Position-torque double-closed-loop servo system parameter optimization control method with stable and rapid dynamic response

Abstract

The position-torque double closed-loop servo system parameter optimization control method provided by the invention is stable and rapid in dynamic response. On the basis that a position regulator is composed of first-order advanced feedback of a unit proportionality coefficient and regulation with proportion and integration as main components, a simplest expectation mathematical model of a closed-loop single-zero-point type 3 (a forward channel of the system has three integration links) control system is provided, and the maximum phase angle margin of the system is used as an optimization target. And deriving an analytic formula of system open-loop gain optimization setting, and further providing a position regulator parameter optimization setting control method which enables the position-torque double-closed-loop servo system to have low-overshoot, stable and rapid performance on step response. The method has important guiding significance on design of the position-torque double-closed-loop servo system requiring stable and rapid dynamic response, product development (including experimental equipment), on-site commissioning, debugging and the like, and meanwhile, the design theory of the motor position-torque double-closed-loop servo system is also perfected.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of automatic control, and relates to a parameter optimization control method of a position-torque double closed loop servo system with stable and fast dynamic response, which is suitable for a position control system with an AC motor or a DC motor as an execution component. BACKGROUND

[0002] Among several structure schemes of modern position servo systems with an AC or DC motor as an execution component, a double closed loop system structure is the most simple and economical structure form of position servo systems, in which a position is used as an outer ring to ensure the accuracy of a controlled quantity, and a current or torque is used as an inner ring to realize the constraint control of the maximum current or torque allowed by the motor. However, the main problem is that there are two integral links in the controlled object, and the load disturbance appears before the two integral links. In order to meet the static performance, the position regulator must contain an integral component to form a type 3 control system (the system has three integral links in the forward channel), but it also causes difficulties in improving the dynamic performance of the system. For this problem, there are two selection schemes. One is that the position regulator also contains two zeros and both are in the forward channel, such as using a PID regulation law, but the disadvantage is that the system has a large overshoot for a step response, and the dynamic process is not stable enough. The other is that the two zeros of the above-mentioned position regulator are respectively set in the forward channel and the feedback channel, such as using a PI (proportion + integral) law for the position regulator in the forward channel and using a PD (proportion + differential) law for the feedback, which is helpful to reduce the overshoot for a step response when the system parameters are properly set, but how to optimize and set these regulation parameters to improve the dynamic performance of the system, especially the parameter optimization control method which can meet the development, setting and operation of the position-torque double closed loop servo system in engineering practice is an important problem to be solved. This not only has important significance for the product development (including experimental equipment) and engineering application of the position-torque double closed loop servo system, but also fills the gap of the position-torque double closed loop servo system quantitative design in the teaching materials of motor control and motion control in colleges and universities. This is also the main starting point of the present application. SUMMARY

[0003] The present application aims at the deficiencies of the existing control method of the position-torque double closed loop servo system with an AC or DC motor as an execution component. On the basis of a position regulator composed of a unit proportion coefficient first-order lead feedback and a proportion + integral main regulation, a most simple expected mathematical model of a closed loop single zero type 3 system (the system has three integral links in the forward channel) is proposed, and the maximum phase angle margin (γ maxTo optimize the system's open-loop gain (K), an analytical formula for optimal tuning is derived. Furthermore, a method for optimizing the tuning of position regulator parameters is proposed to achieve low overshoot, smooth operation, and rapid response in a position-torque dual-closed-loop servo system to step responses. This invention provides significant guidance for the design, product development (including experimental equipment), field commissioning, and debugging of position-torque dual-closed-loop servo systems requiring smooth and rapid dynamic response. It also improves the design theory of motor position-torque dual-closed-loop servo systems.

[0004] This invention provides a parameter optimization control method for a dynamic, stable, and fast-responding position-torque dual closed-loop servo system, comprising the following steps:

[0005] Step 1. Construct the simplest expected transfer function of the system in open-loop double-zero and closed-loop single-zero form;

[0006] The simplest expected transfer function includes the system's simplest open-loop transfer function and its corresponding simplest closed-loop transfer function.

