CN106094525A

CN106094525A - A kind of TSM control device based on fractional calculus and control method

Info

Publication number: CN106094525A
Application number: CN201610533238.XA
Authority: CN
Inventors: 杨宁宁; 吴朝俊; 韩宇超; 贾嵘; 徐诚
Original assignee: Xian University of Technology
Current assignee: Xian University of Technology
Priority date: 2016-07-08
Filing date: 2016-07-08
Publication date: 2016-11-09
Anticipated expiration: 2036-07-08
Also published as: CN106094525B

Abstract

The invention discloses a terminal sliding mode controller based on fractional calculus, the function form of which is: Among them μ ∈ (0, 1], α is a normal number greater than 0, β = q/p, where p and q are both positive odd numbers satisfying 0<q/p<1. The control of the terminal sliding mode controller is adopted The method is: for the controlled object under fractional-order terminal sliding mode control, obtain its state equation; then bring the state equation of the controlled object into the fractional-order terminal sliding mode control function to obtain the terminal sliding mode control of the controlled object The function is used to control the system. The system is controlled by this controller, which has short response time, strong anti-interference, and smaller steady-state error.

Description

A Terminal Sliding Mode Controller and Control Method Based on Fractional Calculus

技术领域technical field

本发明属于自动控制技术领域，具体涉及一种基于分数阶微积分的终端滑模控制器，还涉及了采用该控制器的控制方法。The invention belongs to the technical field of automatic control, and in particular relates to a terminal sliding mode controller based on fractional calculus, and also relates to a control method using the controller.

背景技术Background technique

分数阶微积分(FOC)的阶次可以是任意的，它拓展了整数阶微积分的描述能力。传统的整数阶微积分是分数阶微积分在特定情况下的特例，对于分数阶微积分的开发是时下研究的热点。The order of fractional calculus (FOC) can be arbitrary, which extends the descriptive ability of integral calculus. The traditional integral calculus is a special case of fractional calculus in specific circumstances, and the development of fractional calculus is a hot research topic nowadays.

滑模控制(sliding mode control,SMC)也叫滑模变结构控制，是20世纪50年代提出来的一种有效的鲁棒控制策略，多运用在非线性控制方面，其基本思想是根据系统所期望的动态特性来设计系统的滑模面，具有切换控制规则功能，使系统的状态轨迹从初始状态到达预定义的具有所期望动态特性的滑模面。通过滑动模态控制器使系统状态从滑模面之外向滑模面运动。系统一旦到达滑模面，控制作用将保证系统沿滑模面到达系统平衡点。Sliding mode control (Sliding mode control, SMC) is also called sliding mode variable structure control. It is an effective robust control strategy proposed in the 1950s. It is mostly used in nonlinear control. Its basic idea is based on the The sliding mode surface of the system is designed according to the desired dynamic characteristics, with the function of switching control rules, so that the state trajectory of the system reaches the predefined sliding mode surface with the desired dynamic characteristics from the initial state. The state of the system moves from outside the sliding mode surface to the sliding mode surface through the sliding mode controller. Once the system reaches the sliding surface, the control action will ensure that the system reaches the system equilibrium point along the sliding surface.

与滑模控制相比，终端滑模控制克服了其闭环响应对于内部参数的不确定性以及外部扰动的敏感问题，其具有系统有限时间内的收敛特性，在稳定状态下具有更高的准确度，在接近平衡点处收敛速度明显加快等优点。但其对于扰动的鲁棒性较差，无法满足部分极高精度控制需求。Compared with sliding mode control, terminal sliding mode control overcomes the sensitivity of its closed-loop response to the uncertainty of internal parameters and external disturbances. It has the convergence characteristics of the system within a limited time and has higher accuracy in a stable state. , the convergence speed is obviously accelerated when it is close to the equilibrium point. However, its robustness to disturbances is poor, and it cannot meet some extremely high-precision control requirements.

发明内容Contents of the invention

本发明的一个目的是提供一种基于分数阶微积分的终端滑模控制器，解决了传统滑模控制和终端滑模控制对于扰动的不敏感的问题。An object of the present invention is to provide a terminal sliding mode controller based on fractional calculus, which solves the problem of insensitivity of traditional sliding mode control and terminal sliding mode control to disturbance.

本发明的另一个目的是提供使用上述控制器进行系统控制的方法。Another object of the present invention is to provide a system control method using the above controller.

