Problems in cascade control systems

In the two-step tuning method, the secondary controller is tuned first, followed by the primary controller. 1. Secondary controller tuning: The secondary controller uses a P-control law, and the proportional coefficient Kp can be set based on the proportional band Xp. In the absence of specific tuning rules, let’s assume we use classical tuning methods, such as the Ziegler-Nichols method. For a P controller, the proportional gain Kp can usually be determined using the critical gain method or a method based on the attenuation ratio. Since the parameters of the attenuation process are given, we can use the following empirical formula: Kp = 0.3 / (T2S * δ2S). Here, 0.3 is a constant derived from the Ziegler-Nichols empirical formula. - T2S is the time constant of the subsystem (given as 10s). - δ2S is the attenuation rate of the subsystem (given as 40%). Substitute the values to calculate the proportional coefficient of the secondary controller: Kp = 0.3 / (10s * 0.4) = 0.3 / 4 = 0.075. The proportional coefficient Kp of the secondary controller should be 0.075. 2. Main controller tuning: The main controller uses a PID control law. Before tuning the main controller, it is necessary to first determine the equivalent parameters of the main circuit. Since a secondary controller has been installed, the secondary circuit functions as a precursor to the primary circuit; we can assume that the equivalent time constant T1e and the equivalent attenuation rate δ1e of the primary circuit are respectively T1S and δ1S. Using the Ziegler-Nichols tuning method, the parameters of the PID controller can be determined using the following empirical formulas: – Kp (proportional gain) = 1.2 / (T1e * δ1e) – Ti (integral time) = 2 * T1e – Td (derivative time) = 0.5 * T1e. By substituting the given values of T1e = T1S = 100s and δ1e = δ1S = 8%, the parameters of the main controller are calculated as follows: Kp = 1.2 / (100s * 0.08) = 1.2 / 8 = 0.15; Ti = 2 * T1e = 2 * 100s = 200s; Td = 0.5 * T1e = 0.5 * 100s = 50s. Therefore, the proportional gain Kp for the main controller should be 0.15, the integral time Ti should be 200s, and the derivative time Td should be 50s. .

For reference ---- Applications of cascade control systems: 1. The process capacity has a large time lag, and there are intense disturbances with large amplitudes within the system. 2. The pure lag of the controlled object is relatively long. 3. The controlled object exhibits high non-linearity, and the load varies significantly.

For reference ---- Design of the secondary loop in a cascade control system: 1. The selection of secondary parameters should ensure that the secondary loop includes as many disturbances as possible; in particular, the main disturbances must be included in this secondary loop. 2. There should be a certain inherent relationship between the primary and secondary parameters. 3. The secondary parameters should be selected so that the time constants of the primary and secondary objects match, thereby preventing the occurrence of a \"resonance effect\".

For reference——Selection of the primary and secondary controllers in a cascade control system: 1. Selection of the control laws for the primary and secondary controllers. In a cascade system, the primary and secondary controllers serve different functions. The main controller performs setpoint control, while the secondary controller performs follow-up control; this is the basic basis for selecting the control law. A cascade control system is used to adjust the main parameters with high precision; generally, a PI or PID control law should be selected for the main controller. The setting of the secondary parameters is intended to ensure the control quality of the primary parameters; generally, it is required to comply with the need for constant primary parameters, and it is permissible for it to vary within a certain range with some tolerance. Therefore, the secondary controller employs proportional control. Generally, a secondary controller cannot have a differential action, as this would cause the control valve to move excessively, which is detrimental to control. 2. Selection of the forward and reverse actions for the main and auxiliary controllers (1) The selection of the forward and reverse actions for the auxiliary controller is the same as the method used for selecting such actions in a simple control system. (2) The selection of the forward or reverse action for the main controller is determined based on the following method, once the forward or reverse action of the secondary controller has been decided: when both the main and secondary parameters increase (or decrease) simultaneously, and process analysis requires that the actuation direction of the control valve be consistent, the main controller is set to use reverse action ； Conversely, if the directions of motion are not consistent, a direct-acting type should be selected.

The attachment is: “Chemical Process Instruments and Automation (4th Edition)”.

For reference ---- Design of the secondary loop in a cascade control system: 1. The selection of secondary parameters should ensure that the secondary loop includes as many disturbances as possible; in particular, the main disturbances must be included in this secondary loop. 2. There should be a certain inherent relationship between the primary and secondary parameters. 3. The secondary parameters should be selected so that the time constants of the primary and secondary objects match, thereby preventing the occurrence of a \"resonance effect\".

1. The parameter values for the main controller are: δ1 = 0.8δ1S = 0.8 x 8% = 6.4%; TI1 = 0.3T1S = 0.3 x 100 = 30s; TD1 = 0.3T2S = 0.1 x 10 = 1s. 2. The parameter values for the secondary controller are: δ2 = δ2S = 40% = 40%