What is the Shortest Interval of Time Ever Measured?

Minimum-time control is also called time optimal control, also known as fast control. Under the specified initial and terminal conditions, it is required to find a certain control effect to make it move from a given initial state to The final equilibrium state minimizes the time spent, that is, the objective function is excessive process time.

Generally speaking, different control functions will make the system run along different paths (ie, trajectories), but which one is the best is defined by the objective function (ie, the functional index functional). Therefore, different objective functions have different "optimal" meanings. Moreover, the requirements are different for different systems. For example, in machine tool processing, the minimum processing cost can be required to be optimal, the fuel consumption can be minimized to be optimal in missile flight control, and the shortest optional time can be optimal in the interception problem. Therefore, optimization refers to minimizing the functional of a selected performance index.

The minimum time control system is also called a fast system, and it is widely used in attitude control of missiles and spacecraft. If the attitude of the spacecraft deviates from the given equilibrium state by some disturbance, when the deviation does not exceed the range allowed by the control, the attitude of the controlled spacecraft can be restored to the given equilibrium state in the shortest time Is the concept of minimum time control. Minimum time control is another example of the application of the minimum principle.

The claim that the minimum principle estimates the position of the minimum point of the overharmonic function is one of the basic principles of potential theory if f is overharmonic in the region D (DCR ").

Where D is the boundary of D in R- = R {}; if f reaches a minimum value at some x ₀ D, then ff (x ₀ ). In particular, if the internal harmonic function of D is very Numbers cannot reach the minimum at the inner point. These properties are called the minimum principle of the overharmonic function and the harmonic function. Similarly, for the downharmonic function and the harmonic function, there is a maximum principle.

Can complete the prescribed control action in the shortest time

The shortest time control problem is also called the fast control problem. Find an optimal control to make the system transfer from the initial state to the specified target set (ie the terminal state) with the least time, which is the problem to be solved by the rapid control. The following takes the double integral system as an example to study the shortest time control problem. ^[1]

A method of sequentially controlling motor starting or braking at predetermined time intervals. For example, within a certain time range, the starting resistance is cut off in stages in order to achieve automatic motor starting. Usually realized by the time relay. At certain intervals, the time relay issues a command to make the acceleration contactor act, and then the acceleration (or braking) resistor is cut off in order to accelerate (or brake) the motor. Widely used in electric drag of cranes and marine machinery.

The main mathematical basis of the state space method is linear algebra. In the state space method, vectors are widely used to represent various groups of variables in the system, including

When a hydro-generator unit is put into parallel operation in a large power grid, the change in the output power of the unit does not affect the unit frequency. In this operating state, the governor becomes an open-loop system, and the turbine guide vanes are adjusted according to the artificial load setting value. The degree of opening is shown in Figure 1. At this time, the governor becomes a follow-up adjusting device.

Figure 1 Schematic diagram of unit load adjustment

When the speed governor works as a follow-up speed governor, its adjustment effect is lagging. To significantly improve the speed adjustment of the adjustment, the operation mode of the unit to cut off the buffer can be adopted. This is operated in parallel with the large-capacity power grid, and the unit capacity It is suitable when the proportion is small. In fact, in practical shortest time control, the dual feedback model structure is generally adopted, that is, large deviations are eliminated in a fast and optimal process, and small deviations are eliminated in a conventional manner. This can avoid the shortest time control process. The limit cycle is conducive to improving the stability of the control system. It only needs to switch from switch control to conventional PID (or PI) control when the deviation is less than the allowable error. Therefore, when the load is adjusted for the unit, it can be removed first. Transient feedback to eliminate large deviations in a fast optimal process. When the deviation is less than a certain allowable error, re-enter the transient feedback for PID (or PI) adjustment under a certain head. When the unit is stable, it is determined by (2) It can be known that the opening of the turbine guide vane corresponds to the torque of the turbine, and the torque multiplied by the angular velocity is equal to the power, and the angular velocity can be obtained by calculating the system frequency. In this way, the minimum time control for unit load adjustment can be converted into the shortest time control for the corresponding adjustment of the turbine vane opening degree. In other words, when the load P of the unit needs to be adjusted to P ₀ , the hydraulic turbine torque m _t0 corresponding to P ₀ can be calculated according to the system frequency, from m _t0 and the head h at that time. ^[2]