[0007] Step 2. Based on the simplest open-loop transfer function, take the maximum corresponding system phase margin as the optimization objective to obtain the analytical formula for optimizing the system open-loop gain K.

[0008] Step 3. Based on the simplified closed-loop transfer function and the system open-loop gain K, perform simulation optimization to obtain the integral time constant τ. i =mT and differential time constant τ d =hT and the relationship between system performance, where T is the system equivalent time constant, h is the mid-frequency band width of the system open-loop amplitude-frequency characteristic, which is also the ratio of the differential time constant to the equivalent time constant, and m is the ratio of the integral time constant to the equivalent time constant;

[0009] Step 4. Based on the integration time constant τ i =mT, differential time constant τ d =hT and position adjuster gain k p A parameter optimization and tuning control method for the position regulator in the system is constructed.

[0010] Preferably, the system's minimum expected open-loop transfer function W III (s), in the following form:

[0011]

[0012] The simplest closed-loop transfer function W corresponding to the simplest open-loop transfer function mentioned above cl3 (s), in the following form:

[0013]

[0014] The system phase margin γ(ω) corresponding to the simplest open-loop transfer function described above c (,m,h), in the following form:

[0015] γ(ω c (m,h)=-90°+arctan(mω) c T)+arctan(hω c T)-arctan(ω c T);

[0016] Where n is the ratio of m to h, n = m / h, ω c θ is the crossover frequency in the open-loop amplitude-frequency response of the system, s is the Laplace transform factor; * θ is the system's position command signal; θ is the position feedback signal; T is the system's equivalent object time constant; τ d It is the differential time constant; τ i It is the integral time constant.

[0017] Preferably, in step 2, the optimization objective is to maximize the system phase margin, resulting in an analytical formula for optimizing the open-loop gain K of the system. This formula specifically includes:

[0018] Depend on The maximum phase margin γ is obtained max and its corresponding open-loop shear frequency ω c With respect to the system open-loop gain K;

[0019] The maximum phase margin γ max Its relationship with h and m is as follows:

[0020]

[0021] The relationship between the system open-loop gain K and h, m, and T is as follows:

[0022]

[0023] Preferably, the differential time constant τ d =hT=4.5T, integration time constant τ i When mT = 31.5T: System phase margin γ max =35.9°, shear frequency ω c =0.533 / T, step response overshoot σ% = 4.95%, transient response time t s =7.38T.

[0024] Preferably, the position adjuster in the system outputs a torque loop command signal. The format is as follows:

[0025]

[0026] wherein, is the torque loop command signal, and is also the output signal of the position regulator, τ0 is the first order inertia filter time constant of the position command signal θ * and the position feedback signal θ, k p is the position regulator gain, τ ∑T is the equivalent time constant of the torque loop, C T is the torque feedback coefficient, k θ is the actuator constant, J is the total inertia of the system, and i is the reduction ratio of the actuator;

[0027] Preferably, the parameter optimization control method of the dynamic response smooth and fast position-torque double closed loop servo system further comprises the following steps:

[0028] the calculated value of the torque loop command signal output by the position regulator is subjected to a limit judgment:

[0029] if the calculated value of is output as the actual command signal of the torque loop, wherein is the position regulator output limit value;

[0030] if the reverse limit value is output as the actual command signal of the torque loop;

[0031] if the positive limit value is output as the actual command signal of the torque loop;

[0032] wherein T emax is the maximum electromagnetic torque allowed by the motor.

[0033] Preferably, the measurement and control implementation method of the position regulator in an interrupt sampling control period comprises the following steps:

[0034] First, the position command signal θ * and the position feedback signal θ are collected;

[0035] Then, the position command signal θ * is subjected to first order inertia filtering and output Meanwhile, the position feedback signal θ is subjected to first order inertia filtering and first order lead (τ d s+1) operation and output and then the input position deviation signal e θ, and the form is as follows:

[0036]

[0037] The position deviation signal e θ is subjected to a "proportional + integral" operation, and the result is output as a torque loop command signal , and the form is as follows:

[0038]

[0039] The torque loop command signal output by the position regulator is subjected to a limit judgment:

[0040] When , the calculated value of is output as the actual command signal of the torque loop;

[0041] When , the reverse limit value is output as the actual command signal of the torque loop;

[0042] When , the positive limit value is output as the actual command signal of the torque loop.

