CN103117657A - Control method of full-bridge DC-DC system based on on-chip model predictive control - Google Patents

Abstract

The invention discloses a control method of a full-bridge DC-DC system based on on-chip model predictive control. The control method includes following steps: (1) dividing an object state of the non-linear full-bridge DC-DC system into different polyhedral areas, and obtaining a best control law according to the control laws in each polyhedral area; (2) storing edge constraint conditions of each polyhedral area and the best control law in step (1) into a control chip of the on-chip model predictive control; (3) inquiring the corresponding area in the control chip according to the actual object state of the non-linear full-bridge DC-DC system, and then controlling a feedback control input of the full-bridge DC-DC system according to the best control law in the polyhedral areas. By the control method, rapid control of the full-bridge DC-DC system is realized and robustness is strong.

Description

Control method based on the full-bridge DC-DC system of Model Predictive Control on sheet

Technical field

The present invention relates to power supply control technology field, be specifically related to a kind of control method of the full-bridge DC-DC system based on Model Predictive Control on sheet.

Background technology

full-bridge DC-DC system has extensive use in power supply control technology field, application publication number be CN102170234A disclosure of the invention a kind of DC/DC converter digital networked control systems, comprise circuit for power conversion, described circuit for power conversion comprises the input that connects successively, the full-bridge circuit that is formed by four field effect transistor, output, be provided with sample circuit on described input and output, key is also to comprise a control unit, the analog-to-digital conversion module that described control unit comprises a control module and is connected with control module, pulse width modulation module, the CAN gateway module, the output of described pulse width modulation module is connected with the control end of described field effect transistor, described control module receives the information of input, output by analog-to-digital conversion module and sample circuit, and controls the output of pulse width modulation module according to this information.

can direct predictive control process the Multivariable Constrained system owing to utilizing full-bridge DC-DC system model, therefore, become one of most widely used optimal control policy, but, traditional full-bridge DC-DC system model PREDICTIVE CONTROL need to be optimized calculating online, Obj State according to the reality of full-bridge DC-DC system calculates corresponding control law, and then find out optimum control parameter, because the amount of calculation in line computation is larger, must cause operating rate slow, cause the hysteresis quality of control, therefore, only applicable for controlling the slow procedure object, such as processes such as petrochemical industries.

Because the sampling period of the converter of full-bridge DC-DC system is very short, and full-bridge DC-DC system self mixes character and multi-constraint condition, and making for full-bridge DC-DC system model in prior art becomes difficult point based on the online Predictive control design that calculates of repeatedly optimizing.

Programmable DSP chip can be used the good signal processing algorithm of performance in real time signal processing easily, simultaneously, based on MATLAB powerful numerical computations and analysis ability, become one of software of algorithm research personnel extensive use, therefore, utilize MATLAB and DSP can facilitate the storage of implementation algorithm and call, become one of candidate's approach that improves full-bridge DC-DC system control efficiency.

Summary of the invention

The invention discloses a kind of control method of the full-bridge DC-DC system based on Model Predictive Control on sheet, by setting up the piecewise affine model of full-bridge DC-DC system, utilize piecewise affine model off-line to find the solution the optimal control law in different Obj States zone, then select corresponding optimal control law according to the Obj State of actual full-bridge DC-DC system, thereby realize the quick control of full-bridge DC-DC system.

A kind of control method of the full-bridge DC-DC system based on Model Predictive Control on sheet comprises the steps:

(1) Obj State with nonlinear full-bridge DC-DC system is divided into different polyhedra regions, and according to the control law of each polyhedra region, obtains the optimal control law in each polyhedra region;

(2) edge-restraint condition and the optimal control law with each polyhedra region in step (1) stores in the control chip of Model Predictive Control on sheet;

(3) inquire about polyhedra region under it according to the Obj State of actual full-bridge DC-DC system in control chip, and according to the optimal control law in this polyhedra region, control the FEEDBACK CONTROL of full-bridge DC-DC system and input.