本发明所采用的技术方案是，一种基于分数阶微积分的终端滑模控制器，其函数形式为；The technical scheme adopted in the present invention is, a kind of terminal sliding mode controller based on fractional calculus, its function form is;

$s the s = = {αx αx}_{11}^{β β} + + {t t}_{00} {D D.}_{t t}^{μ μ - - 11} {x x}_{22} - - - - - - ((44))$

其中μ∈(0，1]，α为大于0的正常数，β＝q/p，其中p和q都是满足0＜q/p＜1的正奇数。Where μ∈(0,1], α is a normal number greater than 0, β=q/p, where p and q are both positive odd numbers satisfying 0<q/p<1.

上述控制器的特点还在于：The above controller is also characterized by:

上述函数中，α＝100，β＝0.6，0.7≤μ≤0.9。In the above functions, α=100, β=0.6, 0.7≤μ≤0.9.

上述公式(4)由以下方法得到：The above formula (4) is obtained by the following method:

步骤1：选用R-L定义分数阶微积分，其α阶的分数阶微分算子定义为：Step 1: Choose R-L to define fractional calculus, and its α-order fractional differential operator is defined as:

${D D.}_{t t}^{- - α α}_{00} f f ((t t)) = = \frac{11}{Γ Γ ((α α))} {&Integral; &Integral;}_{00}^{t t} {((t t - - τ τ))}^{α α - - 11} f f ((τ τ)) d d τ τ - - - - - - ((11))$

其中，欧拉提出的gamma函数定义为：Among them, the gamma function proposed by Euler is defined as:

$Γ Γ ((z z)) = = {&Integral; &Integral;}_{00}^{∞ ∞} {e e}^{- - t t} {t t}^{z z - - 11} d d t t - - - - - - ((22))$

步骤2：分数阶微积分形如并且函数可积，得到Step 2: Fractional calculus is of the form And the function is integrable, we get

${D D.}_{t t}^{- - α α}_{α α} (({D D.}_{t t}^{α α}_{α α} f f ((t t)))) = = f f ((t t)) - - {Σ Σ}_{j j = = 11}^{k k} {[[{D D.}_{t t}^{α α - - j j}_{α α} f f ((t t))]]}_{t t = = a a} \frac{{((t t - - a a))}^{α α - - j j}}{Γ Γ ((μ μ - - j j + + 11))} - - - - - - ((33))$

步骤3：将步骤2的分数阶微积分形式与整数阶终端滑模控制相结合，得到分数阶终端滑模控制函数：Step 3: Combine the fractional-order calculus form of step 2 with the integer-order terminal sliding mode control to obtain the fractional-order terminal sliding mode control function:

该控制器在电力系统、机械系统以及混沌系统中都适用，例如用于buck电路、boost电路、buck-boost电路、逆变电路和整流电路。The controller is applicable in power system, mechanical system and chaotic system, such as buck circuit, boost circuit, buck-boost circuit, inverter circuit and rectification circuit.

本发明的另一个技术方案是，基于分数阶微积分的终端滑模控制方法，采用上述终端滑模控制器，包括以下步骤：Another technical solution of the present invention is that the terminal sliding mode control method based on fractional calculus adopts the above-mentioned terminal sliding mode controller, comprising the following steps:

步骤1，针对分数阶终端滑模控制的被控对象，获取其状态方程；Step 1. Obtain the state equation of the controlled object under fractional-order terminal sliding mode control;

步骤2，将被控对象的状态方程带入所述分数阶终端滑模控制函数，得到该被控对象的终端滑模控制函数，利用该函数对系统进行控制。Step 2: Bring the state equation of the controlled object into the fractional-order terminal sliding mode control function to obtain the terminal sliding mode control function of the controlled object, and use this function to control the system.

本发明的有益效果是，本发明所提出的基于分数阶微积分的终端滑模控制器与传统滑膜控制和终端滑模控制相比，通过该控制器进行控制的方法简单，响应时间短，鲁棒性强，并且具有更小的稳态误差。The beneficial effect of the present invention is that, compared with the traditional sliding film control and terminal sliding mode control, the terminal sliding mode controller based on fractional calculus proposed by the present invention has a simple control method and short response time. It is robust and has smaller steady-state errors.

