| CPC B61L 15/0062 (2024.01) | 8 Claims |
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1. A data-driven integral sliding mode control method for a high-speed electric multiple unit (EMU), comprising:
performing kinetic analysis on an operation process of a high-speed EMU to enable an input and output data set of the EMU to be equivalent to a multi-input-multi-output (MIMO) discrete-time nonlinear system;
constructing an EMU full format dynamic linearization (FFDL) data model involving a generalized disturbance based on the MIMO discrete-time nonlinear system;
designing an equivalent control law and a switching control law based on the FFDL data model involving the generalized disturbance, which comprises:
estimating a disturbance term Δd(t) in the FFDL data model Δym(t+1)=Φ1(t)Δy(t)+Φ2(t)Δu(t)+Δd(t) involving the generalized disturbance through a value of its one-step delay based on a disturbance estimation technique:
Δd(t)=Δd(t−1)=Δym(t)−Φ1(t−1)Δy(t−1)−Φ2(t−1)Δu(t−1),
wherein d(t) is an estimated value of a bounded generalized disturbance d(t); Δd(t)=d(t)−d(t−1); Δy(t)=y(t)−y(t−1) is an output variation at a time t; Δu(t)=u(t)−u(t−1) is an input variation at the time t; Φ1(t) is a submatrix in a time-varying parameter vector Φ(t);
estimating the time-varying parameter vector Φ(t) in real time, and introducing a parameter estimation criterion function:
J(Φ(t))=∥Δym(t)−Δd(t)−Φ(t−1)ΔH(t−1)∥2+μ∥Φ(t)−Φ(t)∥2,
wherein μ>0 is a change rate for constraining adjacent parameters; J is an indicator function symbol; Φ(t)=[Φ1(t),Φ2(t)] is an estimated value of Φ(t)=[Φ1(t),Φ2(t)]; Φ(t)=[Φ1(t),Φ2(t)] is replaced with Φ(t)=[Φ1(t),Φ2(t)] below; H(t) is defined as a system matrix composed of control inputs and outputs within a certain time;
minimizing the parameter estimation criterion function to obtain a following parameter estimation algorithm:
 wherein β∈(0,2] is a step length factor; values of Φ1(t) and Φ2(t) in the FFDL data model involving the generalized disturbance is obtained using the parameter estimation algorithm;
defining a system output error as:
e(t)=ym(t)−yr(t),
wherein yr(t) is an expected output of the system at the time t;
introducing a new integral sliding mode function as follows:
s(t)=e(t)+l1E(t−1)+bl2F(t−1),
wherein 0<l1≤1, 0<l2<1; and s(t) is a sliding mode function; two integral output tracking error terms E(t) and F(t) are defined as follows:
 wherein a parameter α is a constant greater than 0;
sigαe(t)=[sgn(e1)|e1|α, . . . , sgn(en)|en|α]T, sgn being a symbol function; and e(t)=[e1, e2, . . . , en]T, n being a number of power units comprised in the EMU;
designing a sliding mode control strategy based on a following reaching law and the integral sliding mode function:
Δs(t+1)=s(t+1)−s(t)=0;
obtaining a following equation by combining e(t)=ym(t)−yr(t), s(t)=e(t)+l1E(t−1)+bl2F(t−1) and Δs(t+1)=s(t+1)−s(t)=0;
 substituting the EMU FFDL data model involving the generalized disturbance into
 to obtain:
s(t)=ym(t)+Φ1(t)Δy(t)+Φ2(t)Δu(t)+Δd(t)−yr(t+1)+l1E(t)+l2F(t);
deducing an expression of the equivalent control law from
s(t)=ym(t)+Φ1(t)Δy(t)+Φ2(t)Δu(t)+Δd(t)−yr(t+1)+l1E(t)+l2F(t);
Δueq(t)=Φ2−1(t)(s(t)−l1E(t)−l2F(t)−Δd(t)+yr(t+1)−ym(t)−Φ1(t)Δy(t));
designing the switching control law based on the parameter estimation algorithm and the integral sliding mode function:
Δusw(t)=−Φ2−1(t)βsgn(s(t));
establishing a MIMO EMU integral sliding mode control law according to the equivalent control law and the switching control law, which comprises:
establishing the MIMO EMU integral sliding mode control law Δu(t)=Δueq(t)+Δusw(t) according to the equivalent control law Δueq(t) and the switching control law Δusw(t); and
controlling an operation of the high-speed EMU according to the MIMO EMU integral sliding mode control law.
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