The inventive method will be controlled the optimizing process of parameter and be separated with control in real time, namely precompute optimal control law corresponding to all Obj States, and the corresponding relation of Obj State and optimal control law is stored in the control chip of model on sheet, then, Obj State according to the full-bridge DC-DC system of actual acquisition is selected corresponding optimal control law, realizes the quick control to full-bridge DC-DC system.

On sheet, model comprises full-bridge DC-DC system, control chip, power tube drive circuit and detection filter circuit, and full-bridge DC-DC system comprises power supply, full-bridge DC-DC circuit and load, and described load can be to use arbitrarily electric device, for example electric light.

Control chip can adopt dsp chip, utilizes MATLAB that array is compiled as the C language file and is stored in dsp chip.

Full-bridge DC-DC circuit can be unidirectional full-bridge DC-DC circuit, can be also two-way full-bridge DC-DC circuit, can adopt method provided by the invention to control.

Utilize the Obj State number of full-bridge DC-DC system and the dimension that auxiliary controlled quentity controlled variable is determined described polyhedra region.

The Obj State of full-bridge DC-DC system can be setting voltage, set electric current, the bound of voltage and the hard constraint conditions such as bound of electric current, and the number of Obj State can change according to needs.

Auxiliary controlled quentity controlled variable comprises the bound of adjustable setting voltage, adjustable setting electric current, adjustable voltage and bound of adjustable electric current etc., can select according to needs.

As preferably, the control law of the border of each polyhedra region and each polyhedron inside all satisfies Linear Constraints.Linear Constraints is satisfied on the border of each polyhedra region, the control law of each polyhedra region inside also satisfies Linear Constraints, be convenient to the division of polyhedra region and the calculating of optimal control law, the optimal control law of the edge-restraint condition of each polyhedra region and each polyhedron inside form with array is stored in the control chip of model on sheet.

As preferably, at first utilize the mode of modelling by mechanism to set up the piecewise affine model of full-bridge DC-DC system in described step (1), then according to the piecewise affine model, the Obj State of full-bridge DC-DC is divided into different polyhedra regions.

As preferably, by MATLAB, the edge-restraint condition of each polyhedra region and optimal control law are compiled into the C language in described step (2) and are stored in the DSP file directory.Based on MATLAB powerful data operation and analysis ability, can carry out fast the analytical calculation of model, be used for fast exploitation and the debugging of model on sheet, simultaneously, utilize MATLAB can carry out easily the selection of kind and the quantity of Obj State, the array of storing in DSP is in time upgraded, facilitated control chip to carry out the inquiry of optimal control law according to the Obj State of Real-time Collection, and then control the FEEDBACK CONTROL input of full-bridge DC-DC system.

the present invention is a kind of control method of the full-bridge DC-DC system based on Model Predictive Control on sheet, Optimization about control parameter in control procedure is calculated with controlling in real time separate, the piecewise affine model of the full-bridge DC-DC system that utilize to set up, find the solution optimal control law by off-line, full-bridge DC-DC status object state is divided into different polyhedra regions, each polyhedra region is relevant to the control law of Obj State, then select corresponding optimal control law according to the full-bridge DC-DC Obj State of reality online, complete the quick control to full-bridge DC-DC system, and by the serial communication between control chip and computer, realize the real time communication of computer and control chip, purpose to the computer Real Time Monitoring.

Description of drawings

Fig. 1 is the flow chart of control method of the present invention;

Fig. 2 is the system schematic of Model Predictive Control on sheet in the present invention;

Fig. 3 is real-time control procedure flow chart in the inventive method;

Fig. 4 is the voltage control figure as a result in embodiment;

Fig. 5 is the voltage control figure as a result when in embodiment, fluctuation appears in load.

Embodiment

Below in conjunction with accompanying drawing, the control method of the full-bridge DC-DC system that the present invention is based on Model Predictive Control on sheet is described in detail.

