under test is a low-order linear system with non-distinct real poles.

[0026] The further improvement lies in that D11 in the said Step Five and Step Six 1 、D11 2 、D12 1 、D12 2 、D21 1 and D21 2 are calculated by the following formula

[0027] D11 1 = g(1,1)g(2,3)g(3,4) + g(1,4)g(2,1)g(3,3) + g(1,3)g(2,4)g(3,1

[0028] D11 2 = g(1,1)g(2,4)g(3,3) + g(1,3)g(2,1)g(3,4) + g(1,4)g(2,3)g(3,1

[0029] D12 1 = g(1,2)g(2,3)g(3,4) + g(1,4)g(2,2)g(3,3) + g(1,3)g(2,4)g(3,2

[0030] D12 2 = g(1,2)g(2,4)g(3,3) + g(1,3)g(2,2)g(2,2) + g(1,4)g(2,3)g(3,2

[0031] D21 1 = g(2,1)g(3,4)D12 + g(2,4)g(3,2)D11

[0032] D21 2 = g(2,4)g(3,1)D12 + g(2,2)g(3,4)D11

[0033] D22 1 = g(2,3)g(3,4) - g(2,4)g(3,3).

[0034] The further improvement lies in that D3 in the said Step Seven 1 、D32 , D3 3 , D3 4 , D3 5 and D3 6 is calculated by the following formula

[0035] D3 1 = g(1,1)g(2,2)g(2,3)g(3,3)g(3,4)+g(1,1)g(2,3)g(2,4)g(3,2)g(3,3)

[0037] D3 2 = g(1,2)g(2,1)g(2,4)g(3,3)g(3,3)+g(1,2)g(2,3)g(2,3)g(3,1)g(3,4)

[0039] D3 3 = g(1,3)g(2,2)g(2,4)g(3,1)g(3,3)+g(1,3)g(2,1)g(2,3)g(3,2)g(3,4)

[0041] D3 4 = g(1,1)g(2,2)g(2,4)g(3,3)g(3,3)+g(1,1)g(2,3)g(2,3)g(3,2)g(3,4)

[0043] D3 5 = g(1,2)g(2,1)g(2,3)g(3,3)g(3,4)+g(1,2)g(2,3)g(2,4)g(3,1)g(3,3)

[0045] D3 6 = g(1,3)g(2,2)g(2,3)g(3,1)g(3,4)+g(1,3)g(2,1)g(2,4)g(3,2)g(3,4).

[0047] The further improvement lies in that: in the eighth step, when χ Rec (1) = χ Rec (2) = 3, χ Rec (3) = 1, then Num = 0, and the system to be measured is a zero-order system, that is, a proportional system; when Num = -1 and |χ Rec (1) - χ Rec (3) - 2| ≤ Tol, |χ Rec (2) - 2χ Rec (3) - 1| ≤ Tol, then Num = 1, and the system to be measured is a first-order system; when Num = -1 and |χ Rec (1) - χ Rec (2) + χ RecIf |(3) - 1| ≤ Tol, then Num = 2, and the system under test is a second-order system; when Num = -1, Rec = 2, and if |χ 1 (1) - χ 2 (1)| ≤ Tol, |χ 1 (2) - χ 2 (2)| ≤ Tol, |χ 1 (3) - χ 2 (3)| ≤ Tol, then Num = 3, and the system under test is a third-order system.

[0048] A further improvement lies in that when Num = 1, the identification error IdError = max{χ Rec (1) - χ Rec (3) - 2, χ Rec (2) - 2χ Rec (3) - 1}; when Num = 2, the identification error IdError = χ Rec (1) - χ Rec (2) + χ Rec (3) - 1; when Num = 3, the identification error IdError = max{|χ 1 (1) - χ 2 (1)|, |χ 1 I2) - χ 2 (2)|, |χ 1 (3) - χ 2 I3)|}.

[0049] The beneficial effects of the present invention are as follows: The method of the present invention can identify the order of a low-order linear system with distinct real poles, and has the advantages of strong anti-interference ability, high identification accuracy, stable and reliable identification, economic simplicity, high efficiency and directness, laying a solid foundation for automatically and intelligently controlling these low-order linear systems with distinct real poles quickly, accurately, reliably and with high performance, and enabling them to operate safely, efficiently and with high performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a flowchart of the method of the present invention.

[0051] Figure 2 It is an architecture diagram of the test system in an embodiment of the present invention.

[0052] Figure 3 It is a circuit model diagram of each order in an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0053] In order to deepen the understanding of the present invention, the present invention will be further described in detail below in conjunction with embodiments. These embodiments are only used to explain the present invention and do not limit the protection scope of the present invention.

