Time-delay-observer-based adaptive sliding mode control method for water plant dosing system
A technology of adaptive sliding mode and control method, which is applied in the direction of adaptive control, general control system, control/regulation system, etc., and can solve the problems of time variation, low automation level, and large lag
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specific Embodiment approach 1
[0016] Specific implementation one: as figure 1 , an adaptive sliding mode control method for a water plant dosing system based on a time delay observer includes the following steps:
[0017] First, the water plant dosing system model of the lagging link is converted into a delay-free prediction model. Secondly, on this basis, based on sliding mode control theory and adaptive technology, an adaptive sliding mode controller is designed. Finally, the output delay observer is used to observe and estimate the system state information, and finally the adaptive sliding mode controller is realized, which ensures that the dosage can be reasonably controlled according to the raw water turbidity and flow control, and ensures that the filtered water turbidity meets the requirements. And the effectiveness of the designed adaptive sliding mode controller is verified by an example.
[0018] Step 1: Convert the water plant dosing system model with lag links into a delay-free prediction mod...
specific Embodiment approach 2
[0021] Embodiment 2: The difference between this embodiment and Embodiment 1 is that: the specific process of converting a water plant dosing system model with a lag link into a delay-free prediction model in the above step 1 is:
[0022] The transfer function G(s) of the controlled object identified under the nominal operating conditions is expressed as:
[0023]
[0024] Among them, C, T, and τ are steady-state gain, natural oscillation period, damping coefficient and process delay time, respectively; b=1 / T 2 , k=C / T 2 .
[0025] Then the second-order differential equation corresponding to formula (1) is:
[0026]
[0027] The delay time τ is removed from equation (2), and the delay-free prediction model is obtained:
[0028]
[0029] where: y f (t) is the estimated output value obtained by using the no-delay model by one delay time period τ (ie, time t+τ).
[0030] In order to consider an uncertain model of the system, equation (3) can be rewritten as
[...
specific Embodiment approach 3
[0033] Embodiment 3: This embodiment is different from Embodiment 1 or 2 in that: in step 2, an adaptive sliding mode controller is designed based on sliding mode control theory and adaptive technology:
[0034] Define the tracking error e 1 =r-y f , and select the linear sliding surface s;
[0035]
[0036] where k 0 is the sliding mode coefficient, k 0 > 0;
[0037] Taking the derivative of formula (5), we can get
[0038]
[0039] According to formula (6), the sliding mode guidance law is designed
[0040]
[0041]
[0042] in is the unknown upper bound estimate of system uncertainty; h is the parameter to be designed;
[0043] Theorem 1: For formula (4), select the sliding mode surface formula (5). Under the action of the sliding mode control law designed in formula (7), the sliding mode surface s is exponentially convergent, that is, the system state converges exponentially.
[0044] Proof: Defining a Lyapunov Function
[0045]
[0046] in,
[...
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