附图说明Description of drawings

图1是本发明分数阶终端滑模控制结构图；Fig. 1 is the structural diagram of fractional order terminal sliding mode control of the present invention;

图2是本发明实施例BUCK电路图；Fig. 2 is the BUCK circuit diagram of the embodiment of the present invention;

图3是本发明实施例在改变μ时的输出电压响应；Fig. 3 is the output voltage response when changing μ of the embodiment of the present invention;

图4是本发明实施例R由8Ω减小到2Ω时的输出电压响应；Fig. 4 is the output voltage response when R is reduced from 8Ω to 2Ω in the embodiment of the present invention;

图5为本发明实施例R由2Ω增大到8Ω时输出电压响应；Fig. 5 is the output voltage response when R increases from 2Ω to 8Ω in the embodiment of the present invention;

图6为本发明实施例当输入电压变化阶跃变化时的输出电压响应。FIG. 6 is the output voltage response when the input voltage changes step by step according to the embodiment of the present invention.

具体实施方式detailed description

下面结合附图和具体实施方式对本发明作进一步的详细说明，但本发明并不限于这些实施方式。The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments, but the present invention is not limited to these embodiments.

本发明的基于分数阶微积分的终端滑模控制器的思想为：将分数阶微积分引入整数阶终端滑模控制。该方法具有收敛速度快、精确度高等特点。The idea of the terminal sliding mode controller based on fractional calculus of the present invention is to introduce fractional calculus into integer-order terminal sliding mode control. This method has the characteristics of fast convergence speed and high accuracy.

该控制器如图1所示，其设计方法为：The controller is shown in Figure 1, and its design method is as follows:

步骤1：选用Riemman-Liouville(R-L)定义分数阶微积分，其α阶的分数阶微分算子定义为：Step 1: Choose Riemman-Liouville (R-L) to define fractional calculus, and its α-order fractional differential operator is defined as:

步骤2：当分数阶微积分形如并且函数可积，可有如下形式：Step 2: When fractional calculus is of the form And the function is integrable, which can have the following form:

步骤3：将上述分数阶微积分形式与整数阶终端滑模控制相结合，得到分数阶终端滑模控制器函数形为：Step 3: Combining the above fractional order calculus form with the integer order terminal sliding mode control, the function shape of the fractional order terminal sliding mode controller is obtained as:

在案例中，实际对比发现优选方案，其参数为α＝100，β＝0.6，0.7≤μ≤0.9。In the case, the actual comparison finds the optimal solution, and its parameters are α=100, β=0.6, 0.7≤μ≤0.9.

使用上述基于分数阶微积分的终端滑模控制器进行电路系统控制的方法，具体按照以下步骤实施：The method of using the above-mentioned terminal sliding mode controller based on fractional calculus to control the circuit system is specifically implemented according to the following steps:

步骤1，针对分数阶终端滑模控制的被控对象，得出其输出误差以及误差变化的关系，进而得出状态方程。Step 1. For the controlled object under fractional-order terminal sliding mode control, the relationship between its output error and error change is obtained, and then the state equation is obtained.

步骤2：将被控对象状态方程带入上述分数阶终端滑模控制器函数中，得到被控对象的具体控制函数，利用该控制函数对系统进行控制。Step 2: Bring the state equation of the controlled object into the above fractional order terminal sliding mode controller function to obtain the specific control function of the controlled object, and use the control function to control the system.

下面以如图1所示的BUCK电路为例，对本发明的方法进行进一步地详细说明。Taking the BUCK circuit shown in FIG. 1 as an example below, the method of the present invention will be further described in detail.

根据以下方法获取BUCK电路的状态方程，具体步骤如下：Obtain the state equation of the BUCK circuit according to the following method, the specific steps are as follows:

(1)，当开关S闭合时有：(1), when the switch S is closed:

$[\begin{matrix} \frac{{di di}_{L L} ((t t))}{d d t t} \\ \frac{{dv dv}_{00} ((t t))}{d d t t} \end{matrix}] = = [\begin{matrix} 00 & - - \frac{11}{L L} \\ \frac{11}{C C} & - - \frac{11}{C C R R} \end{matrix}] [\begin{matrix} {i i}_{L L} ((t t)) \\ {v v}_{00} ((t t)) \end{matrix}] + + [\begin{matrix} \frac{11}{L L} \\ 00 \end{matrix}] {v v}_{i i n no} ((t t)) - - - - - - ((55))$

当开关S断开时有：When switch S is off:

