历史查询   



 没有找到相关例句 
 In this paper the general synthesis problem of optimal control systems with the criterion of transient responses as a positive integral functional (3) is discussed.In the first part it is assumed that the motion of controlled object is described by a system of ordinary differential equations and that the final states of the system form a bounded and closed convex region in ndimentional euclidian phase space. A method is proposed for finding all optimal control functions which lead any starting state into the... In this paper the general synthesis problem of optimal control systems with the criterion of transient responses as a positive integral functional (3) is discussed.In the first part it is assumed that the motion of controlled object is described by a system of ordinary differential equations and that the final states of the system form a bounded and closed convex region in ndimentional euclidian phase space. A method is proposed for finding all optimal control functions which lead any starting state into the given final region of states. Some conclusions are obtained from the maximum principle by using transversal conditions of optimal trajectories in terminal points, and the particular properties of the stated problem are pointed out. The case of linear differential equations with integral quadratic functional criterion is investigated in detail.Further, in the second part the fundamental properties of isoloss regions, the relations between the isoloss region and optimal control functions are indicated. As a direct result a partial differential equation determining the optimal lossfunction J (x) is found and the connection between function J (x)and optimal vector control function u (x) is also stated. The methods proposed are practically the extension of the methods used by us for designing time optimal control systems as seen in [5, 6 ,7].Finally, an example is illustrated with optimal trajectories shown in phase plane.The necessary numerical data is calculated by an analog computer with high accuracy.  文中研究了具有公式(3)表示的一般正积分泛函的最优控制系统的综合问题.在第一部分中研究了具有控制参数的一阶微分方程组.控制系统的终点状态为n维相空间内的某一逐段光滑边界的闭性区域Ω.文中指出了根据极大值原理和轨道终点的横截条件寻找引到Ω的所有最优轨迹的方法.这里详细地研究了具有二次泛函和被积函数中不明显含有控制参数的质量指标泛函的线性方程情况.在文中第二部分研究了等损耗区的主要特性.指出了等损耗区与最优控制函数之间的关系.导出了求算最优损耗函数J(x)的偏微分方程,以及这一函数与最优控制函数u(x)的关系.上述方法是我们曾在文献[5,6,7]中用过的最优快速系统的综合方法的推广.文章最后举有例证.  Formulas are derived for the solution of the transient currents of dissipative lowpass Ttype electric wave filters. Oscillograms taken by cathode ray oscillograph for dc. and ac. cases are found to agree with results calculated from these formulas. From these calculations, the following conclusions are derived. When terminating resistance is gradually increased from O, the damping constants of the sine terms begin to differ from each other, ranging in decreasing magnitude from term of the lowest frequency... Formulas are derived for the solution of the transient currents of dissipative lowpass Ttype electric wave filters. Oscillograms taken by cathode ray oscillograph for dc. and ac. cases are found to agree with results calculated from these formulas. From these calculations, the following conclusions are derived. When terminating resistance is gradually increased from O, the damping constants of the sine terms begin to differ from each other, ranging in decreasing magnitude from term of the lowest frequency to the last term of cutoff frequency. Hence the transient is ultimately of the cutoff frequency. At cutoff frequency, this constant is near to but greater than R/2L. For each increase of section, there is introduced an additional sine term with smaller damping constant. Therefore transients die out faster in filters of smaller number of sections. Since transient amplitudes are of the same order of magnitude before and after cutoff, filtering property only exists in the steady states.  此篇先推求收端加电阻时,低频滤波器瞬流之公式。依此公式算出之图与用阴极光示波器映出之曲线相符合。自推算之结果,可得下列结论: (一)在滤波器收端电阻渐加时,瞬流各项之挫率渐互异,其数量由低频项至隔阻频之项顺序渐减;其最小数仍比收端无电阻时之挫率(R/2L)为大。故瞬流终必变为隔阻频之电流;而较收端无电阻时易于消减。 (二)当滤波器增加一段时,瞬流之项数亦加一。所加项之挫率皆比前有者为小。故少段滤波器之瞬流易于消减。 (三)在隔阻频後瞬流之数量与在其前者相彷恒较隔阻频後之安定数量大数十倍,故滤波之特性仅能见之于安定状态。  Formulas are derived for the solution of the transient currents of resistanceterminated dissipative πtype lowpass, T and πtype highpass electric wave filters. Oseillograms taken by cathode ray oscillograph for dc. and ac. cases are found to agree with the results calculated from these formulas. From these calculations, the following conclusions are derived: (1) When the terminating resistance is gradually increased from 0, the damping constants of the damped sine terms begin to differ greatly from... Formulas are derived for the solution of the transient currents of resistanceterminated dissipative πtype lowpass, T and πtype highpass electric wave filters. Oseillograms taken by cathode ray oscillograph for dc. and ac. cases are found to agree with the results calculated from these formulas. From these calculations, the following conclusions are derived: (1) When the terminating resistance is gradually increased from 0, the damping constants of the damped sine terms begin to differ greatly from each other, ranging in decreasing magnitudes from the first damped sine term to the last term of cutoff frequency. Hence the transient is ultimately of the cutoff frequency. At the cutoff frequency, this constant is greater than the corresponding constant (R/2L) when the termination is absent. (2) For each increase of one section, there is introduced an additional damped sine term with smaller damping constants. Therefore transients die out faster in filters of small no. of sections. (3) With the same network constants, the damping constants of πtype filters are greater than the corresponding values of Ttype filters. As a result, transients die out faster in πtype filters. (4) The amplitudes of the transient terms in the attenuation and transmission ranges are of the same order of magnitude, and the filtering property only exists in the steady states. (5) The cutoff frequency of the πtype filters varies with the no. of sections used. When only two sections of low, or, highpass filter are used, the variation amounts to nearly 26 per cent from the theoretical value.  此篇先推求收端加电阻时,低频与高频滤波器瞬流之公式依此公式算出之图与用阴极光示波器映出之曲线相符合。自推算之结果,可得下列结论: (一)在滤波器收端电阻渐加时,瞬流各项之挫率渐渐互异其数量,由第一挫波项至最後隔阻频项,顺序渐减;其最小数仍比收端无电阻时之挫率(约等于R/2L)为大。故瞬流终必变为隔阻频之电流,而较收端无电阻时易于消灭。 (二)当滤波器增加一段时,瞬流之项数亦加一,所加项之挫率皆比前有者为小,故少段滤波器之瞬流易于消灭。 (三)在π式滤波器中,其瞬流各项之挫率恒较同一电恒数T式滤波器中之相当项之挫率为大故在π式滤波器中,瞬流消灭较易。 (四)在隔阻频后瞬流之数量与在其前者相彷,恒较隔阻频后之安定数量大数十倍,故滤波器之特性仅能见之于安定状态之下。 (五)π式滤波器之隔阻电频随所用之段数而变化在二段之滤波器中,此变化数为最高,其数与理想之数相差百分之二十六。   << 更多相关文摘 
相关查询  



