Control-value theory of achievement emotions argues that achievement related emotions (e.g., pride, boredom, hope, anger, enjoyment) can be classified in terms of both their valence and the degree to which they motivate achievement related behaviors in educational settings (e.g., negative activating/deactivating emotions, positive activating/deactivating emotions). Within this framework, how can we define 'surprise'? Recent research on the valence of surprise suggests that it can be defined as a mildly negative emotion although the content of surprise is highly contextual.
My own understanding of affect is largely through structural models such as Russell's (1980) Circumplex Model of Affect, and the 'prototypical emotional episodes' he uses to describe emotions such as surprise, so I wouldn't know how to frame this in terms of this control-value theory of achievement.
My take on 'surprise' would be this: In the first instance, surprise is characterised primarily by a high activation but neutrally valenced state. Surprise can be thought of as a state of alert readiness in response to an unexpected stimulus. It therefore only takes on valence once an appraisal of the 'affective quality' of whatever caused the state of alert is complete. If the thing causing the 'alarm' turns out to be something likely to involve threat or other negative consequences, then the activated state becomes one of fear, anxiety, anger (towards the negative valence, high activation portion of the Circumplex), but if the stimulus is judged positive, such as a friend appearing suddenly, then it becomes something akin to excitement or elation (towards the positive valence, high activation portion of the Circumplex).
I hope this conceptualisation is useful in helping you place it within control-value theory.
Surprise is produced by an unexpected event that happens suddenly. So in this sense it is uncontrollable and no negative nor positive value, the moderate negativity comes from the uncertainty regardless the nature of the event.
Also, there could be a, say, secondary surprise coming from an unexpected outcome of action but that produced another kind of emotion.
Large regions of the brain are dedicated to anticipation or prediction. From a biological perspective, accurate prediction is important and surprise represents a predictive failure. So surprise always evokes a quick negatively valence feeling state. Of course there can be pleasant surprises, but the positively valence state arises from a cognitive assessment that occurs after the initial negative response. The ITPRA theory of expectation offers a detailed exposition of this process and is described in the first chapter of my book "Sweet anticipation" (MIT Press, 2006).
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