ECE486 - Lab5 Report

Lab 5 PD C ONTROL U SING A NALOG C OMPUTER & W IN C ON 1 of 6 Report By: Justin Habana Lab Partner: John Truong Lab TA: Usman Ahmed Syed Section: AB2 Part 1. ___/44 (A). Theoretical Performance Criterion. __/8 We note the following … ?(?) = 900𝑃 1 𝐾 𝑎?? 𝐾 ??? ? 2 + ?(5 + 900𝑃 2 𝐾 𝑎?? 𝐾 ?𝑎𝑐ℎ ) + 900𝑃 1 𝐾 𝑎?? 𝐾 ??? 𝜔 ? = √900𝑃 1 𝐾 𝑎?? 𝐾 ??? 𝜁 = 5 + 900𝑃 2 𝐾 𝑎?? 𝐾 ?𝑎𝑐ℎ 2𝜔 ? = 5 + 900𝑃 2 𝐾 𝑎?? 𝐾 ?𝑎𝑐ℎ √ 900𝑃 1 𝐾 𝑎?? 𝐾 ??? 𝑀 ? = { exp (− 𝜋𝜁 √1 − 𝜁 2 ) , 0 < 𝜁 < 1 0, 𝜁 ≥ 1 ? ? ≈ { 1.2 − 0.45𝜁 + 2.6𝜁 2 𝜔 ? , 0 < 𝜁 < 1.2 4.7𝜁 − 1.2 𝜔 ? , 1.2 ≤ 𝜁 < 3 ? ? ≈ { − 0.5 𝜁𝜔 ? ln ( 1 − 𝜁 2 400 ) , 0 < 𝜁 ≤ 0.69 6.6𝜁 − 1.6 𝜔 ? , 0.69 < 𝜁 < 3 Table 1, Theoretical Values according to Fig 5.1 Gains 1 P1 = 0.15 P2 = 0 Gains 2 P1 = 0.25 P2 = 0.35 Gains 3 P1 = 0.1 P2 = 0.5 Gains 4 P1 = 0.88 P2 = 0.8 Σ 0.1101 0.4721 1.0086 0.5167 ω n 22.7082 29.3162 18.5412 55.0020 M p (%) 70.61% 18.59% 0 15.02% t r (s) 0.0521 0.0535 0.1829 0.0302 t s (s) 1.2007 0.2256 0.2727 0.1109 Total ___/90

Lab 5 PD C ONTROL U SING A NALOG C OMPUTER & W IN C ON 2 of 6 (B). Experimental Performance Criterion. __/12 Table 2, Experimental Values, Section I (Analog Computer) Gains 1 P1 = 0.15 P2 = 0 Gains 2 P1 = 0.25 P2 = 0.35 Gains 3 P1 = 0.1 P2 = 0.5 Gains 4 P1 = 0.88 P2 = 0.8 M p (%) 51.64% 0.94% 0.16% 3.47% t r (s) 0.0550 0.0720 0.2390 0.0400 t s (s) 0.2740 0.0980 0.3090 0.0550 Table 3, Experimental Values, Section II (WinCon) Gains 1 P1 = 0.15 P2 = 0 Gains 2 P1 = 0.25 P2 = 0.35 Gains 3 P1 = 0.1 P2 = 0.5 Gains 4 P1 = 0.88 P2 = 0.8 M p (%) 61.30% 1.83% 0.37% 5.90% t r (s) 0.0480 0.0640 0.1820 0.0340 t s (s) 0.3000 0.0860 0.2360 0.0780 Table 4, Experimental Values, Section III (WinCon with Friction Compensation) Gains 1 P1 = 0.15 P2 = 0 Gains 2 P1 = 0.25 P2 = 0.35 Gains 3 P1 = 0.1 P2 = 0.5 Gains 4 P1 = 0.88 P2 = 0.8 M p (%) 28.13% 5.47% 0.89% 3.52% t r (s) 0.0580 0.0560 0.1460 0.0400 t s (s) 0.9840 0.1180 0.2180 0.0440 Compare results from Section I with those from Section II ___/8 Compared to section II, the section I 𝑀 ? values appear lower overall, ? ? values appear higher, and no trend was for ? ? values. These differences are likely due to physical forces present in the relatively large physical components of the Analog Computer used in section I compared to mainly computational processes of Simulink used in section II.

Lab 5 PD C ONTROL U SING A NALOG C OMPUTER & W IN C ON 4 of 6 Part 2. ___/18 Compare performance of your design to the Specs ___/10 Our selected theoretical gains (Gains 4) did not meet the prelab specifications. However, through trial and error, 𝑃 1 = 0.9845 and 𝑃 2 = 0.625 produced gains that met the prelab specifications when using the Analog Computer. Gains of 𝐾 1 = 9.6 and 𝐾 2 = 6.5 met the prelab specifications using WinCon without friction compensation. Explain how unmodeled plant dynamics might cause problems ___/8 We acknowledge that there are dynamics not modeled in the pre-lab which may influence real world systems.

Lab 5 PD C ONTROL U SING A NALOG C OMPUTER & W IN C ON 5 of 6 Part 3. ___/16 Theoretical and measured E ss ___/8 We take note of the block diagram of the system shown below. In which … 𝐸 𝑉 ? = 1 1 + 1 ? 𝐾 1 𝐾 ??? ?(?) , ?(?) = 𝐾 𝑎?? ?(?) 1 + 𝐾 2 𝐾 𝑎?? 𝐾 ?𝑎𝑐ℎ ?(?) , ?(?) = 18 1 + 0.2? 𝐸 𝑉 ? = 0.2? 2 + ( 18 𝐾 2 𝐾 𝑎?? 𝐾 ?𝑎𝑐ℎ + 1 )? 0.2? 2 + ( 18 𝐾 2 𝐾 𝑎?? 𝐾 ?𝑎𝑐ℎ + 1 )? + 18𝐾 1 𝐾 ??? 𝐾 𝑎?? lim ?→0 ?𝐸 = 1 18𝐾 1 𝐾 ??? 𝐾 𝑎?? , 𝐾 1 = 10𝑃 1 Gains 1 P1 = 0.15 P2 = 0 Gains 2 P1 = 0.25 P2 = 0.35 Gains 3 P1 = 0.1 P2 = 0.5 Gains 4 P1 = 0.88 P2 = 0.80 Theoretical 0.97% 0.58% 1.45% 0.17% Section I 2.11% 0.16% 9.49% 0.59% Section II 2.05% 1.17% 9.08% 0.29% Section III 4.39% 0.10% 1.56% 0.10% Table 5, Steady-state error What gain adjustments helped decrease steady-state error? ___/8 In general, steady state error increases as gain 𝐾 1 decreases.