As shown in Figure 1, a kind of control method of the full-bridge DC-DC system based on Model Predictive Control on sheet comprises the steps:

(1) utilize the mode of modelling by mechanism to set up the piecewise affine model of full-bridge DC-DC system, then according to the piecewise affine model, the Obj State of full-bridge DC-DC is divided into different polyhedra regions, and calculates the optimal control law in each polyhedra region;

The power tube switch periods of non-linear full-bridge DC-DC system is carried out piecewise affine, each power tube switch periods T is divided into σ section (being σ subcycle), in each section, controlled device (full-bridge DC-DC system) is approximately linear object, sets up the piecewise affine model;

x(k+1)=A _σx(k)+B _σu(k)+f _σ

y(k)=C _σx(k)+D _σu(k)+g _σ

subj.to

y _min≤y(k)≤y _max

u _min≤u(k)≤u _max

Wherein, k is the moment of full-bridge DC-DC system operation;

U is control inputs, and u ∈ [0,1];

X is Obj State;

Y is the output of controlled device;

A _σ, B _σ, C _σ, D _σBe the coefficient of controlled device discrete state spatial model, f _σ, g _σBe the input and output coefficient of disturbance, the sampling period is T/ σ.

The piecewise affine model can be divided into based on the cyclic variation di/dt of the output current of nonlinear full-bridge DC-DC system that output current increases and output current reduces two states, these two states according to output current carry out with continuous model the discretization that the sampling period is T/ σ, obtain the spatial model of two states, see following formula:

$x(k+1)=\left\{\begin{array}{cc}\mathrm{Fx}\left(k\right)+\mathrm{gu}\left(k\right)& \mathrm{when}(\mathrm{di}/\mathrm{dt})>0\\ \mathrm{Gx}\left(k\right)+\mathrm{gu}\left(k\right)& \mathrm{when}(\mathrm{di}/\mathrm{dt})<0\end{array}\right.$

Wherein, k is the moment of full-bridge DC-DC system operation;

X is Obj State;

F, G, g are the coefficient of the discrete state spatial model of controlled device (full-bridge DC-DC system), and the sampling period is T/ σ.

The sampling period of output current is the power tube switch periods

In the sampling period of arbitrary output current, spatial model satisfies the following formula equation all the time, but when output current by from di/dt 0 when jumping to di/dt＜0, need the value of averaging modeling, suppose that saltus step is in μ subcycle of power tube switch periods, can obtain spatial model to be

$x(k+1)=\left\{\begin{array}{cc}\mathrm{Fx}\left(k\right)+\mathrm{gu}\left(k\right)& \mathrm{when}(\mathrm{di}/\mathrm{dt})>0\\ \mathrm{Gx}\left(k\right)+\mathrm{gu}\left(k\right)& \mathrm{when}(\mathrm{di}/\mathrm{dt})<0\\ [(\mathrm{\&sigma;u}-u+1)F+(\mathrm{\&mu;}-\mathrm{\&sigma;u})G]x\left(k\right)+\mathrm{gu}\left(k\right)& \mathrm{when}(\mathrm{di}/\mathrm{dt})\mathrm{switches}\end{array}\right.$

Wherein, k is the moment of full-bridge DC-DC system operation;

X is Obj State;

F, G, g are the coefficient of discrete state spatial model, and the sampling period is T/ σ;

U is control inputs, and u ∈ [0,1];

F is equivalent to the A in the piecewise affine model _σ

G is equivalent to the A in the piecewise affine model _σ

(σ u-μ+1) F+ (μ-σ u) G is equivalent to the A in the piecewise affine model _σ

G is equivalent to the B in the piecewise affine model _σ

This spatial model is more accurate than traditional model average period, because this modeling method approximate modeling in the subcycle of curent change saltus step only, and traditional model average period is that whole power tube switch periods is carried out modeling, error is larger.The control law of the Obj State of full-bridge DC-DC system is the optimal control of satisfying the finite time constraint, satisfies following formula:

$J_N(x_k,u_k)=\underset{u_0,...u_{N-1}}{\min }{\left|\right|Q_f{x}_N\left|\right|}_1+\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}({\left|\right|{\mathrm{Ru}}_k\left|\right|}_1+{\left|\right|{\mathrm{Qx}}_k\left|\right|}_1)$

$\mathrm{subj}.\mathrm{to}{x}_k\&Element;\mathrm{\&Phi;},\&ForAll;k\&Element;\{1,...,N\},$

$u_k\&Element;\mathrm{\&Psi;},\&ForAll;k\&Element;\{1,...,N-1\},$

x ₀=x(0).