$[\begin{matrix} \frac{{di di}_{L L} ((t t))}{d d t t} \\ \frac{{dv dv}_{00} ((t t))}{d d t t} \end{matrix}] = = [\begin{matrix} 00 & - - \frac{11}{L L} \\ \frac{11}{C C} & - - \frac{11}{C C R R} \end{matrix}] [\begin{matrix} {i i}_{L L} ((t t)) \\ {v v}_{00} ((t t)) \end{matrix}] + + [\begin{matrix} 00 \\ 00 \end{matrix}] {v v}_{i i n no} ((t t)) - - - - - - ((66))$

(2)，将(5)与(6)结合有：(2), combining (5) and (6) has:

$[\begin{matrix} \frac{{di di}_{L L} ((t t))}{d d t t} \\ \frac{{dv dv}_{00} ((t t))}{d d t t} \end{matrix}] = = [\begin{matrix} 00 & - - \frac{11}{L L} \\ \frac{11}{C C} & - - \frac{11}{C C R R} \end{matrix}] [\begin{matrix} {i i}_{L L} ((t t)) \\ {v v}_{00} ((t t)) \end{matrix}] + + [\begin{matrix} \frac{11}{L L} \\ 00 \end{matrix}] {uv uv}_{i i n no} ((t t)) - - - - - - ((77))$

其中u为输入控制，当开关闭合时u为1，当开关断开时u为0。Among them, u is the input control, u is 1 when the switch is closed, and u is 0 when the switch is open.

(3)，定义输出电压误差为x₁，即为：(3), define the output voltage error as x ₁ , that is:

x₁＝v₀-V_ref (8)x ₁ =v ₀ -V _ref (8)

其中V_ref是输出电压的参考值，对公式(8)对时间求微分，可以得到x₂，输出电压误差的变化率：Among them, V _ref is the reference value of the output voltage. Differentiate the formula (8) with respect to time to get x ₂ , the rate of change of the output voltage error:

${x x}_{22} = = {\overset{\cdot &Center Dot;}{x x}}_{11} = = {\overset{\cdot &Center Dot;}{v v}}_{00} - - - - - - ((99))$

(4)，此时x₂的动态特性可以表示为：(4), at this time the dynamic characteristics of x ₂ can be expressed as:

${\overset{\cdot &Center Dot;}{x x}}_{22} = = \frac{11}{L L C C} (({uV uV}_{i i n no} - - {V V}_{r r e e f f} - - {x x}_{11})) - - \frac{{x x}_{22}}{R R C C} - - - - - - ((1010))$

(5)，最终，BUCK电路的输出电压误差及其变化率的状态方程模型为：(5), finally, the state equation model of the output voltage error and its rate of change of the BUCK circuit is:

$[\begin{matrix} {\overset{\cdot &Center Dot;}{x x}}_{11} \\ {\overset{\cdot &Center Dot;}{x x}}_{22} \end{matrix}] = = [\begin{matrix} 00 & 11 \\ - - \frac{11}{L L C C} & - - \frac{11}{R R C C} \end{matrix}] [\begin{matrix} {x x}_{11} \\ {x x}_{22} \end{matrix}] + + [\begin{matrix} 00 \\ {uV uV}_{i i n no} - - {V V}_{r r e e f f} \end{matrix}] \frac{11}{L L C C} - - - - - - ((1111))$

将以上状态方程带入分数阶终端滑模控制函数式(4)中，得到其具体控制函数：Bring the above state equation into the fractional-order terminal sliding mode control function formula (4) to obtain its specific control function:

$u u = = [[\frac{{x x}_{22}}{R R C C} - - {D D.}^{11 - - μ μ} (({αβx αβx}_{11}^{β β - - 11} {x x}_{22}))]] \frac{L L C C}{{V V}_{i i n no}} + + \frac{(({V V}_{r r e e f f} + + {x x}_{11}))}{{V V}_{i i n no}} - - K K s the s i i g g n no ((s the s)) - - K K s the s - - - - - - ((1212))$

其中0＜β＜1，k＞0，0＜μ＜1，最终状态变量x₁，x₂在有限时间内收敛到零。Where 0<β<1, k>0, 0<μ<1, the final state variables x ₁ and x ₂ converge to zero within a finite time.

为了验证本发明方法的有效性，对该控制方法和传统控制方法分别进行仿真实验，BUCK电路参数如表1所示。In order to verify the effectiveness of the method of the present invention, the control method and the traditional control method are simulated respectively, and the parameters of the BUCK circuit are shown in Table 1.

