Selection of Basis Function The control input introduced in PFC is represented as a linear combination of several known basis functions Fj(j=1, 2,, n): u(k+i)=∑nj=1jfj(i) (i= 0,1,,P-1). (1) where: is a basis function, which is a linear combination coefficient, indicating the value of the basis function at the time, and P is the prediction step size.
Predictive model For single-input and single-output systems, the model predictor can be composed of two parts: the model free output and the model function output.
(1) Model free output: yM(k+i)=F(X(k))(i=1, 2,, P).
(2) where X(k) is known information and F is a mathematical expression of the object prediction model.
(2) Model function output: yf(i)=∑nj=1jhj(i) (i=1, 2,, P).
(3) where: hj(i) is the basis function response and j is the weighting coefficient.
If the set value is ys(k+i) and the parameter trajectory is yr(k+i), the error between the two is (k+i), then: (k+i)=ys(k+ik+i ) = ir(k). (4) where: the attenuation coefficient r = exp(-TsTr), Ts is the sampling period, and Tr is the transition time of the desired reference trajectory reaching 95%, then the reference trajectory in the form of the first order exponent is: yr(k+i )=ys(k+i)-ir(ys(k)-yp(k)). (5) Error prediction In the prediction function control, the error is predicted by a predictor in the future time domain, and is recorded as a feedforward amount into the reference trajectory, using polynomial error prediction: e(k+i) =e(k)+∑meq=1q(k)iq.
(6) where: me is the order of the error extrapolator, pq(q=1, 2,, me) can be obtained by a low-pass filter from the value before k, and the error predictor is used by the extrapolator And low pass filter.
The rolling optimization algorithm in the prediction function control, for the linear system, the compensated prediction output: yp(k+i)=yM(k+ik+i)(i=1, 2,, P).
(7) The optimization goal is to find a set of weighting coefficients j (j = 1, 2,, n) so that the predicted output is as close as possible to the reference trajectory in the optimized time domain.
The known value of the i step from the k-th time and the function output required at the i-th time are respectively expressed as vector forms: Y(k+i)={yr(k+i)-yM(k+i)-e(k+ i)=∑nj=1jhj(i), i=1, 2,, P}.
(9) System error curve Usually the optimization target is generally expected to be min (10) This is an optimization problem of the weighting coefficient j (j=1, 2,, n). After solving j, the control input u(k+i) generated by the basis function at time k can be obtained by (1) ( i=1, 2,, P-1). This is a rolling optimization process, and each time a new amount of control action is obtained. Expert control principle expert system and control theory are combined, especially heuristic reasoning and feedback control theory are combined to form an expert control system. The expert system has five main parts: the knowledge base, the database, the inference engine, the interpretation part, and the knowledge acquisition part. The control knowledge (rules, facts) controlled by experts is summarized and summarized from the operation process of control experts or specialized operators. Taking the system error curve shown as an example, the acquisition rule of the control rule is as follows: e(t)e(t)>0t∈(t0,t12) or (t3,t4)e(t)e(t=1)< 0 (11) where the extreme point is at t1, t3. According to the above analysis, when the system response is far away from the set value area, the switch mode can be used to control, so that the system quickly returns to the set value; when the error trend increases, the ratio is taken, M1, M2 are the error boundary, Kp, K3 is the proportional gain, and K1 and K2 are the gain coefficients. The application temperature of the expert predictive function control in the electric heating furnace is one of the main controlled parameters in the industrial object. Electric heating furnaces are widely used in industrial production. Maintaining uniform temperature stability in the furnace has a great impact on product quality, which puts high demands on temperature control. In industry, the dynamic characteristics of the furnace temperature are generally first-order inertia plus pure hysteresis. Here we use expert predictive function control. The basic idea is to start the expert control system when the deviation is large or the change speed of the deviation near the equilibrium point is fast, and use the characteristics of the expert control to respond quickly, improve the response speed at the start of the system and quickly suppress the strong interference; When the error is small or the change speed of the deviation is slow, the predictive function control is used to improve the robustness of the control system. The conversion between the two is automatically realized by the program's comprehensive judgment of the error rate and the error rate. Assume that the transfer function of the electric heating furnace control system is G(s)=180e-60s80s+1, and the actual transfer function is G(s)=200e-80ss2+30s+1, the sampling period is 5 seconds, and the input step response signal is input. Rin(k)=1.0. The system is controlled by PID control and expert prediction function respectively, and the output temperature waveform is shown. It can be seen that for the electric heating furnace temperature system, the expert predictive function control is adopted, the response speed is faster than the PID control, and the robustness is stronger than the latter. Conclusion Predictive function control is a simple and robust predictive control algorithm, while expert control has the characteristics of fast response. Combining the advantages of these two, this paper proposes a method of expert predictive function control. It can be seen from the simulation that the control effect of this control method is obviously superior to the conventional PID control and has strong tracking performance. (Finish)
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