{"id":7084,"date":"2024-09-01T17:16:20","date_gmt":"2024-09-01T17:16:20","guid":{"rendered":"https:\/\/svestudy.com\/?page_id=7084"},"modified":"2025-05-11T10:52:22","modified_gmt":"2025-05-11T10:52:22","slug":"ame-unit-11-q3-answer","status":"publish","type":"page","link":"https:\/\/svestudy.com\/?page_id=7084","title":{"rendered":"AME Unit 11 Q3 \u2013 Answer"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

(a) Control Terms:<\/p>\n\n\n\n

(i) Proportional Bandwidth (PB):<\/p>\n\n\n\n

Proportional bandwidth (PB) refers to the range of input values around the setpoint that will cause the proportional controller’s output to span its entire range. It can be expressed as a percentage of the setpoint and is calculated as the inverse of the proportional gain (K_p):<\/p>\n\n\n\n

PB = 100 \/ K_p<\/p>\n\n\n\n

A higher PB corresponds to a smaller gain, meaning the controller reacts less aggressively to input changes, leading to slower but more stable behavior. Conversely, a lower PB signifies a higher gain, resulting in faster response but potentially causing oscillations if not tuned properly.<\/p>\n\n\n\n

(ii) Integral Action:<\/p>\n\n\n\n

Integral action, also known as “reset” or “I action,” accumulates the error over time and contributes an additional term to the controller output based on the integral of the error signal. This helps eliminate steady-state errors that proportional control alone might not address.<\/p>\n\n\n\n

The integral term gradually increases the output as long as the error persists, eventually bringing the output to a value that cancels out the error. The integral gain (K_i) determines how quickly this adjustment occurs. Too high a value can lead to overshoot and instability, while too low a value might leave steady-state errors uncorrected.<\/p>\n\n\n\n

(iii) Derivative Action:<\/p>\n\n\n\n

Derivative action, also known as “rate” or “D action,” considers the rate of change of the error signal and adjusts the controller output accordingly. This helps to anticipate future changes and provides faster response to transient disturbances.<\/p>\n\n\n\n

The derivative term adds a component to the output proportional to the rate of change of the error. The derivative gain (K_d) determines the sensitivity to error rate. High values can lead to excessive control action and instability, while low values might cause sluggish response.<\/p>\n\n\n\n

(b) 3-Step PID Tuning Method:<\/p>\n\n\n\n

    \n
  1. Start with Proportional control only (set Ki and Kd to zero):\n
      \n
    • Increase the proportional gain (K_p) gradually until the system starts to oscillate.<\/li>\n\n\n\n
    • Note the value of K_p at which oscillations begin (P_osc).<\/li>\n\n\n\n
    • Reduce K_p to approximately 50% of P_osc to achieve a stable but oscillatory response.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Introduce Integral action:\n
        \n
      • Increase the integral gain (K_i) slowly while observing the system response.<\/li>\n\n\n\n
      • The integral term will gradually eliminate the steady-state error introduced by the proportional control alone.<\/li>\n\n\n\n
      • Stop increasing K_i when the response becomes sluggish or overshoots significantly.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • Fine-tune with Derivative action (optional):\n
          \n
        • If further response improvement is desired, introduce derivative action cautiously.<\/li>\n\n\n\n
        • Increase the derivative gain (K_d) slightly while monitoring the system’s stability.<\/li>\n\n\n\n
        • The derivative term can help dampen oscillations and improve transient response, but avoid excessive values that might cause instability.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

          (a) Control Terms: (i) Proportional Bandwidth (PB): Proportional bandwidth (PB) refers to the range of input values around the setpoint that will cause the proportional controller’s output to span its entire range. It can be expressed as a percentage of the setpoint and is calculated as the inverse of the proportional gain (K_p): PB = […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"templates\/template-full-width.php","meta":{"nf_dc_page":"","footnotes":""},"class_list":["post-7084","page","type-page","status-publish","hentry"],"featured_image_src":null,"_links":{"self":[{"href":"https:\/\/svestudy.com\/index.php?rest_route=\/wp\/v2\/pages\/7084","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/svestudy.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/svestudy.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/svestudy.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/svestudy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7084"}],"version-history":[{"count":1,"href":"https:\/\/svestudy.com\/index.php?rest_route=\/wp\/v2\/pages\/7084\/revisions"}],"predecessor-version":[{"id":7096,"href":"https:\/\/svestudy.com\/index.php?rest_route=\/wp\/v2\/pages\/7084\/revisions\/7096"}],"wp:attachment":[{"href":"https:\/\/svestudy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7084"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}