Wherein, x _kThat the controlled device state is at k state constantly;

u _kIt is k control inputs constantly;

x ₀It is the initial condition of full-bridge DC-DC system;

Φ is x _kSpan, Ψ is u _kSpan.

Be the weights column vector, N is the prediction time domain;

M is the number of control inputs; N is the state number of controlled device;

Simultaneously,

A wherein, B is the coefficient of controlled device discrete state spatial model, the A of A general reference front _σ(be each A _σAll satisfy this formula), B makes a general reference the B of front _σ

All Obj States all can be expressed by the linear combination of initial condition x (0) and control inputs u.So, target function J _N(x (0)) but abbreviation become

$J_N\left(x\left(0\right)\right)=\mathrm{Hx}\left(0\right)+\underset{U_N}{\min }{\mathrm{VU}}_N$

s.t.GU _N≤W+Ex(0)

Wherein,

Wherein, u ^T ₀U ₀Transposition;

N is the prediction time domain;

A, B are the coefficient of controlled device discrete state spatial model;

M is the number of control inputs;

N is the state number of controlled device.

G, W, E are target function J _NConstraints coefficient in (x (0)), its span can be passed through controlled device x span, and the constraint of the scope of input u and output y is determined, specifically can decide according to design requirement.

Must be greater than waiting 0.5 such as initial condition x (0), i.e. x (0) 〉=0.5, and controlled state number n=1 must satisfy u (k) 〉=0 because of control inputs again, control inputs number m=1, prediction time domain N=2 can obtain so

$\left[\begin{array}{cc}0& 0\\ -1& 0\\ 0& -1\end{array}\right]U_N\&le;\left[\begin{array}{c}-0.5\\ 0\\ 0\end{array}\right]+\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]x\left(0\right)$

U wherein _N=U ₂=[u ₀, u ₁] ^T,

$G=\left[\begin{array}{cc}0& 0\\ -1& 0\\ 0& -1\end{array}\right],$ $W=\left[\begin{array}{c}-0.5\\ 0\\ 0\end{array}\right],$ $E=\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right].$

X (0) is Optimal Parameters, and optimizing decision vector U _N(be optimal control law U _N) depend on x (0).

The Obj State x (0) of full-bridge DC-DC system as parametric variable, when x (0) changes, is obtained optimizing decision vector U in a certain polyhedra region _NChanging Pattern, namely obtain U _NAnd the explicit functional relation between x (0), can avoid like this on-line optimization repeatedly of spatial model predictive control algorithm to calculate.

The space feasible zone of the Obj State of full-bridge DC-DC system is Wherein

And p is the constraints number, and n is the dimension of Obj State x, and i is the number of the polyhedra region that is divided into.

U _NThe piecewise linearity continuous function of x (0), that is: U _N=M _iX (0)+P _i, M wherein _iAnd P _iBe U _NAnd x (0) linear relationship matrix,

X (0) ∈ χ _iWherein

Space polyhedron for Obj State.

Utilize MATLAB to incite somebody to action

And U _N=M _iX (0)+P _iThe array that consists of utilizes the C language to compile, and is stored under the DSP file directory, during working control, finds out affiliated area χ according to the Obj State x of the full-bridge DC-DC of reality _i, can obtain corresponding optimal control law U _N

(2) edge-restraint condition and the optimal control law with polyhedra region stores in the control chip of model on sheet.

Utilize serial communication that the service data of full-bridge DC-DC system is uploaded in MATLAB, can show in real time the ruuning situation of full-bridge DC-DC system by visual interfaces such as GUI.