[0043] Preferably, the system has a 3-type system characteristic with 3 integral links in the forward channel, and further includes a position regulator APR, a torque regulator ATR, a driver UPE, a motor M, and a position sensor PS;

[0044] The position regulator APR receives θ * and θ, and outputs a torque loop command signal The torque regulator ATR receives the torque loop command signal , a torque feedback signal U T , and further calculates a torque deviation signal e T , and outputs a signal U c as a command of the driver UPE, which controls the motor electromagnetic torque T e output by the motor M, and uses the position sensor PS to obtain the rotational position of the motor M to output a position feedback signal θ.

[0045] The beneficial effects of the present application are as follows:

[0046] The present application is based on a position regulator composed of a first-order lead feedback with a unit proportional coefficient and a proportional + integral main adjustment, and proposes a position-torque double closed-loop servo system with a 3-type system characteristic (the forward channel of the system has 3 integral links) and a maximum phase margin (γmax ) as the optimization target, the analytic formula of system open loop gain (K) optimization setting is derived and the optimization control of position regulator and its specific parameter setting is realized by combining simulation optimization, so that the type 3 system also has low overshoot smooth and fast dynamic response performance. The application has guiding significance for the productization (including experimental equipment) development and design, operation, debugging and the like of motor position-torque double closed loop servo system which requires dynamic response smooth and fast and low overshoot, and can also enrich and perfect the design theory of position-torque (or current) double closed loop servo system in the undergraduate and graduate textbooks of modern motor control system and motion control system. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 It is the composition principle block diagram of the position-torque double closed loop servo system involved in the application and also the research object of the application.

[0048] Figure 2 It is the simplest expected mathematical model block diagram of type 3 control system with open loop double zero point and closed loop single zero point proposed by the application.

[0049] Figure 3 It is the mathematical model block diagram of position-torque double closed loop servo system parameter optimization control of the application.

[0050] Figure 4 It is the position regulator control flow chart of the application.

[0051] Explanation of codes in the drawings:

[0052] Explanation of codes in the drawings: M is a motor (DC motor or AC motor); PS is a position sensor, UPE is a driver; APR is a position regulator; ATR is a torque regulator, and its equivalent transfer function is W clT (s)≈(1 / C T ) / (τ ∑T s+1), wherein τ ∑T is a torque loop equivalent time constant; C T is a torque feedback coefficient; s is a Laplace transform factor; θ * is a position command signal of the system; is a position command signal filtered by a first order inertia; θ is a position feedback signal; θ0 is a position signal filtered by a first order inertia and a first order lead operation; n is a speed; T e is a motor electromagnetic torque; is an APR output signal (also a torque loop command signal), and its maximum value is T emax is a maximum electromagnetic torque allowed by the motor; U T is a torque feedback signal; e θIt is the system position deviation signal input to APR; e T It is a torque deviation signal; U c It is the ATR output signal; T L It is the equivalent load torque; K is the system open-loop gain; T is the system equivalent object time constant; τ0 is the first-order filter time constant; τ d It is the differential time constant; τ i It is the integration time constant; k p J is the position adjuster gain; J is the total system moment of inertia; i is the actuator reduction ratio; k θ It is an actuator constant. Detailed Implementation

[0053] Step 1. Establish a position-torque dual closed-loop servo system with stable and rapid dynamic response (see attached). Figure 1 The simplest expectation mathematical model (with appendix) Figure 2 ) and their parameter optimization matching relationship,

[0054] In the dynamic, stable, and fast position-torque dual closed-loop servo system, the position adjuster APR receives θ. * And θ, output torque loop command signal The torque regulator ATR receives torque loop command signals. Torque feedback signal U T Then calculate the torque deviation signal e T Its output signal U c As a command from the driver UPE, the driver UPE outputs the electromagnetic torque T to the motor M. e To control the motor, a position sensor PS is used to obtain the rotational position of the motor M, and a position feedback signal θ is output.

