ELE3105 – Computer controlled systems 5 Assignment 1 A temperature control system can be modelled by the following transfer function G(s), where represents a pure time delay in the system and . You are required to implement a digital PID controller to track the temperature setting without error. 1. Analytically find the open-loop system response c(t) to a unit step input and plot out this response. (30 marks) 2. Based on sampling theorem, determine a suitable sample interval T for the following parts of the assignment. (Hint: Use Bode plots of G(s) to determine the system’s cut-off frequency. At cut-off frequency the magnitude plot is about 3dB below the magnitude of the low frequency. The cut-off frequency can be considered as the highest frequency component. Choose as an integer for calculation convenience). (40 marks) 3. Derive the discrete-time system transfer function GHP(Z) from G(s). (Hint: , where , and keep T as a parameter until the final results are available). (30 marks) 4. Design a digital Proportional (P) controller to form a unit feedback control system, and optimise its parameter with respect to the performance criterion using the steepest descent minimisation process. Simulate this P controller system and plot its response. (Please provide the plots that show the initial and the final/optimal responses). (50 marks) 5. If the P controller is replaced by a PID controller, determine the PID controller’s parameters with respect to the performance criterion for a unit step input. (Hint: Applying the steepest descent optimisation method again. Please also provide the plots that show the initial and the final/optimal responses). (50 marks) Due date: 14 April 2014 Value: 20% Total marks: 200 Penalty for late submission: 5% per day e–ts t = 1 G(s) C(s) M(s) ————5e –ts s + 5 = = ————k = t/T Z e –ts[ G(s)] zk= Z[G(s)] k = t/T ITAE ek k = 0 M?= IAE ek k = 0 M?=
6 ELE3105 – Computer controlled systems Please note that marks will be awarded…