As shown in Figure 2, of the present invention upper model comprises control chip (comprising DSP and MATLAB), full-bridge DC-DC system (comprising power supply, DC-DC, load), detection filter circuit, and power tube drive circuit.

The Obj State of full-bridge DC-DC system is divided into output voltage, filter inductance electric current, last control input and voltage setting value.

The Mathematical Modeling of controlled device state is poured in MATLAB, division and the control law in respective regions that off-line carries out full-bridge DC-DC Obj State zone calculate, and the rule of the optimum state in Obj State zone and respective regions is compiled into the C language file stores in DSP.

(3) on line real time control, dsp controller calls corresponding C language file, in controlling in real time, the actual motion states such as Obj State (such as current value and magnitude of voltage) that obtain according to detection, DSP seeks these Obj States and drops on which zone in the C language file by fast search algorithm, thereby obtain the optimal control law in respective regions.

For example, the virtual voltage x of full-bridge DC-DC system ₁∈ [0,0.5], actual current x ₂∈ [0,1], last control inputs x ₃∈ [0,1] and voltage setting value x ₄∈ [0.2,1] forms Obj State, thereby the upper and lower bound of setting each Obj State has formed the spatial model of various dimensions, wherein, and to x ₁, x ₂, x ₃Carry out respectively standardization, according to control inputs d ∈ [0,1], the switch periods of the power tube of control inputs is divided into three affine zones [0,1/3], (1/3 according to the input amplitude, 2/3] and (2/3,1], set up the piecewise affine model according to these three affine zones.

Affine model 1:

A ₁=[0.9579?-0.2169?0?0;0.3756?0.9391?0?0;0?0?0?0;0?0?0?1]?B ₁=[0.2158;0.06986;1;0]

f ₁=[0;0;0;0]?C ₁=[0.1895?0.9757?0?-1;0?0?-1?0]?D ₁=[0.03043;1]?g ₁=[0;0]

0≤u(1)≤0.33333?-3≤x(1)≤3?-1≤x(2)≤1?0≤x(3)≤1?0.2≤x(4)≤1

0.973477*x(1)-0.072084*x(2)+0.217132*u(1)≥-2.9342

0.973477*x(1)-0.072084*x(2)+0.217132*u(1)≤2.9342

0.965634*x(1)-0.143913*x(2)+0.216425*u(1)≥-2.9524

0.965634*x(1)-0.143913*x(2)+0.216425*u(1)≤2.9524

0.952591*x(1)-0.215715*x(2)+0.214562*u(1)≥-2.9832

0.952591*x(1)-0.215715*x(2)+0.214562*u(1)≤2.9832

Affine model 2:

A ₂=[0.9579?-0.2169?0?0;0.3756?0.9391?0?0;0?0?0?0;0?0?0?1]?B ₂=[0.2199;0.04227;1;0]

f ₂=[-0.001383;0.009197;0;0]?C ₂=[0.1895?0.9757?0?-1;0?0?-1?0]?D ₂=[0.01175;1]?g ₂=[0.00623;0]

0.33333≤u(1)≤0.66667?-3≤x(1)≤3?-1≤x(2)≤1?0≤x(3)≤1?0.2≤x(4)≤1

0.997270*x(1)-0.073846*x(2)<=2.9318

0.965204*x(1)-0.143849*x(2)+0.218377*u(1)≥-2.9504

0.965204*x(1)-0.143849*x(2)+0.218377*u(1)≤2.9517

0.951741*x(1)-0.215523*x(2)+0.218493*u(1)≥-2.9792

0.951741*x(1)-0.215523*x(2)+0.218493*u(1)≤2.9819

Affine model 3:

A ₁=[0.9579?-0.2169?0?0;0.3756?0.9391?0?0;0?0?0?0;0?0?0?1]?B ₁=[0.222;0.0141;1;0]

f ₁=[-0.002771;0.02798;0;0]C ₁=[0.1895?0.9757?0?-1;0?0?-1?0]?D ₁=[0.00235;1]?g ₁=[0.01249;0]

0.66667≤u(1)≤1?-3≤x(1)≤3?-1≤x(2)≤1?0≤x(3)≤1?0.2≤x(4)≤1

0.997270*x(1)-0.073846*x(2)≤2.9318

0.989076*x(1)-0.147407*x(2)≤2.8755

0.951309*x(1)-0.215425*x(2+0.220462*u(1)≤2.982

As shown in Figure 3, the step of controlling in real time in control method of the present invention comprises:

A, detection obtain actual Obj State

X wherein ₄Be voltage setting value, set according to the actual requirements.