[0055] The system's simplest expected value mathematical model is a transfer function in the form of a Laplace transform. The transfer function of the feedback channel has a differential time constant of τ. d The forward path transfer function of the system consists of an open-loop gain K, three integrators (forming a type 3 system), and an integration time constant τ, and is composed of a first-order lead element with a unit proportional coefficient. i It consists of the product of a first-order leading element and a first-order lagging element with a time constant of T in the equivalent system object;

[0056] The differential time constant τ of the first-order lead element in the feedback channel d The integral time constant τ is h times the equivalent object's time constant T, where h is the mid-frequency bandwidth of the system's open-loop amplitude-frequency response, h > 1, and the integral time constant τ of the first-order lead element in the forward channel. i It is m times the time constant T of the equivalent object, where m > h / (h-1).

[0057] The desired system minimum open-loop transfer function W III (s) is in the form of

[0058]

[0059] The minimum closed-loop transfer function W cl3 (s) corresponding to the above minimum open-loop transfer function is in the form of

[0060]

[0061] The system phase margin γ(ω c , m, h) corresponding to the above minimum open-loop transfer function is as follows:

[0062] γ(ω c , m, h) = -90° + arctan(mω c T) + arctan(hω c T) - arctan(ω c T)

[0063] wherein n is the ratio of the integral time constant τ i = mT to the differential time constant τ d = hT, n = m / h, and ω c is the cut-off frequency in the open-loop amplitude-frequency characteristic of the system.

[0064] Step 2. The system open-loop gain K is optimized with the maximum phase margin γ max as the optimization index, and the maximum phase margin γ max and the corresponding open-loop cut-off frequency ω c , open-loop gain K and the parameters m and h are derived, which are in the forms of

[0065]

[0066] Step 3. Table 1 shows the relationship between the main performance indexes of the closed-loop single-zero type 3 control system based on the γ max optimization of the present application and the parameters, and the data in the table are obtained from the related formulas and MATLAB simulation in the present application. In Table 1, only the parameter combinations are listed when the system phase margin is greater than 35° and the overshoot of the step response is greater than 1%, and when the mid-frequency band width h is less than the value in the table, the system phase margin is less than 35° and is not recommended to be used. In addition, from Table 1, it can be seen that when the n = m / h ratio is large, including when it is continuously increased, the effect on the system dynamic performance is not large, and therefore, the preferred specific parameter combinations are as follows:

[0067] When h = 4.5 and m = 31.5 are selected: the system phase margin γ max= 35.9°, shear frequency ω c = 0.533 / T, step response overshoot σ% = 4.95%, transition process time t s = 7.38T. The dynamic steady fast and low overshoot target is achieved for step response, and the system phase angle margin is large enough.

[0068] Table 1 is based on γ max The main performance index of the optimized closed-loop single-zero type 3 type control system and the relationship between parameters

[0069]

[0070]

[0071] The parameter KT in table 1 3 10 3 is the product of the system open loop gain and the cube of the system equivalent object time constant, such as h = 4.5, m = 31.5 is selected as above, KT 3 10 3 = 3.757, that is: the system open loop gain K = 3.757 / (T 3 × 10 3 ), the rise time t r refers to the time of the system position output to the first time to reach 100% steady state value for step response, the peak time t p is the time corresponding to the maximum overshoot point of the system for step response, the transition process time t s is the time when the system for step response enters ± 5% steady state value error band and remains in it.

[0072] Step 4. The position-force torque double closed loop servo system position regulator parameter optimization setting control method for making dynamic response steady and fast, which is as follows:

[0073]

[0074] wherein, is the torque ring command signal, which is also the output signal of the position regulator, θ * is the system position command signal, θ is the system position feedback signal, s is the Laplace transform factor, τ0 is the first order filter time constant for position command signal θ * and position feedback signal θ, k p is the position regulator gain, τ ∑T is the equivalent time constant of torque ring, C T is the torque feedback coefficient, k θ is the actuator constant, J is the total inertia of the system, and i is the speed reduction ratio of the actuator;

[0075] Step 5. The method of measuring and controlling the position regulator in an interrupt sampling control cycle is as follows:

[0076] 5.1 First, the position command signal θ * is sampled.