[0054] Embodiment

[0055] According to Figure 1 、 Figure 2 and Figure 3 As shown, this embodiment provides an experimental simulation of a direct identification method for the order of a low-order distinct real-pole linear system with a small amount of computation, specifically as follows:

[0056] As shown in the attached Figure 2 of the specification, a second-order linear lumped-parameter circuit model is established in the simulink environment on the Matlab platform, and its capacitor voltage is used as the output, denoted as u 2 (t). The voltage sensor and the sampling module are used to collect u 2 (t) and send it to the working platform for storage. White noise simulates the interference signal in actual work. It is mixed into a step signal with an amplitude of 20V and controls the controlled voltage source together with this step signal to generate a 20V step DC voltage source with an interference signal to supply this circuit. In the figure, R 2 = 6Ω, L 2 = 1H, C 2 = 0.2F. The mathematical model of this circuit is:

[0057]

[0058] where the two poles are -1 and -5 respectively.

[0059] The specific experimental process is as follows:

[0060] (1) Set the circuit input to 0V, initialize the capacitor voltage in the circuit to 0V, and the inductor current to 0A to complete the zero-state initialization of this circuit.

[0061] (2) Set the gain after white noise to 0, that is, no interference is mixed in, and the circuit and the detection system will work in an ideal situation. Apply a 20V step DC voltage source to this circuit, and at the same time use the acquisition system to collect the output u 2 It) of this circuit at a period of T = 0.13 microseconds and save it. Stop sampling after 1s and stop the excitation. Denote f(r) = u 2 (rT), which is the output value u 2 (t) of the circuit collected in the rth cycle, r = 1, 2, 3.......7.69×10 6 .

[0062] (3) Calculate the sample element h(r,j) = f(r) - f(j), where r = 1, 2, 3...N, j = 2, 3...N, r ≠ j. Initialize the identification times Rec = 1, the order Num = -1, and BasicL = 100.

[0063] (4) m = BasicL × Rec, r 0 = m ― BasicL + 1, a = 1, 2, 3, b = 1, 2, 4, calculate the identification primitive g(a, c), c = 1, 2, 3, 4. Among them,

[0064]

[0065] (5) Calculate

[0066] D11 1 = g(1, 1)g(2, 3)g(3, 4) + g(1, 4)g(2, 1)g(3, 3) + g(1, 3)g(2, 4)g(3, 1)

[0067] D11 2 = g(1, 1)g(2, 4)g(3, 3) + g(1, 3)g(2, 1)g(3, 4) + g(1, 4)g(2, 3)g(3, 1)

[0068] D12 1 = g(1, 2)g(2, 3)g(3, 4) + g(1, 4)g(2, 2)g(3, 3) + g(1, 3)g(2, 4)g(3, 2),

[0069] D12 2 = g(1, 2)g(2, 4)g(3, 3) + g(1, 3)g(2, 2)g(3, 4) + g(1, 4)g(2, 3)g(3, 2)

[0070] D11 = D11 1 ― D11 2 = -4.0390×10 -28

[0071] D12 = D12 1 ― D12 2 = -4.0390×10 -28 。

[0072] (6) Calculate

[0073] D21 1 = g(2, 1)g(3, 4)D12 + g(2, 4)g(3, 2)D11

[0074] D21 2 = g(2, 4)g(3, 1)D12 + g(2, 2)g(3, 4)D11

[0075] D21 = D21 1 ― D21 2 = 1.3364×10 -51

[0076] D22 = g(2,3)g(3,4) - g(2,4)g(3,3) = 1.3364×10 -51 。

[0077] (7) Calculate

[0078] D3 1 = g(1,1)g(2,2)g(2,3)g(3,3)g(3,4) + g(1,1)g(2,3)g(2,4)g(3,2)g(3,3) D3 2 = g(1,2)g(2,1)g(2,4)g(3,3)g(3,3) + g(1,2)g(2,3)g(2,3)g(3,1)g(3,4) D3 3 = g(1,3)g(2,2)g(2,4)g(3,1)g(3,3) + g(1,3)g(2,1)g(2,3)g(3,2)g(3,4) D3 4 = g(1,1)g(2,2)g(2,4)g(3,3)g(3,3) + g(1,1)g(2,3)g(2,3)g(3,2)g(3,4) D3 5 = g(1,2)g(2,1)g(2,3)g(3,3)g(3,4) + g(1,2)g(2,3)g(2,4)g(3,1)g(3,3) D3 6 = g(1,3)g(2,2)g(2,3)g(3,1)g(3,4) + g(1,3)g(2,1)g(2,4)g(3,2)g(3,3)

[0079] D3 = D3 1 + D3 2 + D3 3 - D3 4 - D3 5 - D3 6 = 1.3350×10 -51 。

[0080] (8) Calculate the discrimination factor χ Rec (1), χ Rec (2), χ Rec (3), D12 and D22 are small but not zero, calculate They are equal to 1, 1, 0.9990 respectively.