B, Obj State is deducted set point X obtain Obj State error amount Δ x=x-X;

C, judge that whether the Obj State error amount is less than in permissible error scope τ.If so, u is inputted in retentive control _k+1Be previous moment input u _k, otherwise Obj State error amount Δ x=x-X is searched for calculating;

D, seek out the Obj State region according to the Obj State value, then according to control law U _N=M _iX (0)+P _iControlled input U _N, and with U _NCorresponding u _k(U _NBe a vector, with the u in this vector ₀As u _k) assignment is to u _k+1If Obj State is selected nearby from the nearest Obj State value of virtual condition not in area of feasible solutions;

E, by power tube drive circuit, control inputs is applied in full-bridge DC-DC system;

F, with the Obj State of full-bridge DC-DC system and the u of acquisition _k+1Form a new Obj State, return to step a;

The ruuning situation that finally can obtain object according to above-mentioned step sees Table 1.

Table 1

Input voltage	200V
		Setting voltage	50V
Weights Q f	[1?2?1?1]
		Weights R	1
Weights Q	[1?2?1?1]
		The number σ of subcycle	3
Sample frequency	10kHz

As shown in Figure 4, controlling the control Voltage-output that can obtain full-bridge DC-DC according to the inventive method is 50V, and namely reached setting voltage at 4ms, as shown in Figure 5, variation has occured in load when 0.05s, but full-bridge DC-DC system namely obtains proofreading and correct within the time of 0.02s and follows the tracks of, and illustrates that control method of the present invention has very strong robustness.

Claims (6)

1. the control method based on the full-bridge DC-DC system of Model Predictive Control on sheet, is characterized in that, comprises the steps:

(1) Obj State with nonlinear full-bridge DC-DC system is divided into different polyhedra regions, and according to the control law of each polyhedra region, obtains the optimal control law in each polyhedra region;

(2) edge-restraint condition and the optimal control law with each polyhedra region in step (1) stores in the control chip of Model Predictive Control on sheet;

(3) inquire about polyhedra region under it according to the Obj State of actual full-bridge DC-DC system in control chip, and according to the optimal control law in this polyhedra region, control the FEEDBACK CONTROL of full-bridge DC-DC system and input.

2. the control method of the full-bridge DC-DC system based on Model Predictive Control on sheet as claimed in claim 1, is characterized in that, the control law of the border of each polyhedra region and each polyhedron inside all satisfies Linear Constraints.

3. the control method of the full-bridge DC-DC system based on Model Predictive Control on sheet as claimed in claim 1, is characterized in that, described full-bridge DC-DC system comprises power supply, full-bridge DC-DC circuit and load.

4. the control method of the full-bridge DC-DC system based on Model Predictive Control on sheet as claimed in claim 1, is characterized in that, utilizes the Obj State number of full-bridge DC-DC system and the dimension that auxiliary controlled quentity controlled variable is determined described polyhedra region.

5. the control method of the full-bridge DC-DC system based on Model Predictive Control on sheet as claimed in claim 1, it is characterized in that, at first utilize the mode of modelling by mechanism to set up the piecewise affine model of full-bridge DC-DC system in described step (1), then according to the piecewise affine model, the Obj State of full-bridge DC-DC is divided into different polyhedra regions.

6. the control method of the full-bridge DC-DC system based on Model Predictive Control on sheet as claimed in claim 1, it is characterized in that, by MATLAB, the edge-restraint condition of each polyhedra region and optimal control law are compiled into the C language in described step (2) and are stored in the DSP file directory.

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