[0077] 5.2 Then, the position command signal θ * is filtered by a first order inertia filter and output. Meanwhile, the position feedback signal θ d is filtered by a first order inertia filter and a first order lead (τ θ s+1) filter and output. Further, the input position error signal e θ to the forward channel position regulator is calculated, which is as follows:

[0078]

[0079] 5.3 The "proportion + integral" operation is performed on the above-mentioned position error signal e emax , and the result is output as the calculated value of the torque loop command signal , which is as follows:

[0080]

[0081] 5.4 The amplitude limiting judgment is performed on the calculated value of the torque loop command signal output by the position regulator:

[0082] 5.4.1 When , the calculated value of is output as the actual command signal of the torque loop, in which is the output amplitude limiting value of the position regulator.

[0083] 5.4.2 When , the reverse amplitude limiting value is output as the actual command signal of the torque loop, i.e. the reverse maximum command signal of the torque loop.

[0084] 5.4.3 When , the forward amplitude limiting value is output as the actual command signal of the torque loop, i.e. the forward maximum command signal of the torque loop.

[0085] In which T T is the maximum electromagnetic torque allowed by the motor.

[0086] Description: (1) The main relationship formula described in the present application adopts a pull-type transformation expression form in order to intuitively reflect the system concept, which is easily converted into a difference expression form when the position regulator is programmed and implemented, without substantial difference. (2) The specific data in Table 1 may have slight differences due to different versions of simulation software and simulation time, step size, etc. set during simulation, which is a non-substantial problem and is known by peers. (3) Although the present application is based on a motor position-torque double closed-loop servo system, the method is also completely applicable to a motor position-current double closed-loop control system which requires smooth and rapid dynamic response and low overshoot. (4) Although the present application takes a rotating motor as an example, the method is also applicable to an alternating current linear motor or a direct current linear motor position-force double closed-loop servo system, an alternating current linear motor or a direct current linear motor position-current double closed-loop servo system. (5) Figure 1 The torque regulator ATR in the torque loop generally adopts a PI regulation law, and the parameters are generally set based on the ITAE index optimization, and then the torque loop closed-loop equivalent transfer function can be described as Kp+Ks / s, as shown in the description and attached drawings of the present application. Figure 3 The torque feedback coefficient C T in the description is the reciprocal of the gain, and the time constant is the equivalent time constant τ ∑T of the torque loop first-order inertia link, which belongs to the conventional method, and thus is not described in detail.

Claims

1. A dynamic response smooth and fast position-torque double closed loop servo system parameter optimization control method, characterized in that, The method comprises the following steps: Step 1. Constructing a system minimum desired transfer function of open-loop double zero point and closed-loop single zero point type; The minimum desired transfer function comprises a system minimum open-loop transfer function and a corresponding minimum closed-loop transfer function thereof; Step 2. Based on the minimum open-loop transfer function, a system open-loop gain K optimization setting analytical formula is obtained with maximum system phase angle margin as an optimization target; Step 3. Simulation optimization based on the minimum closed-loop transfer function and system open-loop gain K to obtain integral time constant τ i = mT and differential time constant τ d = hT and system performance relationship, where T is the equivalent object time constant of the system, h is the mid-frequency width of the open-loop amplitude-frequency characteristic of the system, which is also the ratio of the differential time constant to the equivalent object time constant, and m is the ratio of the integral time constant to the equivalent object time constant. Step 4. The integral time constant τ i = mT, the derivative time constant τ d = hT and the position regulator gain k p A parameter optimization tuning control method for constructing the position regulator in the system.

