Cascade control problem

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May I ask, in a cascade control system, can the selection of PID parameters for the primary and secondary controllers affect whether the final steady-state values of the primary and secondary variables are the same as their initial values? For example, in the same cascade control system, if both the primary and secondary controllers use a PI control law, can it be ensured that the primary variable Y1(∞) = Y1(0) and the secondary variable Y2(∞) = Y2(0)? My understanding is that the secondary variable Y2(∞)=Y2(0) can be ensured, and thanks to the integral action of the secondary loop, the residual error e2 can be set to 0. At the same time, the integral action of the main controller can also ensure that Y1(∞) = Y1(0). Of course, anti-integral saturation measures should be applied to both of these values. The secondary loop can handle this using the limiting element of a single-loop system, while the main control loop uses the measurement values from the secondary loop as integral feedback. Regarding this question, I would like to ask: if neither the primary nor the secondary controller employs anti-integration saturation, can the primary and secondary variables still ensure that the final value is the same as the initial value? 2. If the main controller uses a PI control law while the secondary controller employs a pure proportional P control law, can it be ensured that the primary variable Y1(∞) = Y1(0) and the secondary variable Y2(∞) = Y2(0)? As I understand it, since the secondary controller lacks an integral action and thus cannot eliminate the residual error, it is certainly impossible to make the secondary variable Y2(∞) = Y2(0). At this point, the integrating action of the main controller should ensure that the main variable Y1(∞) = Y1(0). Regarding this issue, I’m not entirely sure: due to the persistent deviation e2 in the secondary circuit, will the controller of the primary circuit have its output u1 remain constant as a result of this e2 value? This, in turn, might prevent the input to the main controller, namely the deviation signal e1 of the primary circuit, from being 0. If it is not possible to ensure that e1=0, then there will also be a residual error in the main circuit; therefore, it is not possible to guarantee that the main variable Y1(∞)=Y1(0). The above two issues are based on my personal analysis; I’m not sure if this understanding is correct. I hope experts out there can help!