[0081] (9) The allowable error is denoted as Tol = 0.001, χRec (1), χ Rec (2) and χ Rec (3) satisfy |χ Rec (1) - χ Rec (2) + χ Rec (3) - 1| ≤ Tol, so Num = 2, IdError = -0.0044.

[0082] (10) The final experimental result is: Num = 2, indicating that the circuit of the output y 3 (t) is a second-order system.

[0083] The identification result of step (10) shows that when there is no interference, the above method proposed in this patent can accurately and effectively identify the order of the circuit system in the attached instructions of the specification Figure 2 However, in actual work, interference is inevitable.

[0084] To examine the anti-interference ability of the above method of this patent, the above experiments were also carried out many times. The difference is that in step (2) above, "set the gain after adding white noise to 0, that is, no interference is mixed in" is changed to "adjust the gain after adding white noise to" 5, 10, 20, 40, 60.

[0085] Then, the above identifications were carried out on the zero-order, first-order, third-order, and fourth-order circuit systems shown in (a), (b), (c), and (d) in the attached instructions of the specification to more comprehensively verify the method. In the figure, R Figure 3 0 = 100Ω, R 1 = 10Ω, C 1 = 0.5F, R 2 = 6Ω, L 2 = 1H, C 2 = 0.5F, R 3 = 1Ω, C 3 = 1F, R 40 = 1Ω, R 41 = 1Ω, C 4 = 1F. Their mathematical models are respectively

[0086] i 1 (t) = 0.2u(t)

[0087]

[0088] The poles are 0, -0.2, {-3.2470, -1.5550, -0.1981}, {-0.7794, -0.7013, -0.5000, -0.1076} respectively. The identification results are shown in Tables 1 and 2 below. Among them, Table 1 is the identification factors calculated based on the step responses of each circuit in the experiment, and Table 2 is the order of each system analyzed based on the mutual relationship between these identification factors.

[0089] Table 1 Specific situation of identification factors of low-order linear circuits in the experiment

[0090]

[0091]

[0092] Table 2 Specific situation of the order of low-order linear circuits in the experiment, the identified order Num (identification error IdError)

[0093]

[0094] Table 2 shows that for both the ideal system without interference and the system with the interference signal amplitude not exceeding three times the signal amplitude, the identification method proposed in this patent can correctly and effectively identify the order of the 5 circuits in the experiment. As can be seen from Tables 1 and 2, as the white noise amplitude increases or the noise-to-signal ratio increases, the identification index error of this method gradually increases, but it does not affect the final identification result. Among them, this method has small identification errors and high precision for the second-order and third-order systems, and shows very good robustness to interference. When the interference amplitude is 300% of the signal, this method accurately identifies their orders with errors of 0.0290 and 3.2389 respectively. Relatively speaking, for the first-order system, this method is more sensitive to interference, but its anti-interference ability is also very strong. When the interference amplitude is 300% of the signal, it can identify that the system is a first-order system, and the identification error is -0.6061. In addition, similar studies have also been carried out on other low-order systems with distinct real poles, and the results are similar. These situations indicate that the identification method proposed in this patent has strong anti-interference ability, high identification precision, and stable and reliable identification.

[0095] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for direct identification of the order of low-order linear systems with different real poles with small computational complexity, characterized in that: The following steps are involved: Step 1: Set the input of the system to be tested to zero, and release the constraints to make the system in a zero equilibrium state, that is, the output and state of the system are equal to zero, and are in equilibrium and unchanged. Then prepare a constant input excitation with an amplitude of b and an output y(t) acquisition system; Step 2: Apply the constant input stimulus prepared in step 1 to the input end of the system to be tested, and use the prepared acquisition system to collect the output y(t) and save it. Let f(r)=y(rT), which is the system output value y(t) collected in the rth period, r=1, 2, 3...N, T is the sampling period, and N is the number of samples collected; Step 3: Calculate the sample element h(r,j), h(r,j)=f(r)-f(j), where r=1, 2, 3...N, j=2, 3...N, r≠j, initialize the identification times Rec=1, and the order Num=-1; Step 4: Let m = BasicL × Rec, r0 = m-BasicL + 1, MaxL be an integer of 0.5N, 20 < BasicL < MaxL, calculate the recognition primitive g(a,c), a = 1, 2, 3, c = 1, 2, 3, 4, where, Where b = 1, 2, 4; Step 5: Calculate the primary identification elements D111, D112, D121, D122, and the primary identification factors D11, D12, where D11 = D111-D112, D12 = D121-D122; Step 6: Calculate the secondary identification elements D211, D212, D221, and the secondary identification factors D21, D22, where D21 = D211 - D212, D22 = g(2,3)g(2,4)D12 - g(2,4)g(3,3)D12; Step 7, calculate the third-level identification elements D31, D32, D33, D34, D35, D36, and the third-level identification element D3, where D3 = D31 + D32 + D33 - D34 - D35 - D36; Step 8: Calculate the identification factor χ Rec (1) χ Rec (2) χ Rec (3); If D12 = 0, then χ Rec (1)=3, otherwise If D22=0, then χ Rec (2) = 3, χ Rec (3)=1, otherwise, Step 9: The allowable error is recorded as Tol, according to χ Rec (1) χ Rec (2) χ Rec (3) Analyze the order Num of the system to be tested; Step 10: If Num=-1 and Rec=1, then Rec=2, and go to step 4 for calculation; otherwise, end. At this time, if Num=-1, the system to be measured is a low-order linear system with non-distinct real poles.

