Abstract
The control of time-delay systems is a hot research topic. Ever since the theory of linear active disturbance rejection control (LADRC) was put forward, considerable progress has been made. LADRC shows a good control effect on the control of time-delay systems. The problem about the parameter stability region of LADRC controllers has been seldom discussed, which is very important for practical application. In this study, the dual-locus diagram method, which is used to solve the upper limit of the LADRC controller bandwidth, is studied for both first-order time-delay systems and second-order time-delay systems. The characteristic equation roots distribution is firstly transformed into the problem of finding the frequency of the dual-locus diagram intersection point. To solve the problem for second-order time-delay system LADRC controllers, which is a dual 10-order nonlinear equation, a transformation has been made through Euler’s formula and genetic algorithm (GA) has been adopted to search for the optimal parameters. Simulation results and experimental results on coupled tanks show the effectivity of the proposed method.
Highlights
In most industrial processes such as level control, boiler temperature control, and internal pressure control of distillation columns, the time-delay phenomenon is widespread
If the second-order linear active disturbance rejection control (LADRC) controller estimates the states of the controlled system accurately, and the unknown variable b0 can be approximately equal to the steady-state gain b of the controlled plant, only two parameters are in Equation (18)
The function block of the current discrete extended state observer (CDESO) is written first, and the function block of LADRC is written on the basis of the CDESO
Summary
In most industrial processes such as level control, boiler temperature control, and internal pressure control of distillation columns, the time-delay phenomenon is widespread. By analyzing how the control algorithm can reject the disturbance in completely unknown circumstances, Han proposed a new concept of estimating compensation for the error, which subsequently evolved into ADRC [7]. The parameter stability region of LADRC controllers in higher-order time-delay systems is not discussed. The dual-locus diagram method for solving the parameter stability region of the first-order time-delay system LADRC controllers is validated on the actual device by programmable logic controller (PLC). The process of obtaining the parameter stability region of the LADRC for the second-order time-delay systems is introduced. Combined with the dual-locus diagram method, the theory of solving the stability region of the controller parameters is given. Where k1 , k2 , · · · kn are the undetermined coefficients and r is the reference signal
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