表1 buck电路参数Table 1 buck circuit parameters

描述describe 参数parameter 值value 输入电压Input voltage V_in V _in 10V10V 电容capacitance CC 1000μF1000μF 电感inductance LL 1mH1mH 最小负载阻抗Minimum Load Impedance R_min _Rmin 2Ω2Ω 最大负载阻抗Maximum Load Impedance R_max _Rmax 8Ω8Ω 期望输出电压Expected output voltage V₀ V ₀ 5V5V

针对不同阶数的终端滑模控制进行分析，阶数如表2所示：The terminal sliding mode control with different orders is analyzed, and the orders are shown in Table 2:

项目project αalpha βbeta μmu 滑模控制sliding mode control 100100 -- -- 终端滑模控制terminal sliding mode control 100100 0.60.6 -- 分数阶终端滑模控制1Fractional-order terminal sliding mode control 1 100100 0.60.6 0.90.9 分数阶终端滑模控制2Fractional-order terminal sliding mode control 2 100100 0.60.6 0.80.8 分数阶终端滑模控制3Fractional-order terminal sliding mode control 3 100100 0.60.6 0.70.7

按照表2中的控制器进行仿真实验，其结果如图3所示，可以发现当减小阶数时输出响应迅速加快，但随着阶次的降低，会出现超调量。因此，实际选择时要将二者折中处理。According to the controller in Table 2, the simulation experiment is carried out, and the results are shown in Figure 3. It can be found that when the order is reduced, the output response is rapidly accelerated, but as the order decreases, overshoot will appear. Therefore, the actual choice should be a compromise between the two.

由图4可以看出，本发明所提出的方法，分数阶滑模控制的响应时间远短于其他两种，0.15秒时，将负载R减小(8Ω减小到2Ω)，此时发现本发明所提出方法的输出电压响应在负载突然减小时，对于扰动的抗干扰性也强于其他两种控制。由图5可看出，将负载电阻从2Ω增加到8Ω，本发明提出的分数阶终端滑模控制仍然优于其他两种控制。由图6可知，当输入电压发生阶跃变化时，本发明所提出的方法较其他两种未改进之方法具有更小的稳态误差。As can be seen from Fig. 4, the method proposed by the present invention, the response time of the fractional-order sliding mode control is much shorter than the other two, when the load R is reduced (8Ω to 2Ω) in 0.15 seconds, it is found that this The output voltage response of the method proposed by the invention is also stronger than the other two controls in terms of disturbance immunity when the load suddenly decreases. It can be seen from Fig. 5 that the fractional-order terminal sliding mode control proposed by the present invention is still better than the other two controls when the load resistance is increased from 2Ω to 8Ω. It can be seen from FIG. 6 that when the input voltage changes stepwise, the method proposed by the present invention has a smaller steady-state error than the other two unimproved methods.

除了BUCK电路，本发明的基于分数阶微积分的终端滑模控制器还可以用于其他系统，如boost电路、buck-boost电路、逆变电路、整流电路等。例如，针对boost电路，将其状态方程可以写为：In addition to the BUCK circuit, the terminal sliding mode controller based on fractional calculus of the present invention can also be used in other systems, such as boost circuit, buck-boost circuit, inverter circuit, rectifier circuit and so on. For example, for a boost circuit, its state equation can be written as:

$[\begin{matrix} \frac{{di di}_{d d}}{d d t t} \\ \frac{{du du}_{00}}{d d t t} \end{matrix}] = = [\begin{matrix} 00 & - - \frac{11 - - d d}{L L} \\ \frac{11 - - d d}{{C C}_{00}} & - - \frac{11}{{RC RC}_{00}} \end{matrix}] [\begin{matrix} {i i}_{d d} \\ {u u}_{00} \end{matrix}] + + [\begin{matrix} \frac{11}{L L} \\ 00 \end{matrix}] {u u}_{d d} - - - - - - ((1313))$

带入公式(4)，利用得到的函数对系统进行控制；再例如，针对buck-boost电路，将其状态方程可以写为：Put it into formula (4), and use the obtained function to control the system; for another example, for the buck-boost circuit, its state equation can be written as:

$\frac{d d}{d d t t} [\begin{matrix} i i \\ v v \end{matrix}] = = [\begin{matrix} 00 & - - \frac{11}{L L} \\ \frac{11}{C C} & - - \frac{11}{R R C C} \end{matrix}] [\begin{matrix} i i \\ v v \end{matrix}] + + [\begin{matrix} \frac{11}{L L} ((v v + + {V V}_{s the s})) \\ - - \frac{i i}{C C} \end{matrix}] u u - - - - - - ((1414))$

带入公式(4)，利用得到的函数对系统进行控制；逆变电路、整流电路等方法顺序与前述方法一致，此处不再赘述。Put it into formula (4), and use the obtained function to control the system; the sequence of methods such as inverter circuit and rectifier circuit is the same as the above method, and will not be repeated here.