2. The method for direct identification of the order of a low-order linear system with different real poles with small computational complexity according to claim 1, characterized in that: In step 5 and step 6, D111, D112, D121, D122, D211 and D212 are calculated by the following formula D111=g(1,1)g(2,3)g(3,4)+g(1,4)g(2,1)g(3,3)+g(1,3)g(2,4)g(3,1) D112=g(1,1)g(2,4)g(3,3)+g(1,3)g(2,1)g(3,4)+g(1,4)g(2,3)g(3,1) D121=g(1,2)g(2,3)g(3,4)+g(1,4)g(2,2)g(3,3)+g(1,3)g(2,4)g(3,2) D122=g(1,2)g(2,4)g(3,3)+g(1,3)g(2,2)g(2,2)+g(1,4)g(2,3)g(3,2) D211=g(2,1)g(3,4)D12+g(2,4)g(3,2)D11 D212=g(2,4)g(3,1)D12+g(2,2)g(3,4)D11 D221=g(2,3)g(3,4)-g(2,4)g(3,3).

3. The method for direct identification of the order of a low-order linear system with different real poles with small computational complexity according to claim 1, characterized in that: In step 7, D31, D32, D33, D34, D35 and D36 are calculated by the following formula D31=g(1,1)g(2,2)g(2,3)g(3,3)g(3,4)+g(1,1)g(2,3)g(2,4)g(3,2)g(3,3) D32=g(1,2)g(2,1)g(2,4)g(3,3)g(3,3)+g(1,2)g(2,3)g(2,3)g(3,1)g(3,4) D33=g(1,3)g(2,2)g(2,4)g(3,1)g(3,3)+g(1,3)g(2,1)g(2,3)g(3,2)g(3,4) D34=g(1,1)g(2,2)g(2,4)g(3,3)g(3,3)+g(1,1)g(2,3)g(2,3)g(3,2)g(3,4) D35=g(1,2)g(2,1)g(2,3)g(3,3)g(3,4)+g(1,2)g(2,3)g(2,4)g(3,1)g(3,3) D36=g(1,3)g(2,2)g(2,3)g(3,1)g(3,4)+g(1,3)g(2,1)g(2,4)g(3,2)g(3,4).

4. The method for direct identification of the order of a low-order linear system with different real poles with small computational complexity according to claim 1, characterized in that: In the step eight, when x Rec (1) = x Rec (2) = 3, χ Rec (3)=1, then Num=0, the system to be measured is a zero-order system, that is, a proportional system; when Num=-1 and |χ Rec (1) -χ Rec (3)-2|≤Tol,|χ Rec (2) -2χ Rec (3)-1|≤Tol, then Num=1, the system to be measured is a first-order system; when Num=-1 and |χ Rec (1) -χ Rec (2)+χ Rec (3)-1|≤Tol, then Num=2, and the system to be measured is a second-order system. When Num=-1, Rec=2, and |χ1(1)-χ2(1)|≤Tol, |χ1(2)-χ2(2)|≤Tol, |χ1(3)-χ2(3)|≤Tol, then Num=3, and the system to be measured is a third-order system.

5. The method for direct identification of the order of a low-order linear system with different real poles with small computational complexity according to claim 4, characterized in that: When Num=1, the identification error IdError=max{χ Rec (1) -χ Rec (3) -2, χ Rec (2) -2χ Rec (3)-1}; when Num=2, calculate the identification error IdError=χ Rec (1) -χ Rec (2)+χ Rec (3)-1; when Num=3, the identification error IdError=max{|χ1(1)-χ2(1)|, |χ1(2)-χ2(2)|, |χ1(3)-χ2(3)|} is calculated.

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