2. The parameter optimization control method of the dynamic response stable and fast position-torque double closed-loop servo system according to claim 1, characterized in that, The system's simplest desired open-loop transfer function W III (s), in the form of: The above simplest open-loop transfer function corresponds to the simplest closed-loop transfer function W cl3 (s), in the form of: The system phase margin γ(ω c ,m,h) is of the form γ(ω c , m, h) = -90° + arctan(mω c T) + arctan(hω c T) - arctan(ω c T); where n is the ratio of m to h, n = m / h, ω c is the shear frequency in the open-loop amplitude-frequency characteristic of the system, s is the Laplace transform factor; θ * is the position command signal of the system; θ is the position feedback signal; T is the equivalent object time constant of the system; τ d is the differential time constant; τ i is the integral time constant.

3. The parameter optimization control method of the dynamic response stable and fast position-torque double closed-loop servo system according to claim 2, characterized in that, In step 2, the system open-loop gain K optimization setting analytical formula is obtained with maximum system phase angle margin as an optimization target, and specifically comprises: The phase margin γ corresponding to the maximum phase margin γ max and the corresponding open-loop shear frequency ω c and the system open-loop gain K; The phase angle margin maximum value γ max The relationship between h and m is as follows: The relationship between the system open-loop gain K and h, m and T is as follows:

4. The parameter optimization control method of the dynamic response stable and fast position-torque double closed-loop servo system according to claim 3, characterized in that, The differential time constant τ d = hT = 4.5T, the integral time constant τ i = mT = 31.5T: the system phase margin γ max = 35.9°, the shear frequency ω c = 0.533 / T, the step response overshoot σ% = 4.95%, the transition process time t s = 7.38T.

5. The parameter optimization control method of the dynamic response stable and fast position-torque double closed-loop servo system according to claim 3, characterized in that, The position regulator in the system, whose output torque loop instruction signal is as follows: where is the torque loop command signal, which is also the output signal of the position regulator, τ0is the first order inertia filter time constant for the position command signal θ * and the position feedback signal θ, k p is the position regulator gain, is the torque loop equivalent time constant, C T is the torque feedback coefficient, k θ is the actuator constant, J is the total inertia of the system, and i is the reduction ratio of the actuator.

6. The parameter optimization control method of a dynamic response smooth and fast position-torque dual closed loop servo system according to claim 5, characterized in that, Further comprising the following steps: Torque loop command signal to position regulator output clipping of the calculated value: When the calculated value of is output as the actual command signal for the torque ring, wherein is the position regulator output limit value; When the reverse limit value output as the actual command signal of the torque loop; When the forward limit value output as the actual command signal of the torque loop; wherein T emax is the maximum electromagnetic torque allowed for the electric machine.

7. The parameter optimization control method of a dynamic response smooth and fast position-torque dual closed loop servo system according to claim 6, characterized in that, The measurement and control implementation method of the position regulator in an interrupt sampling control cycle comprises the following steps: The position command signal θ is first acquired * and the position feedback signal θ; Next, the position command signal θ * Output after first-order inertial filtering Simultaneously, the position feedback signal θ is subjected to first-order inertial filtering. and first-order lead (τ) d Output after s+1) operation Then, the input position deviation signal e input to the forward channel position adjuster is obtained. θ Its form is as follows: to the position deviation signal e θ a "proportional + integral" operation is performed and the result is output as a torque ring command signal the calculated value, which has the following form: Torque loop command signal to position regulator output The calculated value is limited to determine When the calculated value of is output as the actual command signal for the torque ring; When the reverse limit value output as the actual command signal of the torque loop; When The positive limit value Output as actual command signal for the torque loop.

8. The parameter optimization control method of a dynamic response smooth and fast position-torque dual closed loop servo system according to claim 1, characterized in that, The system has a 3-type system characteristic with 3 integral links in a forward channel, and further comprises a position regulator APR, a torque regulator ATR, a driver UPE, a motor M and a position sensor PS; The position regulator APR receives θ * and θ, and outputs a torque loop command signal The torque regulator ATR receives the torque loop command signal a torque feedback signal U T and further calculates a torque deviation signal e T whose output signal U c The drive UPE outputs a motor electromagnetic torque T e to the motor M as a command of the drive UPE, and controls the motor electromagnetic torque T using a position sensor PS to output a position feedback signal θ.

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