本发明方法具有极高的精确度以及收敛速度，对于负载的扰动具有更快的响应。该方法在电力系统、机械系统以及混沌系统中都适用。The method of the invention has extremely high accuracy and convergence speed, and has faster response to load disturbance. This method is applicable to electrical systems, mechanical systems and chaotic systems.

本发明以上描述只是部分实施例，但是本发明并不局限于上述的具体实施方式。上述的具体实施方式是示意性的，并不是限制性的。凡是采用本发明的材料和方法，在不脱离本发明宗旨和权利要求所保护的范围情况下，所有具体拓展均属本发明的保护范围之内。The above descriptions of the present invention are only some embodiments, but the present invention is not limited to the above specific implementation manners. The specific implementation manners described above are illustrative, not restrictive. Where materials and methods of the present invention are adopted, all specific expansions shall fall within the protection scope of the present invention without departing from the purpose of the present invention and the protection scope of the claims.

Claims

1. A terminal sliding mode controller based on fractional calculus, characterized in that, its functional form is;

s the s = = {αx αx}_{11}^{β β} + + {t t}_{00} {D D.}_{t t}^{μ μ - - 11} {x x}_{22} - - - - - - ((44))

Where μ∈(0,1], α is a normal number greater than 0, β=q/p, where p and q are both positive odd numbers satisfying 0<q/p<1.

2. The terminal sliding mode controller based on fractional calculus according to claim 1, characterized in that, in the function, α=100, β=0.6, 0.7≤μ≤0.9.

3. the terminal sliding mode controller based on fractional calculus according to claim 1, is characterized in that, described formula (4) obtains by following method:

Step 1: Choose R-L to define fractional calculus, and its α-order fractional differential operator is defined as:

{D D.}_{t t}^{- - α α}_{00} f f ((t t)) = = \frac{11}{Γ Γ ((α α))} {&Integral; &Integral;}_{00}^{t t} {((t t - - τ τ))}^{α α - - 11} f f ((τ τ)) d d τ τ - - - - - - ((11))

Among them, the gamma function proposed by Euler is defined as:

Γ Γ ((z z)) = = {&Integral; &Integral;}_{00}^{} {e e}^{- - t t} {t t}^{z z - - 11} d d t t - - - - - - ((22))

Step 2: Fractional calculus is of the form And the function is integrable, we get

{D D.}_{t t}^{- - α α}_{a a} (({D D.}_{t t}^{α α}_{a a} f f ((t t)))) = = f f ((t t)) - - {Σ Σ}_{j j = = 11}^{k k} {[[{D D.}_{t t}^{α α - - j j}_{a a} f f ((t t))]]}_{t t = = a a} \frac{{((t t - - a a))}^{α α - - j j}}{Γ Γ ((μ μ - - j j + + 11))} - - - - - - ((33))

Step 3: Combine the fractional-order calculus form of step 2 with the integer-order terminal sliding mode control to obtain the fractional-order terminal sliding mode control function:

s the s = = {αx αx}_{11}^{β β} + + {t t}_{00} {D D.}_{t t}^{μ μ - - 11} {x x}_{22} - - - - - - ((44))

4. The terminal sliding mode controller based on fractional calculus according to claim 1, wherein said controller is used for buck circuit, boost circuit, buck-boost circuit, inverter circuit and rectifier circuit.

5. a terminal sliding mode control method based on fractional calculus, is characterized in that, adopts the terminal sliding mode controller based on fractional calculus as claimed in claim 1, comprises the following steps:

Step 1. Obtain the state equation of the controlled object under fractional-order terminal sliding mode control;

Step 2: Bring the state equation of the controlled object into the fractional-order terminal sliding mode control function to obtain the terminal sliding mode control function of the controlled object, and use this function to control the system.

6. The terminal sliding mode control method based on fractional calculus according to claim 5, wherein the controlled object in step 2 is a buck circuit, a boost circuit, a buck-boost circuit, an inverter circuit and a rectifier circuit .