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Dynamic Behavior and Stability of Closed-Loop Control Systems

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## Dynamic Behavior and Stability of Closed-Loop Control Systems

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**Dynamic Behavior and Stability of Closed-Loop Control**Systems**Simulation with Matlab**L y + + + - R**Effect of P- control**K=5 K=2 K=1**Effect of P- control**K=3 K=2 K=1 K=0.5**Effects of P-mode on control performance**• Speed up the response; • Result in offset; • Offset decreases when loop gain increases; • Oscillatory response due to existence of process dead time.**Responses of**PI control for integration process**L**y + + + - R**Effect of K under constant I mode**K=2 K=1 K=0.2**K=2.0**K=1.0 Effect of K under constant I mode K=0.2**Effects of I-mode on control performance**• Eliminate steady state offset; • Speed up response along with increasing proportional constant or decreasing the integral time; • Has dynamic characteristics range from over damped to under damped.**Effect of D mode on controller output**Contributed by derivative mode CO Time**Effect of D-mode**P+D P**K=1.5**K=1 Effect of K under constant D-mode**Effects of D-mode on control performance**• Provides an initial momentum to the process at the moment when input change occurs; • Results in heavier damped dynamics; • Has no direct effect on reducing the offset, nevertheless, offset reducing is usually achieved indirectly due to this D-mode; • Derivative mode will amplify the effect of noises.**PI**PID P**Uses of P, I, D, modes in process control loops**• Level control loops • Flow control loops • Pressure control loops • Temperature control loops**Level control loops**• Tight control at constant height --- constant head for steady process flow, --- protection of centrifugal pumps, --- to provide precise heat transfer rate in an evaporator, --- to guarantee product quality, (e.g. precise sizing in warp yarn coating), --- etc.**Level control loops**• Averaging level control --- to provide storage inventory. --- to absorb disturbances from an upstream units**Level control**• Proportional controller with a wide band is sufficient for most averaging control; • Tight control is usually accomplished with a narrow proportional band; • For constraints or safety such as override or high/low signal selection, a very narrow band of proportional control is used.